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denotes Questions W answer available in Student Solutions Manual/Study Guide; O denotes objective question 10. A child tosses a ball straight up. She says the ball is moving away from her hand because the ball feels an upward force of the throw as well as the gravitational force. (a) Can the force of the throw exceed the gravitational force? How would the ball move if it did? (b) Can the force of the throw be equal in magnitude to the gravitational force? Explain. (c) What strength can accurately be attributed to the force of the throw? Explain. (d) Why does the ball move away from the childs hand? 11. O The third graders are on one side of a schoolyard and the fourth graders on the other. The groups are throwing snowballs at each other. Between them, snowballs of various masses are moving with different velocities as shown in Figure Q5.11. Rank the snowballs (a) through (e) according to the magnitude of the total force exerted on each one. Ignore air resistance. If two snowballs rank together, make that fact clear. 1. A ball is held in a persons hand. (a) Identify all the external forces acting on the ball and the reaction to each. (b) If the ball is dropped, what force is exerted on it while it is falling? Identify the reaction force in this case. (Ignore air resistance.) 2. If a car is traveling westward with a constant speed of 20 m/s, what is the resultant force acting on it? 3. O An experiment is performed on a puck on a level air hockey table, where friction is negligible. A constant horizontal force is applied to the puck and its acceleration is measured. Now the same puck is transported far into outer space, where both friction and gravity are negligible. The same constant force is applied to the puck (through a spring scale that stretches the same amount) and the pucks acceleration (relative to the distant stars) is measured. What is the pucks acceleration in outer space? (a) somewhat greater than its acceleration on the Earth (b) the same as its acceleration on the Earth (c) less than its acceleration on the Earth (d) infinite because neither friction nor gravity constrains it (e) very large because acceleration is inversely proportional to weight and the pucks weight is very small but not zero 4. In the motion picture It Happened One Night (Columbia Pictures, 1934), Clark Gable is standing inside a stationary bus in front of Claudette Colbert, who is seated. The bus suddenly starts moving forward and Clark falls into Claudettes lap. Why did that happen? 5. Your hands are wet and the restroom towel dispenser is empty. What do you do to get drops of water off your hands? How does your action exemplify one of Newtons laws? Which one? 6. A passenger sitting in the rear of a bus claims that she was injured when the driver slammed on the brakes, causing a suitcase to come flying toward her from the front of the bus. If you were the judge in this case, what disposition would you make? Why? 7. A spherical rubber balloon inflated with air is held stationary, and its opening, on the west side, is pinched shut. (a) Describe the forces exerted by the air on sections of the rubber. (b) After the balloon is released, it takes off toward the east, gaining speed rapidly. Explain this motion in terms of the forces now acting on the rubber. (c) Account for the motion of a skyrocket taking off from its launch pad. 8. If you hold a horizontal metal bar several centimeters above the ground and move it through grass, each leaf of grass bends out of the way. If you increase the speed of the bar, each leaf of grass will bend more quickly. How then does a rotary power lawn mower manage to cut grass? How can it exert enough force on a leaf of grass to shear it off? 9. A rubber ball is dropped onto the floor. What force causes the ball to bounce? 2 = intermediate 3 = challenging = SSM/SG 12. The mayor of a city decides to fire some city employees because they will not remove the obvious sags from the cables that support the city traffic lights. If you were a lawyer, what defense would you give on behalf of the employees? Which side do you think would win the case in court? 13. A clip from Americas Funniest Home Videos. Balancing carefully, three boys inch out onto a horizontal tree branch above a pond, each planning to dive in separately. The youngest and cleverest boy notices that the branch is only barely strong enough to support them. He decides to jump straight up and land back on the branch to break it, spilling all three into the pond together. When he starts to carry out his plan, at what precise moment does the branch break? Explain. Suggestion: Pretend to be the clever boy and imitate what he does in slow motion. If you are still unsure, stand on a bathroom scale and repeat the suggestion. 14. When you push on a box with a 200-N force instead of a 50-N force, you can feel that you are making a greater effort. When a table exerts a 200-N upward normal force instead of one of smaller magnitude, is the table really doing anything differently? 15. A weightlifter stands on a bathroom scale. He pumps a barbell up and down. What happens to the = symbolic reasoning =qualitative reasoning = ThomsonNOW reading on the scale as he does so? What If? What if he is strong enough to actually throw the barbell upward? How does the reading on the scale vary now? 16. (a) Can a normal force be horizontal? (b) Can a normal force be directed vertically downward? (c) Consider a tennis ball in contact with a stationary floor and with nothing else. Can the normal force be different in magnitude from the gravitational force exerted on the ball? (d) Can the force exerted by the floor on the ball be different in magnitude from the force the ball exerts on the floor? Explain each of your answers. 