Name: Class: APLab02: Projectiles Revisited
PURPOSE
In this lab, you will investigate projectile motion and determine three different quantities from the results of your
experiments:
1. an experimental value of the acceleration due to gravity (g)
2. the accuracy of low angle shots vs. high angle shots
3. an estimation of the drag coefficient of your experimental setup
HYPOTHESIS
In your lab notebook, record what you think the results of the three different experiments will be.
EQUIPMENT




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CPO Marble Launcher with Photo-gate/Timer and marble
Carbon Paper and White Paper
Masking Tape
Meter stick
Spreadsheet Program (Excel/LoggerPro) for analysis
PROCEDURE
Safety



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Never shoot the marbles at people.
Wear safety goggles when launching marbles.
Only launch the black plastic marbles provided for you.
When not in use, make sure the spring is not loaded.
Figure 1
Operation [To Launch Marbles]
 Clamp the Photo-gate to the launcher where indicated, and connect it to the A channel of the timer. Make sure
the timer is set to Interval Mode and the A light is green. It will automatically reset, start and stop when the
beam is broken.
 Pull the launching lever back and slip it sideways into one of the slots.
 Put a marble in the end of the barrel and the Launcher is ready to fire.
 There are [5] notches that change the compression on the spring and give different launch speeds.
 To adjust the angle, loosen the knob on the side and slide the launcher to the desired angle, with the point at the
number of the angle.
 To fire gently flick the lever out of the notch to release the spring.
Preparation
Set up the experiment on top of a lab bench as shown in [Figure 2]. Mark the placement of the Launcher with
tape, and then tape it down to keep it from moving. Before beginning measure the various lengths that will be
constant throughout the experiments [x a y a y b ] and record them in your notebook. Use a plumb bob to get the
point on the ground directly below the edge of the bench top and mark it with tape. Also note the number of
your launcher in your lab notebook.
APLab 02: Projectiles Revisited Mr. Maloney: AP Physics 1/4 Revised: 5/2010 Name: Experiment A: Calculating g
You will use three different angles
(0, 20, 45) to calculate g.
1.
2.
3.
4.
5.
Class: ya
Set the launcher to the first angle,
Carbon
test fire it at a [3 or 4] setting, and
Paper
note where the marble lands.
Choose a setting appropriate to
yb
the room you are in.
Tape down a piece of white paper
xa
approximately where the test fire
hit the ground and lay a piece of
xb
carbon paper (carbon side down)
on top of it.
Fire the launcher at the [4] setting
and allow the marble to hit the
Figure 2
carbon paper. Lift the carbon paper and find the mark left by the marble on the white paper from the carbon paper.
Mark the spot, DO NOT move the white paper. Also take down the time measured by the timer. Fire the launcher 3
more times at the same angle marking the contact spots after each throw and taking down the times.
After 4 shots, use the meter stick to measure the distance x b from [Figure 2] for each trial. Record these values in
your lab notebook.
Repeat the procedure 1-4 for the other two angles, recording all data in your notebook. After all the trials for an angle
is measured, you may have to move the white paper and carbon paper for the next angle, but make sure you move it
only after you have measured all the trials for that angle.
Experiment B: High or Low
We already learned that theoretically when a projectile is shot at an angle, any set of complimentary (sum to equal 90)
angles should each result in the same range on flat ground. Here we will test to see which one is more accurate in
practice, shooting high or low.
1.
Move the setup to the floor, so that you shoot as from as small an elevation as possible. You will not be able to shoot
completely from the ground at the launcher has a height itself, but the floor should be fine.
2.
Pick two sets of complimentary angles between 20 and 80 (i.e. 30 and 60). Due to the fact we are not shooting
completely from the ground, don’t pick too close to 0 or 90.
Set the launcher to the first angle and fire a test shot at the 4 setting. Place white paper and carbon paper as in
Experiment 1 in the approximate location the marble lands.
Fire the launcher making sure it is always at setting 4, take down the time from the timer, and label the hit on the
white paper. Then repeat this process for a total of five trials. Measure the range from the launcher to the hit
positions and take down all the results in your notebook.
Switch the launcher to the complimentary angle and repeat steps 3 and 4.
Now complete steps 3 and 4 for the other set of complimentary angles.
3.
4.
5.
6.
Experiment C: Estimate of Drag Coefficient
In this experiment, you will use a website to model your experimental setup, and estimate the value of the drag
coefficient [C d ] of your marble flying through the air based on your experimental results.
