PowerPointReview-1 - ConcepTest 5.1 Tetherball ConcepTest...

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Unformatted text preview: ConcepTest 5.1 Tetherball ConcepTest Tetherball In the game of tetherball, In the struck ball whirls around a pole. In what direction does the net force on the ball point? force 1) toward the top of the pole toward 2) toward the ground toward 3) along the horizontal component of the tension force tension 4) along the vertical component of the tension force tension 5) tangential to the circle tangential T W ConcepTest 5.1 Tetherball Tetherball In the game of tetherball, In the struck ball whirls around a pole. In what direction does the net force on the ball point? force 1) toward the top of the pole toward 2) toward the ground toward 3) along the horizontal component of the tension force tension 4) along the vertical component of the tension force tension 5) tangential to the circle tangential The vertical component of the tension balances the weight. The tension weight horizontal component of tension horizontal provides the centripetal force that centripetal points toward the center of the circle. W W T T ConcepTest 5.2a Around the Curve I Around You are a passenger in a car, not wearing a seat belt. The car makes a sharp left turn. From your perspective in the car, what do you feel is happening to you? (1) you are thrown to the right (2) you feel no particular change (3) you are thrown to the left (4) you are thrown to the ceiling (5) you are thrown to the floor ConcepTest 5.2a Around the Curve I Around You are a passenger in a car, not wearing a seat belt. The car makes a sharp left turn. From your perspective in the car, what do you feel is happening to you? (1) you are thrown to the right (2) you feel no particular change (3) you are thrown to the left (4) you are thrown to the ceiling (5) you are thrown to the floor The passenger has the tendency to continue moving in a straight line. From your perspective in the car, it feels like you are being thrown to the right, hitting the passenger door. ConcepTest 5.2b Around the Curve II Around During that sharp left turn, you found yourself hitting the passenger door. What is the correct description of what is actually happening? (1) centrifugal force is pushing you into the door (2) the door is exerting a leftward force on you (3) both of the above (4) neither of the above ConcepTest 5.2b Around the Curve II Around During that sharp left turn, you found yourself hitting the passenger door. What is the correct description of what is actually happening? (1) centrifugal force is pushing you into the door (2) the door is exerting a leftward force on you (3) both of the above (4) neither of the above The passenger has the tendency to continue moving in a straight line. There is a centripetal force, provided by the door, that forces the passenger into a circular path. ConcepTest 5.2c Around the Curve III Around You drive your dad’s car You too fast around a curve and the car starts to skid. What is the correct description of this situation? situation? (1) car’s engine is not strong enough to keep the car from being pushed out keep (2) friction between tires and road is not (2) strong enough to keep car in a circle strong (3) car is too heavy to make the turn (4) a deer caused you to skid (5) none of the above ConcepTest 5.2c Around the Curve III Around You drive your dad’s car You too fast around a curve and the car starts to skid. What is the correct description of this situation? situation? (1) car’s engine is not strong enough to (1) keep the car from being pushed out keep (2) friction between tires and road is not (2) strong enough to keep car in a circle strong (3) car is too heavy to make the turn (4) a deer caused you to skid (5) none of the above The friction force between tires and road provides the centripetal force that keeps the car moving in a circle. If this force is too small, the car continues in a straight line! Follow-up: What could be done to the road or car to prevent skidding? the ConcepTest 5.3 Missing Link ConcepTest Missing A ping pong ball is shot into a circular tube that is lying flat (horizontal) on a tabletop. When the ping pong ball leaves the track, which path will it follow? ConcepTest 5.3 Missing Link ConcepTest Missing A ping pong ball is shot into a circular tube that is lying flat (horizontal) on a tabletop. When the ping pong ball leaves the track, which path will it follow? q Once the ball leaves the tube, there is no longer a force to keep it going in a circle. Therefore, it simply continues in a straight line, as Newton’s First Law requires! Follow-up: What physical force provides the centripetal force? ConcepTest 5.4 Ball and String ConcepTest Ball Two equal-mass rocks tied to strings are Two whirled in horizontal circles. The radius of radius circle 2 is twice that of circle 1. If the period twice period of motion is the same for both rocks, what same is the tension in cord 2 compared to cord 1? is 1) T2 = 1/4 T1 2) T2 = 1/2 T1 3) T2 = T1 4) T2 = 2 T1 5) T2 = 4 T1 ConcepTest 5.4 Ball and String ConcepTest Ball Two equal-mass rocks tied to strings are Two whirled in horizontal circles. The radius of radius circle 2 is twice that of circle 1. If the period twice period of motion is the same for both rocks, what same is the tension in cord 2 compared to cord 1? is 1) T2 = 1/4 T1 2) T2 = 1/2 T1 3) T2 = T1 4) T2 = 2 T1 5) T2 = 4 T1 The centripetal force in this case is given by the ConcepTest 5.5 Barrel of Fun ConcepTest Barrel A rider in a “barrel of fun” rider finds herself stuck with her back to the wall. Which diagram correctly shows the forces acting on her? on 1 2 3 4 5 ConcepTest 5.5 Barrel of Fun Barrel A rider in a “barrel of fun” rider finds herself stuck with her back to the wall. Which diagram correctly shows the forces acting on her? on 1 2 3 4 5 The normal force of the wall on the normal rider provides the centripetal force centripetal needed to keep her going around in a circle. The downward force of gravity is balanced by the upward frictional force on her, so she does frictional not slip vertically. Follow-up: What happens if the rotation of the ride slows down? ConcepTest 5.6a Going in Circles I ConcepTest Going You’re on a Ferris wheel moving in a You’re vertical circle. When the Ferris wheel is at rest, the normal force N exerted by your seat is equal to your weight mg. mg How does N change at the top of the Ferris wheel when you are in motion? Ferris 1) N remains equal to mg 1) mg 2) N is smaller than mg 2) mg 3) N is larger than mg 3) mg 4) None of the above ConcepTest 5.6a Going in Circles I ConcepTest Going You’re on a Ferris wheel moving in a You’re vertical circle. When the Ferris wheel is at rest, the normal force N exerted by your seat is equal to your weight mg. mg How does N change at the top of the Ferris wheel when you are in motion? Ferris You are in circular motion, so there has to be a centripetal force pointing inward. At the top, the only two inward forces are mg (down) and N (up), so mg N must be smaller than mg. mg Follow-up: Where is N larger than mg? Follow-up: mg 1) N remains equal to mg 1) mg 2) N is smaller than mg 2) mg 3) N is larger than mg 3) mg 4) None of the above ConcepTest 5.6b Going in Circles II Going A skier goes over a small round hill skier with radius R. Since she is in circular Since motion, there has to be a centripetal force. At the top of the hill, what is force. Fc of the skier equal to? 1) Fc = N + mg 1) mg 2) Fc = mg – N 2) mg 3) Fc = T + N – mg 3) mg 4) Fc = N 4) 5) Fc = mg 5) mg v R ConcepTest 5.6b Going in Circles II Going A skier goes over a small round hill skier with radius R. Since she is in circular motion, there has to be a centripetal force. At the top of the hill, what is force. Fc of the skier equal to? 1) Fc = N + mg 1) mg 2) Fc = mg – N 2) mg 3) Fc = T + N – mg 3) mg 4) Fc = N 4) 5) Fc = mg 5) mg v mg N R Follow-up: What happens when the skier goes into a small dip? the ConcepTest 5.7c Going in Circles III Going You swing a ball at the end of string You in a vertical circle. Since the ball is in circular motion there has to be a centripetal force. At the top of the centripetal ball’s path, what is Fc equal to? 1) Fc = T – mg 1) mg 2) Fc = T + N – mg 2) mg 3) Fc = T + mg 3) mg 4) Fc = T 4) 5) Fc = mg mg v top R ConcepTest 5.7c Going in Circles III ConcepTest Going You swing a ball at the end of string You in a vertical circle. Since the ball is in circular motion there has to be a centripetal force. At the top of the centripetal ball’s path, what is Fc equal to? 1) Fc = T – mg 1) mg 2) Fc = T + N – mg 2) mg 3) Fc = T + mg 3) mg 4) Fc = T 4) 5) Fc = mg mg mg F points toward the center of the circle, i.e. downward in this case. The i.e weight vector points down and the weight down tension (exerted by cthe string) also tension points down. The magnitude of the down v T R ConcepTest 2.1 You and your dog go for a walk to the Walking the Dog park. On the way, your dog takes many side trips to chase squirrels or examine fire hydrants. When you arrive at the park, do you and your dog have the same displacement? displacement? 1) yes 2) no ConcepTest 2.1 ConcepTest You and your dog go for a walk to the Walking the Dog park. On the way, your dog takes many side trips to chase squirrels or examine fire hydrants. When you arrive at the park, do you and your dog have the same displacement? displacement? 