17. Suppose a truck loaded with sand accelerates along a highway. If the driving force exerted on the truck remains constant, what happens to the trucks acceleration if its trailer leaks sand at a constant rate through a hole in its bottom? 18. O In Figure Q5.18, the light, taut, unstretchable cord B joins block 1 and the larger-mass block 2. Cord A exerts a force on block 1 to make it accelerate forward. (a) How does the magnitude of the force exerted by cord A on block 1 compare with the magnitude of the force exerted by cord B on block 2? Is it larger, smaller, or equal? (b) How does the acceleration of block 1 compare with the acceleration (if any) of block 2? (c) Does cord B exert a force on block 1? If so, is it forward or backward? Is it larger, smaller, or equal in magnitude to the force exerted by cord B on block 2? 22. O In Figure Q5.22, a locomotive has broken through the wall of a train station. As it did, what can be said about the force exerted by the locomotive on the wall? (a) The force exerted by the locomotive on the wall was bigger than the force the wall could exert on the locomotive. (b) The force exerted by the locomotive on the wall was the same in magnitude as the force exerted by the wall on the locomotive. (c) The force exerted by the locomotive on the wall was less than the force exerted by the wall on the locomotive. (d) The wall cannot be said to exert a force; after all, it broke. 19. Identify the actionreaction pairs in the following situations: a man takes a step, a snowball hits a girl in the back, a baseball player catches a ball, a gust of wind strikes a window. 20. O In an Atwood machine, illustrated in Figure 5.14, a light string that does not stretch passes over a light, frictionless pulley. On one side, block 1 hangs from the vertical string. On the other side, block 2 of larger mass hangs from the vertical string. (a) The blocks are released from rest. Is the magnitude of the acceleration of the heavier block 2 larger, smaller, or the same as the free-fall acceleration g? (b) Is the magnitude of the acceleration of block 2 larger, smaller, or the same as the acceleration of block 1? (c) Is the magnitude of the force the string exerts on block 2 larger, smaller, or the same as that of the force of the string on block 1? 21. Twenty people participate in a tug-of-war. The two teams of ten people are so evenly matched that neither team wins. After the game, the participants notice that a car is stuck in the mud. They attach the tug-of-war rope to the bumper of the car, and all the people pull on the rope. The heavy car has just moved a couple of decimeters when the rope breaks. Why did the rope break in this situation, but not when the same twenty people pulled on it in a tug-of-war? 23. An athlete grips a light rope that passes over a low-friction pulley attached to the ceiling of a gym. A sack of sand precisely equal in weight to the athlete is tied to the other end of the rope. Both the sand and the athlete are initially at rest. The athlete climbs the rope, sometimes speeding up and slowing down as he does so. What happens to the sack of sand? Explain. 24. O A small bug is nestled between a 1-kg block and a 2-kg block on a frictionless table. A horizontal force can be applied to either of the blocks as shown in Figure Q5.24. (i) In which situation illustrated in the figure, (a) or (b), does the bug have a better chance of survival, or (c) does it make no difference? (ii) Consider the statement, The force exerted by the larger block on the smaller one is larger in magnitude than the force exerted by the smaller block on the larger one. Is this statement true only in situation (a)? Only in situation (b)? Is it true (c) in both situations or (d) in neither? (iii) Consider the statement, As the blocks move, the force exerted by the block in back on the block in front is stronger than the force exerted by the front block on the back one. Is this statement true only in situation (a), only in situation (b), in (c) both situations, or in (d) neither? 2 = intermediate 3 = challenging = SSM/SG = ThomsonNOW = symbolic reasoning =qualitative reasoning 25. Can an object exert a force on itself? Argue for your answer. 26. O The harried manager of a discount department store is pushing horizontally with a force of magnitude 200 N on a box of shirts. The box is sliding across the horizontal floor with a forward acceleration. Nothing else touches the box. What must be true about the magnitude of the force of kinetic friction acting on the box (choose one)? (a) It is greater than 200 N. (b) It is less than 200 N. (c) It is equal to 200 N. (d) None of these statements is necessarily true. 27. A car is moving forward slowly and is speeding up. A student claims the car exerts a force on itself or the cars engine exerts a force on the car. Argue that this idea cannot be accurate and that friction exerted by the road is the propulsive force on the car. Make your evidence and reasoning as persuasive as possible. Is it static or kinetic friction? Suggestions: Consider a road covered with light gravel. Consider a sharp print of the tire tread on an asphalt road, obtained by coating the tread with dust. 28. O The driver of a speeding empty truck slams on the brakes and skids to a stop through a distance d. (i) If the truck now carries a load that doubles its mass, what will be the trucks skidding distance? (a) 4d (b) 2d (c) 2 d (d) d (e) d/ 2 (f) d/2 (g) d/4 (ii) If the initial speed of the empty truck were halved, what would be the trucks skidding distance? Choose from the same possibilities (a) through (g). 