Lecture 23short

Lecture 23short - Topics Reference Frames Define Speed,...

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Unformatted text preview: Topics Reference Frames Define Speed, Velocity and Acceleration Key points: Velocity and Acceleration must be specified AFTER you decide on a reference frame. Difference between speed and velocity. Difference between instantaneous and time averaged velocity or acceleration. Reading for the next lecture: Ch. 2: 5--8 Translational motion only falling Translational motion plus rotation The objects can be treated as particles with no dimension Reference Frames For ALL kinematic problems, first define your "frame of reference." People on the train run at 5 km/h A train moves at 80km/h "The people on top of the train run at 5 km/h relative to the train." "The people move at 85 km/h relative to the ground." We typically choose frames fixed with respect to the Earth's surface, but this is not the only possibility. Displacement is 20 m Distance is 20 m Displacement is -20 m Distance is 20 m Displacement is a vector, distance is a scalar! 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? 2) no 1) yes 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? 2) no 1) yes 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 2.2 Does the displacement of an object depend on the specific location of the origin of the coordinate system? Displacement 1) yes 2) no 3) it depends on the coordinate system ConcepTest 2.2 Does the displacement of an object depend on the specific location of the origin of the coordinate system? Displacement 1) yes 2) no 3) it depends on the coordinate system Since the displacement is the difference between two coordinates, the origin does not matter. 10 20 30 40 50 x = 40 - 10 = 30 30 40 50 60 70 x = 60 - 30 = 30 Example: Jane runs completely around a circular track of 1 mile circumference in 10 minutes. What is Jane's average speed? What is her average velocity? Starting and ending point ConcepTest 2.3 Does the speedometer in a Speedometer 1) velocity 2) speed car measure velocity or speed? 3) both 4) neither ConcepTest 2.3 Does the speedometer in a Speedometer 1) velocity 2) speed car measure velocity or 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 2.4a You drive for 30 minutes at 30 mi/hr and then for another 30 minutes at 50 mi/hr. What is your average speed for the whole trip? Cruising Along I 1) more than 40 mi/hr 2) equal to 40 mi/hr 3) less than 40 mi/hr ConcepTest 2.3a You drive for 30 minutes at 30 mi/hr and then for another 30 minutes at 50 mi/hr. What is your average speed for the whole trip? Cruising Along I 1) more than 40 mi/hr 2) equal to 40 mi/hr 3) less than 40 mi/hr It is 40 mi/hr in this case. Since the average speed is distance/time and you spend the same amount of time at each speed, then your average speed would indeed be 40 mi/hr. ConcepTest 2.4b You drive 4 miles at 30 mi/hr and then another 4 miles at 50 mi/hr. What is your average speed for the whole 8-mile trip? Cruising Along II 1) more than 40 mi/hr 2) equal to 40 mi/hr 3) less than 40 mi/hr ConcepTest 2.4b You drive 4 miles at 30 mi/hr and then another 4 miles at 50 mi/hr. What is your average speed for the whole 8-mile trip? Cruising Along II 1) more than 40 mi/hr 2) equal to 40 mi/hr 3) less than 40 mi/hr It is not 40 mi/hr! Remember that the average speed is distance/time. Since it takes longer to cover 4 miles at the slower speed, you are actually moving at 30 mi/hr for a longer period of time! Therefore, your average speed is closer to 30 mi/hr than it is to 50 mi/hr. Follow-up: How much further would you have to drive at 50 mi/hr in order to get back your average speed of 40 mi/hr? =2.0 m/s2 Average velocity vs. velocity a=0 a>0 a<0 ConcepTest 2.13a The graph of position versus time for a car is given below. What can you say about the velocity of the car over time? 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 x t ConcepTest 2.13a The graph of position versus time for a car is given below. What can you say about the velocity of the car over time? 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 x 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? 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? 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 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. x t Example: (a) How long does it take a car to cross a 30.0 m wide intersection after the light turns green if the car accelerates from rest at a constant a=2.00m/s2? (b) What is the velocity of the car after it passes the intersection? (c) If another car crossing the intersection has a constant velocity 15.0m/s, how long does it take the first car to catch up with it? Galileo (1564-1642) Heavier and lighter objects fall at the same constant acceleration g=9.8 m/s2 in absence of air resistance. (a) Find the distance traveled by a falling rock at 1s, 2s, and 3s (b) Find the velocity of the falling rock at 1s, 2s, and 3s (c) If the tower is 120 m high, how long does it take for the rock to fall from the top of the tower to the ground? Quiz 1 (Jan. 23, 2009) 1. 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? 2. a3 a2 a1 (a) (b) (c) (d) (e) both v = 0 and a = 0 v 0, but a = 0 v = 0, but a 0 both v 0 and a 0 not really sure (a) a1 < 0, a2 = 0 and a3 > 0 (b) a1 > 0, a2 = 0 and a3 < 0 (c) a1 < 0, a2 0 and a3 > 0 (d) a1 > 0, a2 0 and a3 < 0 (e) none of above ...
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This note was uploaded on 04/27/2009 for the course PHSX 114 taught by Professor Davis during the Spring '08 term at Kansas.

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