Phys 201A. Lab 6 - Motion with Constant acceleration Kinematic Equations

Transcription

1 Phys 201A Lab 6 - Motion with Constant acceleration Kinematic Equations Problems: It would be good to list your four kinematic equations below for ready reference. Kinematic equations 1) An amateur bowler releases a ball with an initial velocity of 3.0m/s; the ball slows down with a constant negative acceleration of -0.2m/s 2. How far does the ball roll before stopping and how long does it take to stop? Draw three graphs to show this motion - position vs. time, velocity vs. time and acceleration vs. time. 2) A runner bursts out of the starting block 0.10s after the gun signals the start of a race. She runs at constant acceleration for the next 1.9s of the race. If she has gone 8.0m after 2.0s, what are her acceleration and velocity at this time? Once again, plot all three graphs - x vs. t, v x vs. t and a x vs t. 1

2 3) A T-38 training jet has an acceleration of 3.6m/s 2 that lasts 5.0s during the initial phase of the takeoff. The afterburner engines are then turned up to full power for an acceleration of 5.1m/s 2. The speed needed for takeoff is 164 knots (1m/s = 1.94 knots). Calculate the length of the runway needed and the total time of takeoff. Show your solution in graphical form (x vs. t, v vs. t and a vs. t) 4) You are driving down the highway late one night at 20m/s when a deer steps onto the road 35m in front of you. Your reaction time before stepping on the brakes is 0.5s, and the maximum deceleration of your car is 10 m/s 2. a) How much distance is between you and the deer when you come to a stop? b) What is the maximum speed you could have and still not hit the deer? Free Fall A special case! Suppose you drop a ball on the motion sensor (well, not on it directly but when it is protected by its "cage"). Prediction : What would the following three graphs look like? a) Position of the ball vs. time. b) Velocity vs. time c) Acceleration vs. time. Now try the experiment. Were your predictions validated? If not draw the correct graphs next to your predicted graphs. Find the acceleration due to gravity. Report it along with its percentage uncertainty. Acceleration due to gravity 'g' = Percentage uncertainty = 2

3 Draw motion diagrams with the velocity vectors for the following cases: a) The ball is simply dropped (what does this imply about the initial velocity?) b) The ball is thrown straight down. c) The ball that is thrown down, hits the floor and bounces vertically up. d) What is the velocity at the top of the motion for a ball that is thrown straight up? e) What is the acceleration at this point? Stop! Time for a class discussion! Let us now look at some numbers. For the purpose of this exercise, let us take g = 10m/s 2 and y 1 = 500m. t V 2 Y At what time does the ball land? 3

4 Problems on Free Fall - Now we are ready to tackle some problems in Free Fall! 1) A ball is thrown straight up with a speed of 10.0m/s from a third floor window that is located 15.0m above the ground. Calculate the maximum height of the ball, the ball's velocity when it hits the ground, and the total time it takes to reach the ground. Draw graphs of position vs. time, velocity vs. time and acceleration vs. time to describe the motion of the ball. 2) How much later must a second ball be dropped from rest at the same initial height of 10m so that the two balls hit the ground at the same time? 3) A string is to have a series of lead sinkers tied to it. The first is tied to the bottom, and the second is tied 10cm up from the bottom. The string can be held at its to and dropped from a height onto the top of a drum on which the first sinker already rests; each time a sinker hits the drum, a tap is heard. How far above the bottom sinker must the third, fourth and fifth sinkers be tied so that the series of four taps is spaced by equal time intervals when the string is dropped? 4

5 Other Questions to ponder: 4) An object falls freely from a height h. It is released at time zero and strikes the ground at time t. a) When the object is at height 0.5h, is the time earlier than 0.5t, equal to 0.5t or later than 0.5t? b) When the time is 0.5t, is the height of the object greater than 0.5h, equal to 0.5h or less than 0.5h? Give reasons for your answer. 5) You drop a ball from a window on an upper floor of a building. It strikes the ground with speed 'v'. You now repeat the drop, but you have a friend down on the street who throws another ball upward at speed 'v'. Your friend throws the ball upward at exactly the same time that you drop yours from the window. At some location, the balls pass each other. Is this location at the halfway point between the window and the ground, above this point or below this point? Explain. 5