29.OAn object of mass m is sliding with speed v0 at some instant across a level tabletop, with which its coefficient of kinetic friction is . It then moves through a distance d and comes to rest. Which of the following equations for the speed v0 is reasonable (choose one)? (a) v0 = 2 mgd (b) v0 = 2 mgd (c) v0 = (e) v0 = 2 gd (d) v0 = 2 g d 2 d 30. O A crate remains stationary after it has been placed on a ramp inclined at an angle with the horizontal. Which of the following statements is or are correct about the magnitude of the friction force that acts on the crate? Choose all that are true. (a) It is larger than the weight of the crate. (b) It is at least equal to the weight of the crate. (c) It is equal to sn. (d) It is greater than the component of the gravitational force acting down the ramp. (e) It is equal to the component of the gravitational force acting down the ramp. (f) It is less than the component of the gravitational force acting down the ramp. 31. Suppose you are driving a classic car. Why should you avoid slamming on your brakes when you want to stop in the shortest possible distance? (Many modern cars have antilock brakes that avoid this problem.) 32. Describe a few examples in which the force of friction exerted on an object is in the direction of motion of the object. 33. O As shown in Figure Q5.33, student A, a 55-kg girl, sits on one chair with metal runners, at rest on a classroom floor. Student B, an 80-kg boy, sits on an identical chair. Both students keep their feet off the floor. A rope runs from student As hands around a light pulley to the hands of a teacher standing on the floor next to her. The low friction axle of the pulley is attached to a second rope held by student B. All ropes run parallel to the chair runners. (a) If student A pulls on her end of the rope, will her chair or will Bs chair slide on the floor? (b) If instead the teacher pulls on his rope end, which chair slides? (c) If student B pulls on his rope, which chair slides? (d) Now the teacher ties his rope end to student As chair. Student A pulls on the end of the rope in her hands. Which chair slides? (Vern Rockcastle suggested the idea for this question.) 2gd / (f) v0 = 2 md (g) v0 = 2 = intermediate 3 = challenging = SSM/SG = ThomsonNOW = symbolic reasoning =qualitative reasoning Problems The Problems from this chapter may be assigned online in WebAssign. Sign in at www.thomsonedu.com and go to ThomsonNOW to assess your understanding of this chapters topics with additional quizzing and conceptual questions. 1,2,3 denotes straightforward, intermediate, challenging; denotes full solution available in Student Solutions Manual/Study Guide; denotes coached solution with hints available at www.thomsonedu.com; denotes developing symbolic reasoning; denotes asking for qualitative reasoning; denotes computer useful in solving problem Sections 5.1 through 5.6 1. A 3.00-kg object undergoes an acceleration given r by a = (2.00 + 5.00 ) m/s2. Find the resultant force j i acting on it and the magnitude of the resultant force. 2. A force F applied to an object of mass m1 produces an acceleration of 3.00 m/s2. The same force applied to a second object of mass m2 produces an acceleration of 1.00 m/s2. (a) What is the value of the ratio m1/m2? (b) If m1 and m2 are combined into one object, what is its acceleration under the action of the force? 3. To model a spacecraft, a toy rocket engine is securely fastened to a large puck that can glide with negligible friction over a horizontal surface, taken as the xy plane. The 4.00-kg puck has a velocity of 3.00 m/ i s at one instant. Eight seconds later, its velocity is to be (8.00 + 10.0 ) m/s. assuming the rocket engine j i exerts a constant horizontal force, find (a) the components of the force and (b) its magnitude. 4. The average speed of a nitrogen molecule in air is about 6.70 102 m/s, and its mass is 4.68 1026 kg. (a) If it takes 3.00 1013 s for a nitrogen molecule to hit a wall and rebound with the same speed but moving in the opposite direction, what is the average acceleration of the molecule during this time interval? (b) What average force does the molecule exert on the wall? 5. An electron of mass 9.11 1031 kg has an initial speed of 3.00 105 m/s. It travels in a straight line, and its speed increases to 7.00 105 m/s in a distance of 5.00 cm. Assuming its acceleration is constant, (a) determine the force exerted on the electron and (b) compare this force with the weight of the electron, which we ignored. 6. A woman weighs 120 lb. Determine (a) her weight in newtons and (b) her mass in kilograms. 7. The distinction between mass and weight was discovered after Jean Richer transported pendulum clocks from France to French Guiana in 1671. He found that they ran slower there quite systematically. The effect was reversed when the clocks returned to France. How much weight would you personally lose when traveling from Paris, France, where g = 9.809 5 m/s2, to Cayenne, French Guiana, where g = 9.780 8 m/s2? 8. Besides its weight, a 2.80-kg object is subjected to one other constant force. The object starts from rest and in 1.20 s experiences a displacement of (4.20 3.30 ) m, where the direction of is the j j i upward vertical direction. Determine the other force. r r 9. Two forces F1 and F2 act on a 5.00-kg object. Taking F1 = 20.0 N and F2 = 15.0 N, find the accelerations in (a) and (b) of Figure P5.9. r 10. One or more external forces are exerted on each object enclosed in a dashed box shown in Figure 5.1. Identify the reaction to each of these forces. 11. You stand on the seat of a chair and then hop off. (a) During the time interval you are in flight down to the floor, the Earth is lurching up toward you with an acceleration of what order of magnitude? In your solution, explain your logic. Model the Earth as a perfectly solid object. (b) The Earth moves up through a distance of what order of magnitude? 