1) yes 2) no Yes, you have the same displacement. Since you and your dog had the same initial position and the same final position, then you have (by definition) the same displacement. Follow-up: Have you and your dog traveled the same distance? ConcepTest 2.3 If the position of a car is zero, does its speed have to be zero? to Position and Speed 1) yes 2) no 3) it depends on the position ConcepTest 2.3 ConcepTest If the position of a car is zero, does its speed have to be zero? to Position and Speed 1) yes 2) no 3) it depends on the position No, the speed does not depend on position, it depends on the change of position. Since we know that the displacement does not depend on the origin of the coordinate system, an object can easily start at x = –3 and be moving by the time it gets to x = 0. ConcepTest 2.4 Does the odometer in a car measure distance or displacement? displacement? Odometer 1) distance 2) displacement 3) both ConcepTest 2.4 ConcepTest Does the odometer in a car measure distance or displacement? displacement? Odometer 1) distance 2) displacement 3) both If you go on a long trip and then return home, your odometer does not measure zero, but it records the total miles that you traveled. That means the odometer records distance. Follow-up: How would you measure displacement in your car? ConcepTest 3.3 Vector Addition You are adding vectors of length 20 and 40 units. What is the only possible resultant magnitude that you can obtain out of the following choices? 1) 0 2) 18 3) 37 4) 64 5) 100 ConcepTest 3.3 You are adding vectors of length 20 and 40 units. What is the only possible resultant magnitude that you can obtain out of the following choices? Vector Addition 1) 0 2) 18 3) 37 4) 64 5) 100 The minimum resultant occurs when the vectors minimum are opposite, giving 20 units. The maximum opposite 20 maximum resultant occurs when the vectors are aligned, aligned giving 60 units. Anything in between is also 60 possible, for angles between 0° and 180°. ConcepTest 3.4a Firing Balls I A small cart is rolling at constant velocity on a flat track. It fires a ball straight up into the air as it moves. After it is fired, what happens to the ball? 1) it depends on how fast the cart is 1) moving moving 2) it falls behind the cart 3) it falls in front of the cart 4) it falls right back into the cart 5) it remains at rest ConcepTest 3.4a Firing Balls I A small cart is rolling at constant velocity on a flat track. It fires a ball straight up into the air as it moves. After it is fired, what happens to the ball? 1) it depends on how fast the cart is 1) moving moving 2) it falls behind the cart 3) it falls in front of the cart 4) it falls right back into the cart 5) it remains at rest In the frame of reference of the cart, the ball only has a vertical component of vertical velocity. So it goes up and comes back down. To a ground observer, both the cart and the ball have the same horizontal velocity, same so the ball still returns into the cart. when viewed from train when viewed from ground ConcepTest 3.4b ConcepTest Now the cart is being pulled along a horizontal track by an external force (a weight hanging over the table edge) and accelerating. It fires a ball straight out of the cannon as it moves. After it is fired, what happens to the ball? Firing Balls II Firing 1) it depends upon how much the track is tilted 2) it falls behind the cart 3) it falls in front of the cart 4) it falls right back into the cart 5) it remains at rest ConcepTest 3.4b ConcepTest Now the cart is being pulled along a horizontal track by an external force (a weight hanging over the table edge) and accelerating. It fires a ball straight out of the cannon as it moves. After it is fired, what happens to the ball? Firing Balls II Firing 1) it depends upon how much the track is tilted 2) it falls behind the cart 3) it falls in front of the cart 4) it falls right back into the cart 5) it remains at rest Now the acceleration of the cart is completely unrelated to the ball. In fact, the ball does not have any horizontal acceleration at all (just like the first question), so it will lag behind the accelerating cart once it is shot out of the cannon. ConcepTest 4.1a Newton’s First Law I A book is lying at rest on a table. The book will remain there at rest because: 1) there is a net force but the book has too much inertia 2) there are no forces acting on it at all 3) it does move, but too slowly to be seen 4) there is no net force on the book 5) there is a net force, but the book is too heavy to move ConcepTest 4.1a Newton’s First Law I A book is lying at rest on a table. The book will remain there at rest because: 1) there is a net force but the book has too much inertia 2) there are no forces acting on it at all 3) it does move, but too slowly to be seen 4) there is no net force on the book 5) there is a net force, but the book is too heavy to move There are forces acting on the book, but the only There forces acting are in the y-direction. Gravity acts downward, but the table exerts an upward force that is equally strong, so the two forces cancel, leaving no net force. leaving ConcepTest 4.1b Newton’s First Law II A hockey puck slides on ice at constant velocity. What is the net force acting on the puck? 1) more than its weight 2) equal to its weight 3) less than its weight but more than zero 4) depends on the speed of the puck 5) zero ConcepTest 4.1b Newton’s First Law II A hockey puck slides on ice at constant velocity. What is the net force acting on the puck? 1) more than its weight 2) equal to its weight 3) less than its weight but more than zero 4) depends on the speed of the puck 5) zero The puck is moving at a constant velocity, and constant therefore it is not accelerating. Thus, there must not be no net force acting on the puck. no Follow-up: Are there any forces acting on the puck? What are they? Follow-up: ConcepTest 4.1c Newton’s First Law III You put your book on the bus seat next to you. When the bus stops suddenly, the book slides forward off the seat. Why? 1) a net force acted on it 2) no net force acted on it 3) it remained at rest 4) it did not move, but only seemed to 5) gravity briefly stopped acting on it ConcepTest 4.1c Newton’s First Law III You put your book on the bus seat next to you. When the bus stops suddenly, the book slides forward off the seat. Why? 1) a net force acted on it 2) no net force acted on it 3) it remained at rest 4) it did not move, but only seemed to 5) gravity briefly stopped acting on it The book was initially moving forward (since it was on a moving bus). When the bus stopped, the book continued moving forward, which was its initial state continued of motion, and therefore it slid forward off the seat. of Follow-up: What is the force that usually keeps the book on the seat? Follow-up: ConcepTest 6.1 To Work or Not to Work To Is it possible to do work on an object that remains at rest? 1) yes 2) no ConcepTest 6.1 To Work or Not to Work ConcepTest To Is it possible to do work on an object that remains at rest? 1) yes 2) no Work requires that a force acts over a distance. force If an object does not move at all, there is no displacement, and therefore no work done. displacement no ConcepTest 6.2a Friction and Work I ConcepTest Friction A box is being pulled box across a rough floor at a constant speed. What can you say about the work done by friction? by 1) friction does no work at all 2) friction does negative work 3) friction does positive work ConcepTest 6.2a Friction and Work I Friction A box is being pulled box across a rough floor at a constant speed. What can you say about the work done by friction? by 1) friction does no work at all 2) friction does negative work 3) friction does positive work Friction acts in the opposite opposite direction to the displacement, so the work is negative. Or using the negative definition of work: W = F d cos f N displacement Pull mg o ConcepTest 6.2c Play Ball! Play In a baseball game, the catcher stops a 90-mph pitch. What can you say about the work done by the catcher on the ball? 1) catcher has done positive work 2) catcher has done negative work 3) catcher has done zero work ConcepTest 6.2c Play Ball! Play In a baseball game, the catcher stops a 90-mph pitch. What can you say about the work done by the catcher on the ball? 1) catcher has done positive work 2) catcher has done negative work 3) catcher has done zero work The force exerted by the catcher is opposite in direction to the opposite displacement of the ball, so the work is negative. Or using the displacement definition of work (W = F d cos θ ), since θ = 180o, then W < 0. 180 Note that because the work done on the ball is negative, its speed decreases. Follow-up: What about the work done by the ball on the catcher? ConcepTest 7.3a Momentum and Force ConcepTest Momentum A net force of 200 N acts on a 100-kg boulder, and a force of the same magnitude acts on a 130-g pebble. How does the rate of change of the boulder’s momentum compare to the rate of change of the pebble’s momentum? 1) greater than 2) less than 3) equal to ConcepTest 7.3a Momentum and Force Momentum A net force of 200 N acts on a 100-kg boulder, and a force of the same magnitude acts on a 130-g pebble. How does the rate of change of the boulder’s momentum compare to the rate of change of the pebble’s momentum? 1) greater than 2) less than 3) equal to The rate of change of momentum is, in fact, the force. Remember that F = ∆ p/∆ t. Since the force exerted on the boulder and the pebble is the same, then the rate of change of momentum is the same. ConcepTest 7.3b Velocity and Force ConcepTest Velocity A net force of 200 N acts on a 100-kg boulder, and a force of the same magnitude acts on a 130-g pebble. How does the rate of change of the boulder’s velocity compare to the rate of change of the pebble’s velocity? 