Experiment 4: Motion in a Plane

Transcription

1 Experiment 4: Motion in a Plane Part 1: Projectile Motion. You will verify that a projectile s velocity and acceleration components behave as described in class. A ball bearing rolls off of a ramp, becoming a projectile. It flies through the air in darkness, except when illuminated by a strobe light. The shutter is left open on a camera, so that each flash of the strobe makes another image of the ball on the same picture. The end result shows where the ball was at regular time intervals against a centimeter grid in the background. The instructor will make a picture to demonstrate how the apparatus works. You will use pictures that were made in advance. Please don't mark them up so they can be used over again. Take t = 0 to be at the first flash after the ball left the ramp. From the fact that the strobe flashed 42 times per second, fill the time when the ball was at each dot in the picture into the data table. Make marks on a piece of paper that line up with the lines on the photo. Number them. Use this as a ruler to determine x and y for each dot until the ball bounced off the bottom, estimating tenths of a centimeter. Take the origin to be at the lower left corner of the picture. (Any point would do, but this is convenient.) The picture is not full scale, so do not use a regular ruler. Find the x component of the velocity at each dot, except the first and last, as you did in lab 1b: For each dot, compute the change in x from the dot before it to the dot after it. From this, find the average velocity, which equals the instantaneous velocity at the midpoint of the time interval. For instance, in the example below, = ( ) / (2/42). Repeat for the y components. EXAMPLE: v x /s Δx x t sec y Δy v y /s / / / Plot two graphs: horizontal velocity, v x, versus time, and vertical velocity, v y, versus time. As always, time goes on the horizontal axis. Label each so it's clear which graph is which. - Allow enough room for +5 /s error bars. (This is approximately what follows from +1 mm in the positions you read off the picture.) DON T MAGNIFY THE X GRAPH TOO MUCH.

2 - The idea is to display how theory compares to observation. So, for example, if theory predicts a horizontal line, show how a horizontal line compares to the data, as shown here. (Since the uncertainty is the range which the experimental errors are probably in, this line might miss a few of the error bars, but it should pass through most of them, and not miss the rest by much.) - Also, remember the other rules for graphs given in the freefall lab. Include answers to these questions in your report. (This is the conclusion part of your writeup. Also include the objective and apparatus & procedure, as usual.) 1. How are the horizontal components of a projectile's velocity and acceleration supposed to behave? 2. How are the vertical components of a projectile's velocity and acceleration supposed to behave? 3. Is your answer to (1) what your v x vs. t graph actually shows? 4. Is your answer to (2) what your v y vs. t graph actually shows? Part 2: Centripetal Force Your objective is to verify the formula for centripetal force. A rubber stopper, mass m, is at one end of a string, and a counterweight, mass m', is at the other. In between, the string passes through a tube which you hold while twirling the stopper in a circle. You know the centripetal force on the stopper from the counterweight hanging on the string: Gravity pulls on the counterweight, the counterweight pulls on the string, and the string pulls on the stopper. (This assumes that no other force is added to the string as it passes through the tube.) You will separately find mv 2 /r to see if it matches the known force: You get m by putting the stopper on a balance. You get r by measuring the apparatus with a meter stick. You get v by counting the number of revolutions the stopper makes in a minute. Procedure: Use at least 150 grams for m'. Twirl the stopper in a horizontal circle above your head, at the right speed so that the string does not slip up or down through the tube. A piece of tape on the string, maybe half an inch below the tube, makes it easier to watch its movement. Do not interfere with free movement of the string: Touch only the tube, not the string itself, and do not let the tape touch the bottom of the tube. Because of friction, there will be a range of speeds where the tape stays put. Use the slowest speed where the tape does not begin to sink. It is also important that you move your hand in as small a circle as possible. Twirl it from the wrist, not the elbow.

3 After some practice, count N, the number of revolutions the stopper makes in one minute. Then, lay the apparatus on the table with the same size gap between the tube and the tape, and measure r, the radius of the path of the stopper's center. Record the masses of the stopper, m, and the counterweight, m'. Calculations: In your calculations, have all distances in meters, mass in kilograms, and time in seconds. This will make force come out in newtons. Compute the stopper's speed: The distance covered during each revolution is the circumference of the circular path, 2πr. So, in N revolutions, the total distance covered is N(2πr). Speed is distance time; calculate the speed from the fact that the stopper covers this much distance in 60 sec. Compute the quantity mv 2 /r. Also, compute the weight of m', which equals the centripetal force. The value from the formula has a 20% uncertainty; the weight of the counterweight has an uncertainty which is quite small. If your two values do not agree, and you've made no mistakes in your calculations, then your twirler probably hasn't quite perfected his or her technique. Ask the instructor for suggestions, and double-check your data. Did you succeed in verifying that F c = m v 2 /r?

4 PHY 131 Experiment 4: Motion in a Plane I. Projectile Motion. v x Δx x t y Δy v y /s sec /s _ (Attach two graphs.) II. Centripetal Force: m = m' = N = r = Compute v of cork: mv 2 = r m'g =

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