12. A brick of mass M sits on a rubber pillow of mass m. Together they are sliding to the right at constant velocity on an ice-covered parking lot. (a) Draw a freebody diagram of the brick and identify each force acting on it. (b) Draw a free-body diagram of the pillow and identify each force acting on it. (c) Identify all the actionreaction pairs of forces in the brickpillow planet system. 13. A 15.0-lb block rests on the floor. (a) What force does the floor exert on the block? (b) A rope is tied to the block and is run vertically over a pulley. The other end of the rope is attached to a free-hanging 10.0-lb object. What is the force exerted by the floor on the 15.0-lb block? (c) If we replace the 10.0-lb object in part (b) with a 20.0-lb object, what is the force exerted by the floor on the 15.0-lb block? r 14. Three forces acting on an object are given F1 = ( r 2.00 + 2.00 ) N, F2 = (5.00 3.00 ) N, and j j i i r F3 = (45.0 ) N. The object experiences an acceli eration of magnitude 3.75 m/s2. (a) What is the direction of the acceleration? (b) What is the mass of the object? (c) If the object is initially at rest, what is its speed after 10.0 s? (d) What are the velocity components of the object after 10.0 s? Section5.7SomeApplicationsofNewtons Laws 15.Figure P5.15 shows a worker poling a boata very efficient mode of transportationacross a shallow lake. He pushesparallel to the length of the light pole, exerting on the bottom of the lake a force of 240 N. Assume the pole lies in the vertical plane containing the boats keel. At one moment, the pole makes an angle of 35.0 with the vertical and the water exerts a horizontal drag force of 47.5 N on the boat, opposite to its forward velocity of magnitude 0.857 m/s. The mass of the boat including its cargo and the worker is 370 kg. (a) The water exerts a buoyant force vertically upward on the boat. Find the magnitude of this force. (b) Model the forces as constant over a short interval of time to find the velocity of the boat 0.450 s after the moment described. boats hull. (a) Choose the xdirection as east and the y direction as north. Write two component equations representing Newtons second law. Solve the equations for P(the force exerted by the wind on the sail) and for n(the force exerted by the water on the keel). (b) Choose the xdirection as 40.0 north of east and the ydirection as 40.0 west of north. Write Newtons second law as two component equations and solve for nand P. (c) Compare your solutions. Do the results agree?Is one calculation significantly easier? 20.A bag of cement of weight 325 N hangs in equilibrium from three wires as shown in Figure P5.20. Two of the wires make angles 1 = 60.0 and 2 = 25.0 with the horizontal. Assuming the system is in equilibrium, find the tensions T1, T2, and T3 in the wires. 21. A bag of cement of weight Fg hangs in equilibrium from three wires as shown in Figure P5.20. Two of the wires make angles 1 and 2 with the horizontal. Assuming the system is in equilibrium, show that the tension in the left-hand wire is 16.A 3.00-kg object is moving in a plane, with its x and ycoordinates given by x = 5t2 1 and y = 3t3 + 2, where x and y are in meters and t is in seconds. Find the magnitude of the net force acting on this object at t = 2.00 s. 17.The distance between two telephone poles is 50.0 m. When a 1.00-kg bird lands on the telephone wire midway between the poles, the wire sags 0.200 m. Draw a freebody diagram of the bird. How much tension does the bird produce in the wire? Ignore the weight of the wire. 18.An iron bolt of mass 65.0 g hangs from a string 35.7 cm long. The top end of the string is fixed. Without touching it, a magnet attracts the bolt so that it remains stationary, displaced horizontally 28.0 cm to the right from the previously vertical line of the string. (a) Draw a free-body diagram of the bolt. (b) Find the tension in the string. (c) Find the magnetic force on the bolt. 19. Figure P5.19 shows the horizontal forces acting on a sailboat moving north at constant velocity, seen from a point straight above its mast. At its particular speed, the water exerts a 220-N drag force on the sail- T1 = sin ( 1 + 2 ) Fg cos 2 22. You are a judge in a childrens kite-flying contest, and two children will win prizes, one for the kite that pulls the most strongly on its string and one for the kite that pulls the least strongly on its string. To measure string tensions, you borrow a mass hanger, some slotted masses, and a protractor from your physics teacher, and you use the following protocol, illustrated in Figure P5.22. Wait for a child to get her kite well controlled, hook the hanger onto the kite string about 30 cm from her hand, pile on slotted masses until that section of string is horizontal, record the mass required, and record the angle between the horizontal and the string running up to the kite. (a) Explain how this method works. As you construct your explanation, imagine that the childrens parents ask you about your method, that they might make false assumptions about your ability without concrete evidence, and that your explanation is an opportunity to give them confidence in your evaluation technique. (b) Find the string tension if the mass is 132 g and the angle of the kite string is 46.3. 26. A 5.00-kg object placed on a frictionless, horizontal table is connected to a string that passes over a pulley and then is fastened to a hanging 9.00-kg object as shown in Figure P5.26. Draw free-body diagrams of both objects. Find the acceleration of the two objects and the tension in the string. 23. The systems shown in Figure P5.23 are in equilibrium. If the spring scales are calibrated in newtons, what do they read? Ignore the masses of the pulleys and strings, and assume pulleys the and the incline in part (d) are frictionless. 