1) greater than 2) less than 3) equal to ConcepTest 7.3b Velocity and Force Velocity A net force of 200 N acts on a 100 kg boulder, and a force of the same magnitude acts on a 130-g pebble. How does the rate of change of the boulder’s velocity compare to the rate of change of the pebble’s velocity? 1) greater than 2) less than 3) equal to The rate of change of velocity is the acceleration. Remember that a = ∆ v/∆ t. The acceleration is related to the force by Newton’s 2nd Law (F = ma), so the acceleration of the boulder is less than that of the pebble (for the same applied force) because the boulder is much more massive. ConcepTest 7.4 Collision Course ConcepTest Collision A small car and a large truck collide head-on and stick together. Which one has the larger momentum change? 1) the car 2) the truck 3) they both have the same 3) momentum change momentum 4) can’t tell without knowing the 4) final velocities final ConcepTest 7.4 Collision Course ConcepTest Collision A small car and a large truck collide head-on and stick together. Which one has the larger momentum change? 1) the car 2) the truck 3) they both have the same 3) momentum change momentum 4) can’t tell without knowing the 4) final velocities final Since the total momentum of the system is conserved, that means that ∆ p = 0 for the car and truck combined. truck Therefore, ∆ pcar must be equal and opposite to that of the truck (–∆ ptruck) opposite in order for the total momentum change to be zero. Note that this conclusion also follows from Newton’s Follow-up: Which one feels the larger acceleration? the ConcepTest 2.5 Does the speedometer in a car measure velocity or speed? speed? Speedometer 1) velocity 2) speed 3) both 4) neither ConcepTest 2.5 ConcepTest Does the speedometer in a car measure velocity or speed? speed? Speedometer 1) velocity 2) speed 3) both 4) neither The speedometer clearly measures speed, not velocity. Velocity is a vector (depends on direction), but the speedometer does not care what direction you are traveling. It only measures the magnitude of the velocity, which is the speed. Follow-up: How would you measure velocity in your car? ConcepTest 2.7 ConcepTest Velocity in One Dimension 1) yes 2) no 3) it depends If the average velocity is non-zero over average some time interval, does this mean that the instantaneous velocity is never zero instantaneous never during the same interval? during ConcepTest 2.7 ConcepTest Velocity in One Dimension 1) yes 2) no 3) it depends If the average velocity is non-zero over average some time interval, does this mean that the instantaneous velocity is never zero instantaneous never during the same interval? during No!!! For example, your average velocity for a trip home might be 60 mph, but if you stopped for lunch on the way home, there was an interval when your instantaneous velocity was zero, in fact! ConcepTest 2.8a ConcepTest If the velocity of a car is non-zero If (v ≠ 0), can the acceleration of ), the car be zero? the Acceleration I 1) yes 2) no 3) depends on the velocity ConcepTest 2.8a ConcepTest If the velocity of a car is non-zero If (v ≠ 0), can the acceleration of ), the car be zero? the Acceleration I 1) yes 2) no 3) depends on the velocity Sure it can! An object moving with constant velocity constant velocity has a non-zero velocity, but it has zero acceleration zero acceleration since the velocity is not changing. ConcepTest 3.5 You drop a package from You a plane flying at constant speed in a straight line. Without air resistance, the package will: package Dropping a Package 1) quickly lag behind the plane while falling while 2) remain vertically under the 2) plane while falling plane 3) move ahead of the plane while 3) falling falling 4) not fall at all ConcepTest 3.5 You drop a package from You a plane flying at constant speed in a straight line. Without air resistance, the package will: package Dropping a Package 1) quickly lag behind the plane while falling while 2) remain vertically under the 2) plane while falling plane 3) move ahead of the plane while 3) falling falling 4) not fall at all Both the plane and the package have the same horizontal velocity at the same horizontal velocity moment of release. They will maintain this velocity in the xmaintain direction, so they stay aligned. Follow-up: What would happen if air resistance is present? ConcepTest 3.6a Dropping the Ball I From the same height (and at the same time), one ball is dropped and another ball is fired horizontally. Which one will hit the ground first? (1) the “dropped” ball (2) the “fired” ball (3) they both hit at the same time (4) it depends on how hard the ball (4) was fired was (5) it depends on the initial height ConcepTest 3.6a Dropping the Ball I From the same height (and at the same time), one ball is dropped and another ball is fired horizontally. Which one will hit the ground first? (1) the “dropped” ball (2) the “fired” ball (3) they both hit at the same time (4) it depends on how hard the ball (4) was fired was (5) it depends on the initial height Both of the balls are falling vertically under the influence of gravity. They both fall from the same height. Therefore, they will They hit the ground at the same time. hit completely independent !! Follow-up: Is that also true if there is air resistance? The fact that one is moving horizontally is irrelevant – remember that the x and y motions are ConcepTest 3.6b Dropping the Ball II 1) the “dropped” ball In the previous problem, In which ball has the greater velocity at ground level? velocity 2) the “fired” ball 3) neither – they both have the 3) same velocity on impact same 4) it depends on how hard the 4) ball was thrown ball ConcepTest 3.6b Dropping the Ball II 1) the “dropped” ball In the previous problem, In which ball has the greater velocity at ground level? velocity 2) the “fired” ball 3) neither – they both have the 3) same velocity on impact same 4) it depends on how hard the 4) ball was thrown ball Both balls have the same vertical velocity vertical when they hit the ground (since they are both acted on by gravity for the same time). However, the “fired” ball also has a horizontal velocity. When you add the two components vectorially, the “fired” ball has a larger net velocity when it hits the has ground. Follow-up: What would you have to do to have them both reach the same final velocity at ground level? both ConcepTest 4.1d Newton’s First Law IV You kick a smooth flat stone out on a frozen pond. The stone slides, slows down and eventually stops. You conclude that: 1) the force pushing the stone forward finally stopped pushing on it 2) no net force acted on the stone 3) a net force acted on it all along 4) the stone simply “ran out of steam” 5) the stone has a natural tendency to be at rest ConcepTest 4.1d Newton’s First Law IV You kick a smooth flat stone out on a frozen pond. The stone slides, slows down and eventually stops. You conclude that: 1) the force pushing the stone forward finally stopped pushing on it 2) no net force acted on the stone 3) a net force acted on it all along 4) the stone simply “ran out of steam” 5) the stone has a natural tendency to be at rest After the stone was kicked, no force was pushing it along! However, there must have been some force acting on the stone to slow it down and stop force it. This would be friction!! it Follow-up: What would you have to do to keep the stone moving? Follow-up: ConcepTest 4.2a Cart on Track I Consider a cart on a horizontal frictionless table. Once the cart has been given a push and released, what will happen to the cart? 1) slowly come to a stop 2) continue with constant acceleration 3) continue with decreasing acceleration 4) continue with constant velocity 5) immediately come to a stop ConcepTest 4.2a Cart on Track I Consider a cart on a horizontal frictionless table. Once the cart has been given a push and released, what will happen to the cart? 1) slowly come to a stop 2) continue with constant acceleration 3) continue with decreasing acceleration 4) continue with constant velocity 5) immediately come to a stop After the cart is released, there is no longer a force in no the x-direction. This does not mean that the cart stops moving!! It simply means that the cart will continue moving!! continue moving with the same velocity it had at the moment of moving release. The initial push got the cart moving, but that force is not needed to keep the cart in motion. ConcepTest 4.2b Cart on Track II We just decided that the cart continues with constant velocity. What would have to be done in order to have the cart continue with constant acceleration? 1) push the cart harder before release 2) push the cart longer before release 3) push the cart continuously 4) change the mass of the cart 5) it is impossible to do that ConcepTest 4.2b Cart on Track II We just decided that the cart continues with constant velocity. What would have to be done in order to have the cart continue with constant acceleration? 