The Projectile “Lab”

Purpose

The purpose of this lab is to confirm the basic precepts of projectile motion; namely, that the object moves horizontally with constant velocity and vertically with constant acceleration.

Procedure

The best way to study the motion of a projectile is to make and analyze a strobe photograph or a slow motion film. Since neither of these is practical considering our current lab equipment, you will use a strobe photograph. The photograph shows a tennis ball being tossed in the air by a hand. As the ball moved a strobe light illuminated it at regular intervals, producing the multiple images in the single photograph. Print this photograph – it would be advantageous to make your printout as large as possible in order for the measurements to be most precise. Here are some other formats for printing: webpage, pdf file. To analyze the ball's trajectory you will simply use a ruler to measure the position of the ball and then do some graphing.

Data

Fill in the first two columns in the data table by measuring with a ruler the two components of the ball's position, s_x and s_y. The value of s_x is measured from the left edge of the photograph to the right edge of the ball. The value of s_y is measured from the bottom edge of the photograph to the bottom edge of the ball. Consider the time t = 0 to be the first image of the ball where it is free from contact with the hand.

In order to make the graphing and data collection easier use arbitrary units of time and distance. Time will be measured in tocks (tk). For this lab, let 1 tock = the time interval between successive flashes of the strobe. Distance will be measured in centiunits (cu). For this lab, let
(1 centiunit) = (1 centimeter as measured on the photograph). Measure the photo to the nearest 0.01 centimeter but record your units as centiunit (cu). The reason for doing this is that even though you measure in the photo that the ball moved a certain number of centimeters, in reality the ball moved a different distance (it's only a picture!). Later in your report you will convert these arbitrary units into the standard units of seconds and meters.

Interpretation

1. Calculate the values for the remaining column of the table, v_y. This is the vertical component of the object's velocity in units cu/tk. The y-velocity is simply given by v_y = Δs_y/Δt , where Δt = 1 tock in each case. (Just subtract values in the previous column.) You will have some negative values for velocity -- indicating the ball's downward motion.

2. Construct a nice graph of s_x vs t. Determine the best fit and equation – either show work or plot and indicate regression equation including correlation coefficient if available.

3. Construct a nice graph of v_y vs t. Determine the best fit and equation – either show work or plot and indicate regression equation including correlation coefficient if available.

A complete report (50 pts.) will consist of the following (in this order):

q The printed photograph of the ball’s trajectory that you measured (2)

q Completed data table (8)

q 2 graphs with best fit and equation (12 ea)

q Answers to the following questions on separate paper (16)

Questions

1. Describe the horizontal motion of the object. (Is it constant acceleration, constant velocity, or what?) Explain your answer by referring to one of the graphs. (2)

2. The horizontal component of the ball's velocity is given by the slope of one of the graphs. What is the horizontal component of velocity according to the results on the graph? (2)

3. Describe the vertical motion of the object. (Is it constant acceleration, constant velocity, or what?) Explain your answer by referring to one of the graphs. (2)

4. The acceleration of the ball is given by the slope of one of the graphs. What is the acceleration according to the results on the graph? (2)

5. Convert this acceleration into SI units making two assumptions: the flash rate of the strobe was 20 Hz and the diameter of the tennis ball was 6.5 cm. (a) Use the strobe rate to determine the number of seconds in a tock. (1 tock = ? seconds) (b) Use the tennis ball’s actual diameter and a measurement of the ball's apparent diameter in the photo to determine the number of meters in a centiunit. (1 centiunit = ? meters) (c) Then convert your value for acceleration into m/s². Use the factor label method and show all work. (2 ea)

6. Determine the relative error in this converted value of acceleration. Show all work. (2)

Data Table for Projectile Lab

time (tk)	sx (cu)	sy (cu)	vy (cu/tk)
0.00
1.00
2.00
3.00
4.00
5.00
6.00
7.00
8.00
9.00
10.00
11.00
12.00