27. Figure P5.27 shows the speed of a persons body as he does a chin-up. Assume the motion is vertical and the mass of the persons body is 64.0 kg. Determine the force exerted by the chin-up bar on his body at (a) time zero, (b) time 0.5 s, (c) time 1.1 s, and (d) time 1.6 s. 24. Draw a free-body diagram of a block that slides down a frictionless plane having an inclination of = 15.0. The block starts from rest at the top, and the length of the incline is 2.00 m. Find (a) the acceleration of the block and (b) its speed when it reaches the bottom of the incline. 25. A 1.00-kg object is observed to have an acceleration of 10.0 m/s2 in a r direction 60.0 east of north (Fig. P5.25). The force F2 exerted on the object has a magnitude of 5.00 N and is directed north. Determine r the magnitude and direction of the force F1 acting on the object. 28.Two objects are connected by a light string that passes over a frictionless pulley as shown in Figure P5.28. Draw free-body diagrams of both objects. Assuming the incline is frictionless m1 = 2.00 kg, m2 = 6.00 kg, and = 55.0, find (a) the accelerations of the objects, (b) the tension in the string, and (c) the speed of each object 2.00 s after they are released from rest. 29. A block is given an initial velocity of 5.00 m/s up a frictionless 20.0 incline. How far up the incline does the block slide before coming to rest? 30. In Figure P5.30, the man and the platform together weigh 950 N. The pulley can be modeled as frictionless. Determine how hard the man has to pull on the rope to lift himself steadily upward above the ground. (Or is it impossible? If so, explain why.) 33. A 72.0-kg man stands on a spring scale in an elevator. Starting from rest, the elevator ascends, attaining its maximum speed of 1.20 m/s in 0.800 s. It travels with this constant speed for the next 5.00 s. The elevator then undergoes a uniform acceleration in the negative y direction for 1.50 s and comes to rest. What does the spring scale register (a) before the elevator starts to move, (b) during the first 0.800 s, (c) while the elevator is traveling at constant speed, and (d) during the time interval it is slowing down? 34. In the Atwood machine shown in Figure 5.14a, m1 = 2.00 kg and m2 = 7.00 kg. The masses of the pulley and string are negligible by comparison. The pulley turns without friction and the string does not stretch. The lighter object is released with a sharp push that sets it into motion at vi = 2.40 m/s downward. (a) How far will m1 descend below its initial level? (b) Find the velocity of m1 after 1.80 seconds. 31. In r system shown in Figure P5.31, a horizontal the force Fx acts on the 8.00-kg object. The horizontal surface is frictionless. Consider the acceleration of the sliding object as a function of Fx. (a) For what values of Fx does the 2.00-kg object accelerate upward? (b) For what values of Fx is the tension in the cord zero? (c) Plot the acceleration of the 8.00-kg object versus Fx. Include values of Fx from 100 N to +100 N. Section 5.8 Forces of Friction 35. A car is traveling at 50.0 mi/h on a horizontal highway. (a) If the coefficient of static friction between road and tires on a rainy day is 0.100, what is the minimum distance in which the car will stop? (b) What is the stopping distance when the surface is dry and s = 0.600? 36. A 25.0-kg block is initially at rest on a horizontal surface. A horizontal force of 75.0 N is required to set the block in motion, after which a horizontal force of 60.0 N is required to keep the block moving with constant speed. Find the coefficients of static and kinetic friction from this information. 37. Your 3.80-kg physics book is next to you on the horizontal seat of your car. The coefficient of static friction between the book and the seat is 0.650, and the coefficient of kinetic friction is 0.550. Suppose you are traveling at 72.0 km/h = 20.0 m/s and brake to a stop over a distance of 45.0 m. (a) Will the book start to slide over the seat? (b) What force does the seat exert on the book in this process? 38. Before 1960, it was believed that the maximum attainable coefficient of static friction for an automobile tire was less than 1. Then, around 1962, three companies independently developed racing tires with coefficients of 1.6. Since then, tires have improved, as illustrated in this problem. According to the 1990 Guinness Book of Records, the fastest time interval for a piston-engine car initially at rest to cover a distance of one-quarter mile is 4.96 s. Shirley Muldowney set this record in September 1989. (a) Assume the rear wheels lifted the front wheels off the pavement as shown in Figure P5.38. What minimum value of s is necessary to achieve the record time interval? (b) Suppose Muldowney were able to double her engine power, keeping other things equal. How would this change affect the time interval?` 32. An object of mass m1 on a frictionless horizontal table is connected to an object of mass m2 through a very light pulley P1 and a light fixed pulley P2 as shown in Figure P5.32. (a) If a1 and a2 are the accelerations of m1 and m2, respectively, what is the relation between these accelerations? Express (b) the tensions in the strings and (c) the accelerations a1 and a2 in terms of g and of the masses m1 and m2. block and the surface is 0.100. (a) Draw a free-body diagram for each block. (b) Determine the tension T and the magnitude of the acceleration of the system. 