1) push the cart harder before release 2) push the cart longer before release 3) push the cart continuously 4) change the mass of the cart 5) it is impossible to do that In order to achieve a non-zero acceleration, it is necessary to maintain the applied force. The maintain only way to do this would be to continue pushing continue the cart as it moves down the track. This will lead us to a discussion of Newton’s Second Law. ConcepTest 6.2d Tension and Work ConcepTest Tension A ball tied to a string is ball being whirled around in a circle. What can you say about the work done by tension? done 1) tension does no work at all 2) tension does negative work 3) tension does positive work ConcepTest 6.2d Tension and Work ConcepTest Tension A ball tied to a string is ball being whirled around in a circle. What can you say about the work done by tension? done 1) tension does no work at all 2) tension does negative work 3) tension does positive work No work is done because the force acts in a perpendicular direction to perpendicular the displacement. Or using the definition of work: W = F d cos θ T v Follow-up: Is there a force in the direction of the velocity? o ConcepTest 6.3 Force and Work ConcepTest Force A box is being pulled up a rough incline by a rope connected to a pulley. How many forces are doing work on the box? 1) one force 2) two forces 3) three forces 4) four forces 5) no forces are doing work ConcepTest 6.3 Force and Work ConcepTest Force A box is being pulled up a rough incline by a rope connected to a pulley. How many forces are doing work on the box? 1) one force 2) two forces 3) three forces 4) four forces 5) no forces are doing work dis pla ce Any force not perpendicular to the motion will do work: N does no work no T does positive work positive f does negative work mg does negative work me n T t N f mg ConcepTest 6.5a Kinetic Energy I Kinetic By what factor does the kinetic energy of a car change when its speed is tripled? 1) no change at all 2) factor of 3 3) factor of 6 4) factor of 9 5) factor of 12 ConcepTest 6.5a Kinetic Energy I ConcepTest Kinetic By what factor does the kinetic energy of a car change when its speed is tripled? 1) no change at all 2) factor of 3 3) factor of 6 4) factor of 9 5) factor of 12 2 Follow-up: How would you achieve a KE increase of a factor of 2? Since the kinetic energy is 1/2 mv , if the speed increases mv ConcepTest 7.5a Two Boxes I ConcepTest Two Two boxes, one heavier than the other, are initially at rest on a horizontal frictionless surface. The same constant force F acts on each one for exactly 1 second. Which box has more momentum after the force acts? 1) the heavier one 2) the lighter one 3) both the same F light F heavy ConcepTest 7.5a Two Boxes I ConcepTest Two Two boxes, one heavier than the other, are initially at rest on a horizontal frictionless surface. The same constant force F acts on each one for exactly 1 second. Which box has more momentum after the force acts? 1) the heavier one 2) the lighter one 3) both the same We know: so impulse ∆ p = Fav ∆ t. av In this case F and ∆ t are the same for both boxes ! same Both boxes will have the same final momentum. same ∆p Fav = ∆t F light F heavy ConcepTest 7.5b Two Boxes II Two In the previous question, which box has the larger velocity after the force acts? 1) the heavier one 2) the lighter one 3) both the same ConcepTest 7.5b Two Boxes II Two In the previous question, which box has the larger velocity after the force acts? 1) the heavier one 2) the lighter one 3) both the same The force is related to the acceleration by Newton’s 2nd Law (F = ma). The lighter box therefore has the greater acceleration, and will reach a higher speed after the 1-second time interval. Follow-up: Which box has gone a larger distance after the force acts? Follow-up: Which box has gained more KE after the force acts? ConcepTest 7.7 Impulse Impulse A small beanbag and a bouncy rubber ball are dropped from the same height above the floor. They both have the same mass. Which one will impart the greater impulse to the floor when it hits? 1) the beanbag 2) the rubber ball 3) both the same ConcepTest 7.7 Impulse Impulse A small beanbag and a bouncy rubber ball are dropped from the same height above the floor. They both have the same mass. Which one will impart the greater impulse to the floor when it hits? Both objects reach the same speed at the floor. However, while the beanbag comes to rest on the floor, the ball bounces back up with nearly the same speed as it hit. Thus, the change in momentum for the ball is greater, because of the rebound. momentum The impulse delivered by the ball is twice that of the beanbag. For the beanbag: For the rubber ball: ∆ p = pf – pi = 0 – (–mv ) = mv ∆ p = pf – pi = mv – (–mv ) = 2mv 1) the beanbag 2) the rubber ball 3) both the same Follow-up: Which one imparts the larger force to the floor? ConcepTest 2.8b When throwing a ball straight up, which of the following is true about its velocity v and its acceleration a at the highest point in its path? in Acceleration II 1) both v = 0 and a = 0 1) 2) v ≠ 0, but a = 0 2) but 3) v = 0, but a ≠ 0 3) but 4) both v ≠ 0 and a ≠ 0 4) 5) not really sure ConcepTest 2.8b When throwing a ball straight up, When which of the following is true about its velocity v and its acceleration a at the highest point in its path? in Acceleration II 1) both v = 0 and a = 0 1) 2) v ≠ 0, but a = 0 2) but 3) v = 0, but a ≠ 0 3) but 4) both v ≠ 0 and a ≠ 0 4) 5) not really sure At the top, clearly v = 0 because the ball has momentarily stopped. But the velocity of the ball is changing, so its acceleration is definitely not zero! Otherwise it would remain at rest!! Follow-up: …and the value of a is…? y ConcepTest 2.9a Free Fall I You throw a ball straight up into the air. After it leaves your hand, at what point in its flight does it have the maximum value maximum of acceleration? of 1) its acceleration is constant 1) everywhere 2) at the top of its trajectory 2) 3) halfway to the top of its trajectory 4) just after it leaves your hand 5) just before it returns to your hand 5) on the way down on ConcepTest 2.9a Free Fall I You throw a ball straight up into the air. After it leaves your hand, at what point in its flight does it have the maximum value maximum of acceleration? of 1) its acceleration is constant 1) everywhere 2) at the top of its trajectory 2) 3) halfway to the top of its trajectory 4) just after it leaves your hand 5) just before it returns to your hand 5) on the way down on The ball is in free fall once it is released. Therefore, it is entirely under free the influence of gravity, and the only acceleration it experiences is g, which is constant at all points. ConcepTest 2.9b Free Fall II Alice and Bill are at the top of a building. Alice throws her ball throws downward. Bill simply drops drops his ball. Which ball has the greater acceleration just after release? release? 1) Alice’s ball 1) 2) it depends on how hard the ball was thrown the 3) neither -- they both have 3) the same acceleration the 4) Bill’s ball Alice v v A Bill v B ConcepTest 2.9b Free Fall II Alice and Bill are at the top of a building. Alice throws her ball throws downward. Bill simply drops drops his ball. Which ball has the greater acceleration just after release? release? Both balls are in free fall once they are released, therefore they both feel the acceleration due to gravity (g). This acceleration is independent of the initial velocity of the ball. 1) Alice’s ball 1) 2) it depends on how hard the ball was thrown the 3) neither -- they both have 3) the same acceleration the 4) Bill’s ball Alice v v A Bill v B Follow-up: Which one has the greater velocity when they hit the ground? the ConcepTest 3.7a Punts I Which of the 3 punts has the longest hang time? hang h 1 2 3 4) all have the same hang time ConcepTest 3.7a Punts I Which of the 3 punts has the longest hang time? hang h 1 2 3 4) all have the same hang time The time in the air is determined by the vertical motion ! Since all of the punts reach the same height, same they all stay in the air for the same time. same Follow-up: Which one had the greater initial velocity? ConcepTest 3.7b Punts II A battleship simultaneously fires two shells at two enemy battleship submarines. The shells are launched with the same initial same velocity. If the shells follow the trajectories shown, which submarine gets hit first ? first 1 2 3) both at the same time ConcepTest 3.7b Punts II A battleship simultaneously fires two shells at two enemy battleship submarines. The shells are launched with the same initial same velocity. If the shells follow the trajectories shown, which submarine gets hit first ? first The flight time is fixed by the motion in the y-direction. The higher an object goes, the longer it stays in flight. The shell hitting ship #2 goes less high, therefore it stays in flight for less time than the other shell. Thus, ship #2 is hit first. 1 2 3) both at the same time Follow-up: Which one traveled the greater distance? Follow-up: ConcepTest 3.8 Cannon on the Moon For a cannon on Earth, the cannonball would follow path 2. Instead, if the same cannon were on the Moon, where g = 1.6 m/s2, which path would the cannonball take in the same situation? 1 2 3 4 ConcepTest 3.8 Cannon on the Moon For a cannon on Earth, the cannonball would follow path 2. Instead, if the same cannon were on the Moon, where g = 1.6 m/s2, which path would the cannonball take in the same situation? The ball will spend more time in the air because time gMoon < gEarth. With more time, it can travel farther in the horizontal farther direction. Follow-up: Which path would it take in outer space? 1 2 3 4 ConcepTest 4.9a Going Up I A block of mass m rests on the floor of an elevator that is moving upward at constant speed. What is the relationship between the force due to gravity and the normal force on the block? 