The ballistic pendulum is discussed in the text, Sample Problem 10-2. In this lab you will look at a version that is shown in Figure 1.
Figure 1. Ballistic Pendulum. On the left is a schematic of the pendulum showing
the pendulum (pivot, arm, and cage), the ball, and the gun. On the right are
the three positions of interest, Initial with the ball moving, Midway with ball
and pendulum moving, and Final with Ball and pendulum at maximum angle and momentarily
at rest.
The ball is fired by a spring-loaded gun and is caught by a cage at the bottom
of a rod. The cage and rod form a pendulum that swings up to some maximum height,
h. Call the system the ball and the pendulum.
Analyze the system and get an expression for the initial speed of the ball,
its “muzzle speed,” v, in terms of the masses, mball and Mpendulum,
and the maximum height
Safety Considerations:
Do not fire the gun towards anyone or towards a glass-faced cabinet. You may
choose to wear Do not fire the gun towards anyone. Wear safety glasses if provided.
Do not cock the gun before you are ready to fire it; if it hits your fingers
(even without a ball), it could do serious damage.
What to do:
Caution: Treat the pendulum with care since it is easily bent. When you cock the gun, pull the pendulum completely out of the way; do NOT push it sideways!
Details of the apparatus are shown below. Rather than measure height directly, you will measure the angle through which the pendulum swings. Measure the angle as precisely as possible, and use good experimental technique.
Figure 2. Some details of the gun(left) and of the pendulum pivot and angle
indicator (right).Make enough readings so that you can confidently determine
the uncertainty in the angle. You will need to use this to find the uncertainty
in the speed of the ball when it leaves the gun.
Uncertainties: You should have measured theta ± delta theta. You
will now need to get the uncertainty in the speed, v. Your expression for the
height in terms of the angle will probably involve a trig function. How can
you get the uncertainty in the result from the uncertainty in the angle. Here
is a simple example: suppose y = (5.0 m) sin theta, with theta = 30°±1°.
Using the average value, y = (5.0 m) sin 30° = 2.50 m. Using the largest
possible angle we get y'= 5.0 sin 31° = 2.58 m. The difference, y –
y', is the uncertainty, delta y = 0.08 m.
Checking your value
You will check your answer by predicting the horizontal distance that the ball
will travel when it is shot from the horizontal table to hit the floor, as shown
in Figure 3.
Measure the vertical height (with uncertainty), ymax, that the ball will travel
from the horizontal gun to the floor.
Figure 3. Shooting the ball in projectile motion. Think carefully about from
where the measurements of xmax and ymax are taken on the ball.
Predict:
Assume that the ball is in free fall. Use the kinematics equations of projectile
motion to predict the horizontal distance, xmax, that the ball will travel and
determine the uncertainty in this distance.
Now check your prediction. Remove the pendulum from its support and lay
it aside. Place the gun near the edge of a table. Make the gun horizontal. Measure
the predicted horizontal distance xmax and tape a box at this location. Lay
a piece of carbon paper face up in the box and tape a piece of paper over the
carbon paper. On the paper mark the predicted distance and lines indicated the
range of distances you predict. The target paper should look like Figure 4.
Figure 4. This is the target that you are aiming at. The ball is shot from the right. Draw a line at the predicted value of xmax, and lines at xmax ± delta x and xmax ± 2 delta x
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What fraction of the shots fall within 1 deviation of your prediction, (xmax
± delta x)? Statistics predict that 67% of the shots should be in this
range. What fraction of the shots fall within 2 deviations of your prediction,
(xmax ± 2 delta x)? Statistics predicts that 95% of the shots should
be in this range.
This page maintained by Anne G. Young. Last modified February 13, 2004.