39. A 3.00-kg block starts from rest at the top of a 30.0 incline and slides a distance of 2.00 m down the incline in 1.50 s. Find (a) the magnitude of the acceleration of the block, (b) the coefficient of kinetic friction between block and plane, (c) the friction force acting on the block, and (d) the speed of the block after it has slid 2.00 m. 40. A woman at an airport is towing her 20.0-kg suitcase at constant speed by pulling on a strap at an angle above the horizontal (Fig. P5.40). She pulls on the strap with a 35.0-N force. The friction force on the suitcase is 20.0 N. Draw a free-body diagram of the suitcase. (a) What angle does the strap make with the horizontal? (b) What normal force does the ground exert on the suitcase? 44. A block of mass 3.00 kg is pushed against a r wall by a force P that makes a = 50 angle with the horizontal as shown in Figure P5.44. The coefficient of static friction between the block and the wall is 0.250. (a) r Determine the possible values for the magnitude of P that allow the block to remain stationary. r (b) Describe what happens if | P | has a larger value and what happens if it is smaller. (c) Repeat parts (a) and (b) assuming the force makes an angle of = 13.0 with the horizontal. 41. A 9.00-kg hanging object is connected, by a light, inextensible cord over a light, frictionless pulley, to a 5.00-kg block that is sliding on a flat table (Fig. P5.26). Taking the coefficient of kinetic friction as 0.200, find the tension in the string. 42. Three objects are connected on a table as shown in Figure P5.42. The rough table has a coefficient of kinetic friction of 0.350. The objects have masses of 4.00 kg, 1.00 kg, and 2.00 kg, as shown, and the pulleys are frictionless. Draw a free-body diagram for each object. (a) Determine the acceleration of each object and their directions. (b) Determine the tensions in the two cords. 45. A 420-g block is at rest on a horizontal surface. The coefficient of static friction between the block and the surface is 0.720, and the coefficient of kinetic friction is 0.340. A force of magnitude P pushes the block forward and downward as shown in Figure P5.45. Assume the force is applied at an angle of 37.0 below the horizontal. (a) Find the acceleration of the block as a function of P. (b) If P = 5.00 N, find the acceleration and the friction force exerted on the block. (c) If P = 10.0 N, find the acceleration and the friction force exerted on the block. (d) Describe in words how the acceleration depends on P. Is there a definite minimum acceleration for the block? If so, what is it? Is there a definite maximum? 43. Two blocks connected by a rope of negligible mass are being dragged by a horizontal force (Fig. P5.43). Suppose F = 68.0 N, m1 = 12.0 kg, m2 = 18.0 kg, and the coefficient of kinetic friction between each 46. Review problem. One side of the roof of a building slopes up at 37.0. A student throws a Frisbee onto the roof. It strikes with a speed of 15.0 m/s, does not bounce, and then slides straight up the incline. The coefficient of kinetic friction between the plastic and the roof is 0.400. The Frisbee slides 10.0 m up the roof to its peak, where it goes into free fall, following a parabolic trajectory with negligible air resistance. Determine the maximum height the Frisbee reaches above the point where it struck the roof. 47. The board sandwiched between two other boards in Figure P5.47 weighs 95.5 N. If the coefficient of friction between the boards is 0.663, what must be the magnitude of the compression forces (assumed horizontal) acting on both sides of the center board to keep it from slipping? 51. An inventive child named Pat wants to reach an apple in a tree without climbing the tree. Sitting in a chair connected to a rope that passes over a frictionless pulley (Fig. P5.51), Pat pulls on the loose end of the rope with such a force that the spring scale reads 250 N. Pats true weight is 320 N, and the chair weighs 160 N. (a) Draw free-body diagrams for Pat and the chair considered as separate systems, and another diagram for Pat and the chair considered as one system. (b) Show that the acceleration of the system is upward and find its magnitude. (c) Find the force Pat exerts on the chair. 48. A magician pulls a tablecloth from under a 200-g mug located 30.0 cm from the edge of the cloth. The cloth exerts a friction force of 0.100 N on the mug, and the cloth is pulled with a constant acceleration of 3.00 m/s2. How far does the mug move relative to the horizontal tabletop before the cloth is completely out from under it? Note that the cloth must move more than 30 cm relative to the tabletop during the process. 49. A package of dishes (mass 60.0 kg) sits on the flatbed of a pickup truck with an open tailgate. The coefficient of static friction between the package and the trucks flatbed is 0.300, and the coefficient of kinetic friction is 0.250. (a) The truck accelerates forward on level ground. What is the maximum acceleration the truck can have so that the package does not slide relative to the truck bed? (b) The truck barely exceeds this acceleration and then moves with constant acceleration, with the package sliding along its bed. What is the acceleration of the package relative to the ground? (c) The driver cleans up the fragments of dishes and starts over again with an identical package at rest in the truck. The truck accelerates up a hill inclined at 10.0 with the horizontal. Now what is the maximum acceleration the truck can have such that the package does not slide relative to the flatbed? (d) When the truck exceeds this acceleration, what is the acceleration of the package relative to the ground? (e) For the truck parked at rest on a hill, what is the maximum slope the hill can have such that the package does not slide? (f) Is any piece of data unnecessary for the solution in all the parts of this problem? Explain. Additional Problems 50. The following equations describe the motion of a system of two objects: +n (6.50 kg)(9.80 m/s2)cos 13.0 = 0 fk = 0.360 n +T + (6.50 kg)(9.80 m/s2)sin 13.0 fk = (6.50 kg)a + (3.80 kg)(9.80 m/s2) = (3.80 kg)a T (a) Solve the equations for a and T. (b) Describe a situation to which these equations apply. Draw freebody diagrams for both objects. 