1) N > mg mg 2) N = mg 2) mg 3) N < mg (but not zero) 3) mg 4) N = 0 4) 5) depends on the size of the elevator elevator v m ConcepTest 4.9a Going Up I A block of mass m rests on the floor of an elevator that is moving upward at constant speed. What is the relationship between the force due to gravity and the normal force on the block? 1) N > mg mg 2) N = mg 2) mg 3) N < mg (but not zero) 3) mg 4) N = 0 4) 5) depends on the size of the elevator elevator The block is moving at constant speed, so it must have no net force on it. The forces no on it are N (up) and mg (down), so N = mg, mg mg just like the block at rest on a table. v m ConcepTest 4.9b Going Up II A block of mass m rests on the floor of an elevator that is accelerating upward. What is the relationship between the force due to gravity and the normal force on the block? 1) N > mg mg 2) N = mg 2) mg 3) N < mg (but not zero) 3) mg 4) N = 0 4) 5) depends on the size of the elevator elevator a m ConcepTest 4.9b Going Up II A block of mass m rests on the floor of an elevator that is accelerating upward. What is the relationship between the force due to gravity and the normal force on the block? 1) N > mg 1) mg 2) N = mg 2) mg 3) N < mg (but not zero) 3) mg 4) N = 0 4) 5) depends on the size of the elevator elevator The block is accelerating upward, so it must have a net upward force. The net forces on it are N (up) and mg (down), mg so N must be greater than mg in order mg to give the net upward force! net Follow-up: What is the normal force if the elevator is in free fall downward? the N m mg Σ F = N – mg = ma > mg ma 0 ∴ N > mg mg a>0 ConcepTest 4.10 Normal Force Below you see two cases: a Below physics student pulling or pulling pushing a sled with a force F pushing which is applied at an angle θ . In which case is the normal force greater? force 1) case 1 2) case 2 3) it’s the same for both 4) depends on the magnitude of 4) the force F 5) depends on the ice surface Case 1 Case 2 ConcepTest 4.10 Normal Force Below you see two cases: a Below physics student pulling or pulling pushing a sled with a force F pushing which is applied at an angle θ . In which case is the normal force greater? force 1) case 1 2) case 2 3) it’s the same for both 4) depends on the magnitude of 4) the force F 5) depends on the ice surface Case 1 In Case 1, the force F is pushing down down (in addition to mg), so the normal force in mg needs to be larger. In Case 2, the force F larger is pulling up, against gravity, so the up normal force is lessened. lessened Case 2 ConcepTest 6.14 Elastic Potential Energy Elastic How does the work required to stretch a spring 2 cm compare with the work required to stretch it 1 cm? 1) same amount of work 2) twice the work 3) 4 times the work 4) 8 times the work ConcepTest 6.14 Elastic Potential Energy Elastic How does the work required to stretch a spring 2 cm compare with the work required to stretch it 1 cm? 1) same amount of work 2) twice the work 3) 4 times the work 4) 8 times the work The elastic potential energy is 1/2 kx2. So in the second case, kx the elastic PE is 4 times greater than in the first case. Thus, elastic the work required to stretch the spring is also 4 times greater. work ConcepTest 6.15 Springs and Gravity ConcepTest Springs A mass attached to a vertical spring causes the spring to stretch and the mass to move downwards. What can you say about the spring’s potential energy (PEs) and the gravitational potential energy (PEg) of the mass? 1) both PEs and PEg decrease 2) PEs increases and PEg decreases 3) both PEs and PEg increase 4) PEs decreases and PEg increases 5) PEs increases and PEg is constant ConcepTest 6.15 Springs and Gravity Springs A mass attached to a vertical spring causes the spring to stretch and the mass to move downwards. What can you say about the spring’s potential energy (PEs) and the gravitational potential energy (PEg) of the mass? 1) both PEs and PEg decrease 2) PEs increases and PEg decreases 3) both PEs and PEg increase 4) PEs decreases and PEg increases 5) PEs increases and PEg is constant The spring is stretched, so its elastic PE increases, stretched elastic since PEs = 1/2 kx2. The mass moves down to a PE kx lower position, so its gravitational PE decreases, lower gravitational g ConcepTest 6.16 Down the Hill ConcepTest Down Three balls of equal mass start from rest and roll down different ramps. All ramps have the same height. Which ball has the greater speed at the bottom of its ramp? 4) same speed for all balls 1 2 3 ConcepTest 6.16 Down the Hill ConcepTest Down Three balls of equal mass start from rest and roll down different ramps. All ramps have the same height. Which ball has the greater speed at the bottom of its ramp? 4) same speed for all balls 1 2 3 All of the balls have the same initial gravitational PE, same since they are all at the same height (PE = mgh). Thus, same when they get to the bottom, they all have the same final KE, and hence the same speed (KE = 1/2 mv2). KE same Follow-up: Which ball takes longer to get down the ramp? ConcepTest 7.9a Going Bowling I ConcepTest Going A bowling ball and a ping-pong ball are rolling toward you with the same momentum. If you exert the same force to stop each one, which takes a longer time to bring to rest? 1) the bowling ball 1) 2) same time for both 2) 3) the ping-pong ball 4) impossible to say p p ConcepTest 7.9a Going Bowling I ConcepTest Going A bowling ball and a ping-pong ball are rolling toward you with the same momentum. If you exert the same force to stop each one, which takes a longer time to bring to rest? 1) the bowling ball 2) same time for both 2) 3) the ping-pong ball 4) impossible to say e know: re, F and ∆ p are the same for both balls! same It will take the same amount of time same to stop them. ∆ pso Fav = ∆t ∆ p = Fav ∆ t av p p ConcepTest 7.12a Inelastic Collisions I ConcepTest Inelastic A box slides with initial velocity 10 m/s on a frictionless surface and collides inelastically with an identical box. The boxes stick together after the collision. What is the final velocity? 1) 10 m/s 2) 20 m/s 3) 0 m/s 4) 15 m/s 5) 5 m/s vi M M M M vf ConcepTest 7.12a Inelastic Collisions I ConcepTest Inelastic A box slides with initial velocity 10 m/s on a frictionless surface and collides inelastically with an identical box. The boxes stick together after the collision. What is the final velocity? 1) 10 m/s 2) 20 m/s 3) 0 m/s 4) 15 m/s 5) 5 m/s The initial momentum is: M vi = (10) M The final momentum must be the same!! The The final momentum is: f f vi M M M M vf ConcepTest 7.13a Nuclear Fission I ConcepTest Nuclear A uranium nucleus (at rest) undergoes fission and splits into two fragments, one heavy and the other light. Which fragment has the greater momentum? 1) the heavy one 1) 2) the light one 2) 3) both have the same momentum 4) impossible to say 1 2 ConcepTest 7.13a Nuclear Fission I ConcepTest Nuclear A uranium nucleus (at rest) undergoes fission and splits into two fragments, one heavy and the other light. Which fragment has the greater momentum? 1) the heavy one 1) 2) the light one 2) 3) both have the same momentum 4) impossible to say The initial momentum of the uranium was zero, so the final total momentum of the two fragments must also be zero. Thus the individual momenta are equal in magnitude and opposite in direction. 1 2 ConcepTest 2.13a ConcepTest The graph of position versus time for a car is given below. What can you say about the velocity of the car over time? velocity Graphing Velocity I 1) it speeds up all the time 2) it slows down all the time 3) it moves at constant velocity 4) sometimes it speeds up and sometimes it slows down 5) not really sure t ConcepTest 2.13a ConcepTest The graph of position versus time for a car is given below. What can you say about the velocity of the car over time? velocity Graphing Velocity I 1) it speeds up all the time 2) it slows down all the time 3) it moves at constant velocity 4) sometimes it speeds up and sometimes it slows down 5) not really sure The car moves at a constant velocity because the x vs. t plot shows a straight line. The slope of a straight line is constant. Remember that the slope of x versus t is the velocity! t ConcepTest 2.13b The graph of position vs. time for a car is given below. What can you say about the velocity of the car over time? velocity Graphing Velocity II 1) it speeds up all the time 2) it slows down all the time 3) it moves at constant velocity 4) sometimes it speeds up and sometimes it slows down 5) not really sure x t ConcepTest 2.13b The graph of position vs. time for a car is given below. What can you say about the velocity of the car over time? velocity Graphing Velocity II 1) it speeds up all the time 2) it slows down all the time 3) it moves at constant velocity 4) sometimes it speeds up and sometimes it slows down 5) not really sure x The car slows down all the time because the slope of the x vs. t graph is diminishing as time goes on. Remember that the slope of x vs. t is the velocity! At large t, the value of the position x does not change, indicating that the car must be at rest. t ConcepTest 2.14a ConcepTest Consider the line labeled A in the v versus t plot. How does the speed change with time for line A? for v versus t graphs I 1) decreases 2) increases 3) stays constant 4) increases, then decreases 5) decreases, then increases v A t B ConcepTest 2.14a Consider the line labeled A in the v versus t plot. How