1.
2.
Keep the setup in Experiment B.
Measure the initial distance from the top of the barrel to the ground.
3.
4.
Choose two angles, one around 30 and one around 60.
Using the same process with white paper and carbon paper, launch the marble 5 times at each angle, recording the
range and timer reading.
APLab 02: Projectiles Revisited Mr. Maloney: AP Physics 2/4 Revised: 5/2010 Name: Class: ANALYSIS
Experiment A
In order to find g, you must first algebraically determine the correct equation to relate g to the different variables that were
measured. The equations that we have to start with are:
x = V x0 t (eq. 1)
V x0 = V o cos  (eq. 3)
y = V y0 t + ½gt2 (eq. 2)
V y0 = V o sin  (eq. 4)
x = x a + x b (eq. 6)
y = -[y a + y b ] (eq. 7)
tan  
sin 
cos 
(eq. 5)
1.
If you notice, you can determine all the variables in these equations except time. We have two equations to work
with (eq. 1 and 2), so we can use (eq. 1) and solve for t and then substitute it into (eq. 2). From here we can do a little
bit of algebra along with a trig identity (eq. 5) to develop an equation that give g in terms of V 0 , x, y and , and it is
OK if it looks a little ugly.
2.
It is best to do this analysis in a spreadsheet. Create a table of your data in Excel. Then write an Excel program that
will calculate g based on your data and the derived equation you found. You should have 12 calculations of an
experimental value for g. Use Excel to find the average of all your g’s as well as the standard deviation (the STDDEV
function).
3.
Once the average is found, compare this average to the accepted value of g (9.81 m/s2), and determine the percent error
in your final measurement based on the accepted value.
Experiment B
1.
Enter the data from the experiment into Excel and calculate an average and standard deviation for both sets of
complimentary angles.
2.
From your analysis, determine which you deem more accurate, low angle shots or high angle shots, and why you think
this is the case.
Experiment C
1.
Determine the theoretical value for the range at the given angles based on the standard projectile equations.
2.
For each of the two angles, calculate average shot velocity, average shot distance and the standard deviation for each.
3.
Go online to http://phet.colorado.edu/sims/projectile-motion/projectile-motion.swf which is also linked at
http://mrmaloney.com under the chapter 2+3 section of notes. On this site you should be able to model your setup.
4.
First you will have to manually move the cannon to the correct starting height as it is set to 1 m. To do this click on
the little black dot on the left side of the cannon and drag it down a little. Then test fire and see that the height
number is on the top. It should be – [the height of your barrel]. Keep dragging the cannon up and down until the
height is approximately your barrel height.
5.
Select [user choice] and enter in the rest of the variables from your experiment (V 0 , , m and d), make sure they are in
the correct units. Leave drag and altitude blank.
6.
Fire the cannon and compare the range to the average range you measured in your experiments.
7.
Turn on [Air Resistance] and adjust the drag coefficient. Fire the cannon again. Repeat adjusting the drag coefficient
until the range is as close to your experimental value as possible. This final number then would give you an idea of the
air drag your marble is experiencing.
8.
Repeat the process for the other angle, and compare the drag coefficients to each other as well as how much range was
lost due to air resistance in each case.
APLab 02: Projectiles Revisited Mr. Maloney: AP Physics 3/4 Revised: 5/2010 Name: Class: QUESTIONS
Experiment A
A1. What is the equation for g in terms of V 0 , x, y, and .
A2. Derive an equation for Y in terms of V 0 , x, g, and .
A3. Why would A2 and A3 be helpful in the real world?
A4. How close was your experimental value of g to the accepted value? Why might it be different?
Experiment B
B1. What is the theoretical value for that range at your chosen angles?
B2. What is the percent error observed in your experiment based on the theoretical values found
in B1?
B3. Which were more accurate high angle shots or low angle shots and why?
B4. Did both complimentary angles have the same range? If not for what reasons might you expect
this, even though theoretically they should have the same range?
Experiment C
C1. What was the absolute and percent error between you experimental shot and the theoretical
shot without air resistance?
C2. What was the coefficient of drag for each of the angles? If they were not the same why might
they be different?
C3. How much of an effect did the drag have on the flight of the marble?
C4. We often say neglect air resistance when doing problems. Do you think this is a valid
assumption?
APLab 02: Projectiles Revisited Mr. Maloney: AP Physics 4/4 Revised: 5/2010