52. In the situation described in Problem 51 and Figure P5.51, the masses of the rope, spring balance, and pulley are negligible. Pats feet are not touching the ground. (a) Assume Pat is momentarily at rest when he stops pulling down on the rope and passes the end of the rope to another child, of weight 440 N, who is standing on the ground next to him. The rope does not break. Describe the ensuing motion. (b) Instead, assume Pat is momentarily at rest when he ties the end of the rope to a strong hook projecting from the tree trunk. Explain why this action can make the rope break. 53. A time-dependent force, F = (8.00 4.00t ) N, j i where t is in seconds, is exerted on a 2.00-kg object initially at rest. (a) At what time will the object be moving with a speed of 15.0 m/s? (b) How far is the object from its initial position when its speed is 15.0 m/s? (c) Through what total displacement has the object traveled at this moment? 54. Three blocks are in contact with one another on a frictionless, horizontal surface as shown in Figure r P5.54. A horizontal force F is applied to m1. Take m1 = 2.00 kg, m2 = 3.00 kg, m3 = 4.00 kg, and F = 18.0 N. Draw a separate free-body diagram for each block and find (a) the acceleration of the blocks, (b) the resultant force on each block, and (c) the magnitudes of the contact forces between the blocks. (d) You are working on a construction project. A coworker is nailing plasterboard on one side of a light partition, and you are on the opposite side, providing backing by leaning against the wall with your back pushing on it. Every hammer blow makes your back sting. The su- r pervisor helps you to put a heavy block of wood between the wall and your back. Using the situation analyzed in parts (a), (b), and (c) as a model, explain how this change works to make your job more comfortable. 55. A rope with mass m1 is attached to the bottom front edge of a block with mass 4.00 kg. Both the rope and the block rest on a horizontal frictionless surface. The rope does not stretch. The free end of the rope is pulled with a horizontal force of 12.0 N. (a) Find the acceleration of the system, as it depends on m1. (b) Find the magnitude of the force the rope exerts on the block, as it depends on m1. (c) Evaluate the acceleration and the force on the block for m1 = 0.800 kg. Suggestion:You may find it easier to do part (c) before parts (a) and (b). WhatIf?(d) What happens to the force on the block as the ropes mass grows beyond all bounds? (e) What happens to the force on the block as the ropes mass approacheszero? (f) What theorem can you state about the tension in a lightcord joining a pair of moving objects? 56.A black aluminum glider floats on a film of air above a level aluminum air track. Aluminum feels essentially no force in a magnetic field, and air resistance is negligible. A strong magnet is attached to the top of the glider, forming a total mass of 240 g. A piece of scrap iron attached to one end stop on the track attracts the magnet with a force of 0.823 N when the iron and the magnet are separated by 2.50 cm. (a) Find the acceleration of the glider at this instant. (b) The scrap iron is now attached to another green glider, forming a total mass of 120 g. Find the acceleration of each glider when they are simultaneously released at 2.50-cm separation. 57. An object of mass M is held in place by an apr plied force F and a pulley system as shown in Figure P5.57. The pulleys are massless and frictionless. Find (a) the tension in each section of r rope, T1, T2, T3, T4, and T5 and (b) the magnitude of F . Suggestion: Draw a free-body diagram for each pulley. 58. A block of mass 2.20 kg is accelerated across a rough surface by a light cord passing over a small pulley as shown in Figure P5.58. The tension T in the cord is maintained at 10.0 N, and the pulley is 0.100 m above the top of the block. The coefficient of kinetic friction is 0.400. (a) Determine the acceleration of the block when x = 0.400 m. (b) Describe the general behavior of the acceleration as the block slides from a location where x is large to x = 0. (c) Find the maximum value of the acceleration and the position x for which it occurs. (d) Find the value of x for which the acceleration is zero. 59. Physics students from San Diego have come in first and second in a contest and are down at the docks, watching their prizes being unloaded from a freighter. On a single light vertical cable that does not stretch, a crane is lifting a 1 207-kg Ferrari and, below it, a 1 461-kg red BMW Z8. The Ferrari is moving upward with speed 3.50 m/s and acceleration 1.25 m/s2. (a) How do the velocity and acceleration of the BMW compare with those of the Ferrari? (b) Find the tension in the cable between the BMW and the Ferrari. (c) Find the tension in the cable above the Ferrari. (d) In our model, what is the total force exerted on the section of cable between the cars? What velocity do you predict for it at 0.01 s into the future? Explain the motion of this section of cable in cause-and-effect terms. 60. A 2.00-kg aluminum block and a 6.00-kg copper block are connected by a light string over a frictionless pulley. They sit on a steel surface as shown in Figure P5.60, where = 30.0. When they are released from rest, will they start to move? If so, determine (a) their acceleration and (b) the tension in the string. If not, determine the sum of the magnitudes of the forces of friction acting on the blocks. thrown downward with a nonzero speed at the top of the building, what will be the shape of its trajectory? Explain. r 61. A crate of weight Fg is pushed by a force P on a horizontal floor. (a) The coefficient of static friction is r s , and P is directed at angle below the horizontal. Show that the minimum value of P that will move the crate is given by P= s Fg sec 1 s tan (b) Find the minimum value of P that can produce motion when s = 0.400, Fg = 100 N, and = 0, 15.0, 30.0, 45.0, and 60.0. 