does the speed change with time for line A? for v versus t graphs I 1) decreases 2) increases 3) stays constant 4) increases, then decreases 5) decreases, then increases v A t B In case A, the initial velocity is positive and the magnitude of the velocity continues to increase with time. ConcepTest 2.14b ConcepTest Consider the line labeled B in the v versus t plot. How does the speed change with time for line B? for v versus t graphs II 1) decreases 2) increases 3) stays constant 4) increases, then decreases 5) decreases, then increases v A t B ConcepTest 2.14b Consider the line labeled B in the v versus t plot. How does the speed change with time for line B? for v versus t graphs II 1) decreases 2) increases 3) stays constant 4) increases, then decreases 5) decreases, then increases v A t B In case B, the initial velocity is positive but the magnitude of the velocity decreases toward zero. After this, the magnitude increases again, but becomes negative, indicating that the object has changed direction. ConcepTest v ConcepTest 2.15a v Rubber Balls I t 1 v t 3 v 2 t 4 t You drop a rubber ball. Right after it leaves your hand and before it hits the floor, which of the above plots represents the v vs. t graph vs. for this motion? (Assume your y-axis is pointing up.) your ConcepTest v ConcepTest 2.15a v Rubber Balls I t 1 v t 3 v 2 t 4 t You drop a rubber ball. Right after it leaves your hand and before it hits the floor, which of the above plots represents the v vs. t graph vs. for this motion? (Assume your y-axis is pointing up.) your The ball is dropped from rest, so its initial velocity is zero. Since the yinitial axis is pointing upwards and the ball is falling downwards, its velocity is negative and becomes more and more negative negative as it accelerates downward. negative v ConcepTest 2.15b v t Rubber Balls II 1 v 3 t v 2 t 4 t You toss a ball straight up in the air and catch it again. Right after it leaves your hand and before you catch it, which of the above plots represents the v vs. t graph vs. for this motion? (Assume your y-axis is pointing up.) your v ConcepTest 2.15b v t Rubber Balls II 1 v 3 t v 2 t 4 t You toss a ball straight up in the air and catch it again. Right after it leaves your hand and before you catch it, which of the above plots represents the v vs. t graph vs. for this motion? (Assume your y-axis is pointing up.) your The ball has an initial velocity that is positive but diminishing as it slows. It positive stops at the top (v = 0), and then its velocity becomes negative and velocity becomes more and more negative as more it accelerates downward. ConcepTest 3.9 Spring-Loaded Gun Spring-Loaded 1) 15° 2) 30° 3) 45° 4) 60° 5) 75° The spring-loaded gun can launch projectiles at different angles with the same launch speed. At what angle should the projectile be launched in order to travel the greatest distance before landing? ConcepTest 3.9 Spring-Loaded Gun Spring-Loaded 1) 15° 2) 30° 3) 45° 4) 60° 5) 75° The spring-loaded gun can launch projectiles at different angles with the same launch speed. At what angle should the projectile be launched in order to travel the greatest distance before landing? A steeper angle lets the projectile stay in the air longer, but it does not travel so far because it has a small x-component of velocity. On the other hand, a shallow angle gives a large x-velocity, but the projectile is not in the air for very long. The compromise comes at 45°, although this result is best seen in a calculation of the “range formula” as shown in the textbook. ConcepTest 4.21 Going Sledding Your little sister wants you to give her a ride on her sled. On level ground, what is the easiest way to accomplish this? 1) pushing her from behind 2) pulling her from the front 3) both are equivalent 4) it is impossible to move the sled 5) tell her to get out and walk 1 2 ConcepTest 4.21 Going Sledding Your little sister wants you to give her a ride on her sled. On level ground, what is the easiest way to accomplish this? 1) pushing her from behind 2) pulling her from the front 3) both are equivalent 4) it is impossible to move the sled 5) tell her to get out and walk In Case 1, the force F is pushing down pushing (in addition to mg), so the normal force is larger. In Case 2, the force F force is pulling up, against gravity, so the pulling normal force is lessened. Recall that normal the frictional force is proportional to the normal force. 1 2 ConcepTest 4.22 Will It Budge? A box of weight 100 N is at rest on a floor where µ s = 0.5. A rope is attached to the box and pulled horizontally with tension T = 30 N. Which way does the box move? 1) moves to the left 2) moves to the right 3) moves up 4) moves down 5) the box does not move Static friction (µ s = 0.4 ) m T ConcepTest 4.22 Will It Budge? A box of weight 100 N is at rest on a floor where µ s = 0.5. A rope is attached to the box and pulled horizontally with tension T = 30 N. Which way does the box move? 1) moves to the left 2) moves to the right 3) moves up 4) moves down 5) the box does not move The static friction force has a Static friction (µ s = 0.4 ) m T Follow-up: What happens if the tension is 35 N? What about 45 N? Follow-up: 35 What 45 ConcepTest 4.23a Sliding Down I A box sits on a flat board. You lift one end of the board, making an angle with the floor. As you increase the angle, the box will eventually begin to slide down. Why? 1) component of the gravity force parallel to the plane increased 2) coeff. of static friction decreased 3) normal force exerted by the board decreased 4) both #1 and #3 5) all of #1, #2, and #3 Normal Net Force Weight ConcepTest 4.23a Sliding Down I A box sits on a flat board. You lift one end of the board, making an angle with the floor. As you increase the angle, the box will eventually begin to slide down. Why? q 1) component of the gravity force parallel to the plane increased 2) coeff. of static friction decreased 3) normal force exerted by the board decreased 4) both #1 and #3 5) all of #1, #2, and #3 As the angle increases, the component of weight parallel to the plane increases of and the component perpendicular to the plane decreases (and so does the Normal plane force). Since friction depends on Normal force, we see that the friction force gets smaller and the force pulling the box smaller down the plane gets bigger. down Normal Net Force Weight ConcepTest 6.17b Runaway Box A box sliding on a frictionless flat surface runs into a fixed spring, which compresses a distance x to stop the box. If the initial speed of the box were doubled, how much would the spring compress in this case? 1) half as much 2) the same amount 3) √ 2 times as much 4) twice as much 5) four times as much x ConcepTest 6.17b Runaway Box A box sliding on a frictionless flat surface runs into a fixed spring, which compresses a distance x to stop the box. If the initial speed of the box were doubled, how much would the spring compress in this case? 1) half as much 2) the same amount 3) √ 2 times as much 4) twice as much 5) four times as much Use energy conservation: i 2 x initial energy: E = KE = 1/2 mv 1/2 mv f s 2 So if v doubles, x doubles! So ConcepTest 6.19 Cart on a Hill ConcepTest A cart starting from rest rolls down a hill and at the bottom has a speed of 4 m/s. If the cart were given an initial push, so its initial speed at the top of the hill was 3 m/s, what would be its speed at the bottom? 1) 4 m/s 2) 5 m/s 3) 6 m/s 4) 7 m/s 5) 25 m/s ConcepTest 6.19 Cart on a Hill ConcepTest A cart starting from rest rolls down a hill and at the bottom has a speed of 4 m/s. If the cart were given an initial push, so its initial speed at the top of the hill was 3 m/s, what would be its speed at the bottom? 1) 4 m/s 2) 5 m/s 3) 6 m/s 4) 7 m/s 5) 25 m/s q When starting from rest, the cart’s PE is changed into KE: 2 When starting from 3 m/s, the q final KE is: KEf ∆ PE =KEiKE += 1/2 m(4) = KE ∆ 1∆ KE /2 2 = 1/2 m(3)2 + 1/2 m(4) 1/2 Speed is not the same as kinetic energy ConcepTest 6.20a Falling Leaves Falling You see a leaf falling to the ground with constant speed. When you first notice it, the leaf has initial total energy PEi + KEi. You watch the leaf until just before it hits the ground, at which point it has final total energy PEf + KEf. How do these total energies compare? 1) PEi + KEi > PEf + KEf 2) PEi + KEi = PEf + KEf 3) PEi + KEi < PEf + KEf 4) impossible to tell from the information provided ConcepTest 6.20a Falling Leaves Falling You see a leaf falling to the ground with constant speed. When you first notice it, the leaf has initial total energy PEi + KEi. You watch the leaf until just before it hits the ground, at which point it has final total energy PEf + KEf. How do these total energies compare? As the leaf falls, air resistance exerts a force on it opposite to its direction of motion. This force does negative work, which its force prevents the leaf from accelerating. This frictional force is a non-conservative force, so the leaf loses energy as it falls, leaf and its final total energy is less than its initial total energy. final Follow-up: What happens to leaf’s KE as it falls? What is net work done? 1) PEi + KEi > PEf + KEf 2) PEi + KEi = PEf + KEf 3) PEi + KEi < PEf + KEf 4) impossible to tell from the information provided ConcepTest 7.14a Recoil Speed I Recoil Amy (150 lbs) and Gwen (50 lbs) are standing on slippery ice and push off each other. If Amy slides at 6 m/s, what speed does Gwen have? (1) 2 m/s (2) 6 m/s (3) 9 m/s (4) 12 m/s (5) 18 m/s 150 lbs 50 lbs ConcepTest 7.14a Recoil Speed I Recoil Amy (150 lbs) and Gwen (50 lbs) are standing on slippery ice and push off each other. If Amy slides at 6 m/s, what speed does Gwen have? (1) 2 m/s (2) 6 m/s (3) 9 m/s (4) 12 m/s (5) 18 m/s The initial momentum is zero, initial so the momenta of Amy and Gwen must be equal and opposite. Since p = mv, opposite then if Amy has 3 times more mass, we see that more Gwen must have 3 times more speed. more 150 lbs 50 lbs ConcepTest 7.14b Recoil Speed II ConcepTest Recoil A cannon sits on a stationary railroad flatcar with a total mass of 1000 kg. When a 10-kg cannon ball is fired to the left at a speed of 50 m/s, what is the recoil speed of the flatcar? 