Experiment 2: Projectile Motion

Transcription

1 Experiment 2: 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 / / / When plotting uncertain data on a graph, the uncertainty should be shown with an error bar. (Until now, we ve skipped them for simplicity.) This means to draw a line through the whole possible range rather than just a dot at your best guess. The "true" value could lie anywhere on the error bar. For example, if /s was one of your data points, you would draw an error bar from 70 /s to 80 /s. +5 /s would follow from an uncertainty of about +1 mm in the positions you read off the picture, so

2 that would be about right for today s experiment. The uncertainty in the time today is small enough to ignore. 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 the error bars. In particular, don t magnify the x graph too much. - 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? 5. Calculate the slope of the v y graph. Does it match the accepted value within about + 3%? 6. As an additional exercise, also a. Calculate the ball s speed (the magnitude of v ) for the last point in your table. b. Calculate v s direction, given as an angle measured counterclockwise from positive x.

3 PHY 121 Experiment 2: Projectile Motion v x Δx x t y Δy v y /s sec /s (Attach two graphs.)

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