62. Review problem. A block of mass m = 2.00 kg is released from rest at h = 0.500 m above the surface of a table, at the top of a = 30.0 incline as shown in Figure P5.62. The frictionless incline is fixed on a table of height H = 2.00 m. (a) Determine the acceleration of the block as it slides down the incline. (b) What is the velocity of the block as it leaves the incline? (c) How far from the table will the block hit the floor? (d) What time interval elapses between when the block is released and when it hits the floor? (e) Does the mass of the block affect any of the above calculations? 64. A student is asked to measure the acceleration of a cart on a frictionless inclined plane as shown in Figure 5.11, using an air track, a stopwatch, and a meter stick. The height of the incline is measured to be 1.774 cm, and the total length of the incline is measured to be d = 127.1 cm. Hence, the angle of inclination is determined from the relation sin = 1.774/127.1. The cart is released from rest at the top of the incline, and its position x along the incline is measured as a function of time, where x = 0 refers to the carts initial position. For x values of 10.0 cm, 20.0 cm, 35.0 cm, 50.0 cm, 75.0 cm, and 100 cm, the measured times at which these positions are reached (averaged over five runs) are 1.02 s, 1.53 s, 2.01 s, 2.64 s, 3.30 s, and 3.75 s, respectively. Construct a graph of x versus t2, and perform a linear leastsquares fit to the data. Determine the acceleration of the cart from the slope of this graph, and compare it with the value you would get using a = g sin , where g = 9.80 m/s2. 65. A 1.30-kg toaster is not plugged in. The coefficient of static friction between the toaster and a horizontal countertop is 0.350. To make the toaster start moving, you carelessly pull on its electric cord. (a) For the cord tension to be as small as possible, you should pull at what angle above the horizontal? (b) With this angle, how large must the tension be? 66. In Figure P5.66, the pulleys and the cords are light, all surfaces are frictionless, and the cords do not stretch. (a) How does the acceleration of block 1 compare with the acceleration of block 2? Explain your reasoning. (b) The mass of block 2 is 1.30 kg. Find its acceleration as it depends on the mass m1 of block 1. (c) Evaluate your answer for m1 = 0.550 kg. Suggestion: You may find it easier to do part (c) before part (b). What If? (d) What does the result of part (b) predict if m1 is very much less than 1.30 kg? (e) What does the result of part (b) predict if m1 approaches infinity? (f) What is the tension in the long cord in this last case? (g) Could you anticipate the answers (d), (e), and (f) without first doing part (b)? Explain. 63. A couch cushion of mass m is released from rest at the top of a building having height h. A wind blowing along the side of the building exerts a constant horizontal force of magnitude F on the cushion as it drops as shown in Figure P5.63. The air exerts no vertical force. (a) Show that the path of the cushion is a straight line. (b) Does the cushion fall with constant velocity? Explain. (c) If m = 1.20 kg, h = 8.00 m, and F = 2.40 N, how far from the building will the cushion hit the level ground? What If? (d) If the cushion is 71. A mobile is formed by supporting four metal butterflies of equal mass m from a string of length L. The points of support are evenly spaced a distance apart as shown in Figure P5.71. The string forms an angle 1 with the ceiling at each endpoint. The center section of string is horizontal. (a) Find the tension in each section of string in terms of 1, m, and g. (b) Find the angle 2, in terms of 1 , that the sections of string between the outside butterflies and the inside butterflies form with the horizontal. (c) Show that the distance Dbetween the endpoints of the string is 67. What horizontal force must be applied to the cart shown in Figure P5.67 so that the blocks remain stationary relative to the cart? Assume all surfaces, wheels, and pulley are frictionless. Notice that the force exerted by the string accelerates m1. D= L 2 cos 1 + 2 cos tan 1 ( 1 tan 1 ) +1 2 5 ( ). 68. In Figure P5.62, the incline has mass M and is fastened to the stationary horizontal tabletop. The block of mass m is placed near the bottom of the incline and is released with a quick push that sets it sliding upward. The block stops near the top of the incline, as shown in the figure, and then slides down again, always without friction. Find the force that the tabletop exerts on the incline throughout this motion. 69. A van accelerates down a hill (Fig. P5.69), going from rest to 30.0 m/s in 6.00 s. During the acceleration, a toy (m = 0.100 kg) hangs by a string from the vans ceiling. The acceleration is such that the string remains perpendicular to the ceiling. Determine (a) the angle and (b) the tension in the string. 70. An 8.40-kg object slides down a fixed, frictionless inclined plane. Use a computer to determine and tabulate the normal force exerted on the object and its acceleration for a series of incline angles (measured from the horizontal) ranging from 0 to 90 in 5 increments. Plot a graph of the normal force and the acceleration as functions of the incline angle. In the limiting cases of 0 and 90, are your results consistent with the known behavior? ... View Full Document