1) 0 m/s 2) 0.5 m/s to the right 2) 3) 1 m/s to the right 4) 20 m/s to the right 5) 50 m/s to the right ConcepTest 7.14b Recoil Speed II ConcepTest Recoil A cannon sits on a stationary railroad flatcar with a total mass of 1000 kg. When a 10-kg cannon ball is fired to the left at a speed of 50 m/s, what is the recoil speed of the flatcar? Since the initial momentum of the system was zero, the final total momentum must also be zero. Thus, the final momenta of the cannon ball and the flatcar must be equal and opposite. equal pcannonball = (10 kg)(50 m/s) = 500 kgm/s 1) 0 m/s 2) 0.5 m/s to the right 2) 3) 1 m/s to the right 4) 20 m/s to the right 5) 50 m/s to the right ConcepTest 7.17 Shut the Door! ConcepTest Shut You are lying in bed and you want to shut your bedroom door. You have a superball and a blob of clay (both with the same mass) sitting next to you. Which one would be more effective to throw at your door to close it? 1) the superball 2) the blob of clay 3) it doesn’t matter -- they 3) will be equally effective will 4) you are just too lazy to 4) throw anything throw ConcepTest 7.17 Shut the Door! ConcepTest Shut You are lying in bed and you want to shut your bedroom door. You have a superball and a blob of clay (both with the same mass) sitting next to you. Which one would be more effective to throw at your door to close it? 1) the superball 2) the blob of clay 3) it doesn’t matter -- they 3) will be equally effective will 4) you are just too lazy to 4) throw anything throw The superball bounces off the door with almost no loss of speed, so its ∆ p (and that of the door) is 2mv. so The clay sticks to the door and continues to move along with it, so its ∆ p is less than that of the superball, and therefore so less it imparts less ∆ p to the door. ConcepTest 6.13 Up the Hill ConcepTest Up Two paths lead to the top of a big Two hill. One is steep and direct, while the other is twice as long but less steep. How much more potential energy would you gain if you take the longer path? the 1) the same 2) twice as much 3) four times as much 4) half as much 5) you gain no PE in either case ConcepTest 6.13 Up the Hill ConcepTest Up Two paths lead to the top of a big Two hill. One is steep and direct, while the other is twice as long but less steep. How much more potential energy would you gain if you take the longer path? the 1) the same 2) twice as much 3) four times as much 4) half as much 5) you gain no PE in either case Since your vertical position (height) changes by the same amount in each case, the gain in potential energy is the same. Follow-up: How much more work do you do in taking the steeper path? Follow-up: Which path would you rather take? Why? ConcepTest 6.21a Time for Work I ConcepTest Mike applied 10 N of force over 3 m in 10 seconds. Joe applied the same force over the same distance in 1 minute. Who did more work? 1) Mike 2) Joe 3) both did the same work ConcepTest 6.21a Time for Work I ConcepTest Mike applied 10 N of force over 3 m in 10 seconds. Joe applied the same force over the same distance in 1 minute. Who did more work? 1) Mike 2) Joe 3) both did the same work Both exerted the same force over the same same displacement. Therefore, both did the same displacement amount of work. Time does not matter for amount determining the work done. determining ConcepTest 6.21b Time for Work II Mike performed 5 J of work in 10 secs. Joe did 3 J of work in 5 secs. Who produced the greater power? 1) Mike produced more power 2) Joe produced more power 3) both produced the same amount of power ConcepTest 6.21b Time for Work II ConcepTest Mike performed 5 J of work in 10 secs. Joe did 3 J of work in 5 secs. Who produced the greater power? 1) Mike produced more power 2) Joe produced more power 3) both produced the same amount of power Since power = work / time, we see that Mike produced 0.5 W Mike and Joe produced 0.6 W of power. Thus, even though Mike Joe did more work, he required twice the time to do the work, and therefore his power output was lower. ConcepTest 4.5 Force and Mass A force F acts on mass M for a time interval T, giving it a final speed v. If the same force acts for the same time on a different mass 2M, what would be the final speed of the bigger mass? 1) 4 v 2) 2 v 3) v 4) 1/2 v 5) 1/4 v ConcepTest 4.5 Force and Mass A force F acts on mass M for a time interval T, giving it a final speed v. If the same force acts for the same time on a different mass 2M, what would be the final speed of the bigger mass? 1) 4 v 2) 2 v 3) v 4) 1/2 v 5) 1/4 v In the first case, the acceleration acts over time T to give velocity v = aT. In the second case, the mass is doubled, doubled so the acceleration is cut in half, therefore, in the same half time T, the final speed will only be half as much. final Follow-up: What would you have to do to get 2M to reach speed v? ConcepTest 4.7a Gravity and Weight I What can you say about the force of gravity Fg acting on a stone and a feather? 1) Fg is greater on the feather 2) Fg is greater on the stone 3) Fg is zero on both due to vacuum 4) Fg is equal on both always 5) Fg is zero on both always ConcepTest 4.7a Gravity and Weight I What can you say about the force of gravity Fg acting on a stone and a feather? 1) Fg is greater on the feather 2) Fg is greater on the stone 3) Fg is zero on both due to vacuum 4) Fg is equal on both always 5) Fg is zero on both always The force of gravity (weight) depends on the mass of the object!! The stone has more mass, therefore more weight. ConcepTest 4.7b Gravity and Weight II What can you say about the acceleration of gravity acting on the stone and the feather? 1) it is greater on the feather 2) it is greater on the stone 3) it is zero on both due to vacuum 4) it is equal on both always 5) it is zero on both always ConcepTest 4.7b Gravity and Weight II What can you say about the acceleration of gravity acting on the stone and the feather? 1) it is greater on the feather 2) it is greater on the stone 3) it is zero on both due to vacuum 4) it is equal on both always 5) it is zero on both always The acceleration is given by F/m so F/m here the mass divides out. Since we know that the force of gravity (weight) is mg, then we end up with mg acceleration g for both objects. Follow-up: Which one hits the bottom first? v ConcepTest 2.15c v t v Rubber Balls III 1 2 3 t v t 4 t You drop a very bouncy rubber ball. It falls, and then it hits the floor and bounces right back up to you. Which of the following represents the v vs. t graph for this vs. motion? motion? v ConcepTest 2.15c ConcepTest v t v Rubber Balls III 1 2 3 t v t 4 t You drop a very bouncy rubber ball. It falls, and then it hits the floor and bounces right back up to you. Which of the following represents the v vs. t graph for this vs. motion? motion? Initially, the ball is falling down, so its velocity must be negative (if UP is negative positive). Its velocity is also increasing in magnitude as it falls. increasing Once it bounces, it changes direction and then has a positive velocity, positive which is also decreasing as the ball decreasing moves upward. v ConcepTest 2.15d v t v Rubber Balls IV 1 2 3 t v t 4 t You drop a very bouncy rubber ball. It falls, and then it hits the floor and bounces right back up to you. Which of the following represents the v vs. t graph for this vs. motion? motion? v ConcepTest 2.15d v t v Rubber Balls IV 1 2 3 t v t 4 t You drop a very bouncy rubber ball. It falls, and then it hits the floor and bounces right back up to you. Which of the following represents the v vs. t graph for this vs. motion? motion? Initially, the ball is falling down, so its velocity must be negative (if UP is negative positive). Its velocity is also increasing in magnitude as it falls. increasing Once it bounces, it changes direction and then has a positive velocity, positive which is also decreasing as the ball decreasing moves upward. ConcepTest 6.6a Free Fall I ConcepTest Free Two stones, one twice the mass of the other, are dropped from a cliff. Just before hitting the ground, what is the kinetic energy of the heavy stone compared to the light one? compared 1) quarter as much 2) half as much 3) the same 4) twice as much 5) four times as much ConcepTest 6.6a Free Fall I Free Two stones, one twice the mass of the other, are dropped from a cliff. Just before hitting the ground, what is the kinetic energy of the heavy stone compared to the light one? compared 1) quarter as much 2) half as much 3) the same 4) twice as much 5) four times as much Consider the work done by gravity to make the stone fall distance d: ∆ KE = Wnet = F d cosθ ∆ KE = mg d Thus, the stone with the greater mass has the greater greater KE, which is twice as big for the heavy stone. KE twice Follow-up: How do the initial values of gravitational PE compare? Follow-up: ConcepTest 6.6b Free Fall II Free In the previous question, just before hitting the ground, what is the final speed of the heavy stone compared to the light one? 1) quarter as much 2) half as much 3) the same 4) twice as much 5) four times as much ConcepTest 6.6b Free Fall II Free In the previous question, just before hitting the ground, what is the final speed of the heavy stone compared to the light one? 1) quarter as much 2) half as much 3) the same 4) twice as much 5) four times as much All freely falling objects fall at the same rate, which is g. Since All the acceleration is the same for both, and the distance is the acceleration same, then the final speeds will be the same for both stones. same final ConcepTest 6.7 Work and KE ConcepTest Work A child on a skateboard is moving at a speed of 2 m/s. After a force acts on the child, her speed is 3 m/s. What can you say about the work done by the external force on the child? 1) positive work was done 2) negative work was done 3) zero work was done ConcepTest 6.7 Work and KE Work A child on a skateboard is moving at a speed of 2 m/s. After a force acts on the child, her speed is 3 m/s. What can you say about the work done by the external force on the child? 1) positive work was done 2) negative work was done 3) zero work was done The kinetic energy of the child increased because her speed increased. This increase in KE was the result of speed increase positive work being done. Or, from the definition of work, positive f i Follow-up: What does it mean for negative work to be done on the child? ConcepTest 4.11 On an Incline Consider two identical blocks, one resting on a flat surface, and the other resting on an incline. For which case is the normal force greater? 1) case A 2) case B 3) both the same (N = mg) 4) both the same (0 < N < mg) 5) both the same (N = 0) ConcepTest 4.11 On an Incline Consider two identical blocks, one resting on a flat surface, and the other resting on an incline. For which case is the normal force greater? 1) case A 2) case B 3) both the same (N = mg) 4) both the same (0 < N < mg) 5) both the same (N = 0) In Case A, we know that N = Case W. In Case B, due to the angle Case of the incline, N < W. In fact, we can see that N = W cos(θ ). y N f x θ W θW ConcepTest 4.14a Collision Course I 1) the car A small car collides with small a large truck. Which experiences the greater impact force? impact 2) the truck 3) both the same 4) it depends on the velocity of each 5) it depends on the mass of each ConcepTest 4.14a Collision Course I 1) the car A small car collides with small a large truck. Which experiences the greater impact force? impact 2) the truck 3) both the same 4) it depends on the velocity of each 5) it depends on the mass of each According to Newton’s 3rd Law, both vehicles experience the same magnitude of force. ConcepTest 4.14b Collision Course II In the collision between In the car and the truck, which has the greater acceleration? acceleration? 1) the car 1) 2) the truck 3) both the same 4) it depends on the velocity of each 5) it depends on the mass of each ConcepTest 4.14b Collision Course II In the collision between In the car and the truck, which has the greater acceleration? acceleration? 1) the car 1) 2) the truck 3) both the same 4) it depends on the velocity of each 5) it depends on the mass of each We have seen that both vehicles experience the same magnitude of force. But the acceleration is given by F/m so the car F/m car has the larger acceleration, larger since it has the smaller mass. mass ConcepTest 6.8a Slowing Down ConcepTest Slowing If a car traveling 60 km/hr can 60 brake to a stop within 20 m, what 20 what is its stopping distance if it is traveling 120 km/hr? Assume 120 Assume that the braking force is the same in both cases. same 1) 20 m 2) 30 m 3) 40 m 4) 60 m 5) 80 m ConcepTest 6.8a Slowing Down ConcepTest Slowing If a car traveling 60 km/hr can 60 brake to a stop within 20 m, what 20 what is its stopping distance if it is traveling 120 km/hr? Assume 120 Assume that the braking force is the same in both cases. same 1) 20 m 2) 30 m 3) 40 m 4) 60 m 5) 80 m F d = Wnet = ∆ KE = 0 – 1/2 mv2 2 thus: |F| d = 1/2 mv ConcepTest 6.9a Work and Energy I ConcepTest Work Two blocks of mass m1 and m2 (m1 > m2) slide on a frictionless floor and have the same kinetic energy when they hit a long rough stretch (µ > 0), which slows them down to a stop. Which one goes farther? 1) m1 2 ) m2 3) they will go the same distance m1 m2 ConcepTest 6.9a Work and Energy I ConcepTest Work Two blocks of mass m1 and m2 (m1 > m2) slide on a frictionless floor and have the same kinetic energy when they hit a long rough stretch (µ > 0), which slows them down to a stop. Which one goes farther? 1) m1 2 ) m2 3) they will go the same distance With the same ∆ KE, both blocks must have the same work done same to them by friction. The friction m1 m2 Follow-up: Which block has the greater magnitude of acceleration? ConcepTest 6.9b Work and Energy II Work A golfer making a putt gives the ball an initial velocity of v0, but he has badly misjudged the putt, and the ball only travels one-quarter of the distance to the hole. If the resistance force due to the grass is constant, what speed should he have given the ball (from its original position) in order to make it into the hole? 1) 2 v0 2) 3 v0 3) 4 v0 4) 8 v0 5) 16 v0 ConcepTest 6.9b Work and Energy II Work A golfer making a putt gives the ball an initial velocity of v0, but he has badly misjudged the putt, and the ball only travels one-quarter of the distance to the hole. If the resistance force due to the grass is constant, what speed should he have given the ball (from its original position) in order to make it into the hole? 1) 2 v0 2) 3 v0 3) 4 v0 4) 8 v0 5) 16 v0 In traveling 4 times the distance, the resistive force will times do 4 times the work. Thus, the ball’s initial KE must be times 4 times greater in order to just reach the hole — this times requires an increase in the initial speed by a factor of 2 ConcepTest 4.16a Tension I You tie a rope to a tree and you pull on the rope with a force of 100 N. What is the tension in the rope? 1) 0 N 2) 50 N 3) 100 N 4) 150 N 5) 200 N ConcepTest 4.16a Tension I You tie a rope to a tree and you pull on the rope with a force of 100 N. What is the tension in the rope? 1) 0 N 2) 50 N 3) 100 N 4) 150 N 5) 200 N The tension in the rope is the force that the rope “feels” across any section of it (or that you would feel if you replaced a piece of the rope). Since you are pulling with a force of 100 N, that is the tension in the rope. ConcepTest 4.16b Tension II Two tug-of-war opponents each pull with a force of 100 N on opposite ends of a rope. What is the tension in the rope? 1) 0 N 2) 50 N 3) 100 N 4) 150 N 5) 200 N ConcepTest 4.16b Tension II Two tug-of-war opponents each pull with a force of 100 N on opposite ends of a rope. What is the tension in the rope? 1) 0 N 2) 50 N 3) 100 N 4) 150 N 5) 200 N This is literally the identical situation to the literally previous question. The tension is not 200 N !! The Whether the other end of the rope is pulled by a person, or pulled by a tree, the tension in the rope is still 100 N !! 100 ConcepTest 4.19 A box sits in a pickup truck on a frictionless truck bed. When the truck accelerates forward, the box slides off the back of the truck because: Friction 1) the force from the rushing air pushed it off 2) the force of friction pushed it off 3) no net force acted on the box 4) truck went into reverse by accident 5) none of the above ConcepTest 4.19 A box sits in a pickup truck on a frictionless truck bed. When the truck accelerates forward, the box slides off the back of the truck because: Friction 1) the force from the rushing air pushed it off 2) the force of friction pushed it off 3) no net force acted on the box 4) truck went into reverse by accident 5) none of the above Generally, the reason that the box in the truck bed would move with the truck is due to friction between the box and the bed. friction If there is no friction, there is no force to push the box along, and it remains at rest. The truck accelerated away, essentially and leaving the box behind!! ConcepTest 6.10 Sign of the Energy I Sign Is it possible for the kinetic energy of an object to be negative? 1) yes 2) no ConcepTest 6.10 Sign of the Energy I Sign Is it possible for the kinetic energy of an object to be negative? 1) yes 2) no The kinetic energy is 1/2 mv2. The mass 1/2 mass and the velocity squared will always be velocity positive, so KE must always be positive. positive KE ConcepTest 6.11 Sign of the Energy II Sign Is it possible for the gravitational potential energy of an object to be negative? 1) yes 2) no ConcepTest 6.11 Sign of the Energy II Sign Is it possible for the gravitational potential energy of an object to be negative? 1) yes 2) no Gravitational PE is mgh, where height h is measured relative to Gravitational mgh some arbitrary reference level where PE = 0. For example, a some book on a table has positive PE if the zero reference level is chosen to be the floor. However, if the ceiling is the zero level, ceiling then the book has negative PE on the table. It is only book differences (or changes) in PE that have any physical meaning. differences ...
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This note was uploaded on 10/02/2010 for the course PHYS 1301 taught by Professor Ordonez during the Fall '09 term at University of Houston.

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