Union College
Winter 2014
Physics 120: Lab 7
The Ballistic Pendulum
1 Introduction
In this experiment you will determine the muzzle speed of a gun using a setup called a
ballistic pendulum. The ball will be fired into the ballistic pendulum (shown in Figure 1)
and by measuring the angle that the pendulum rises and applying conservation of
momentum and conservation of energy to analyze the collision and the pendulum
swing, you will determine “the muzzle speed.”
Figure 1: The ballistic pendulum
apparatus
Figure 2: A ball of mass, m, and speed,
v, is caught by the pendulum, which
swings up to an angle .
2 Derivation of Muzzle Speed from the Ballistic Pendulum
A ball fired with a certain speed will get caught by the ballistic pendulum, which
will then swing upward to some maximum angle, as shown in Figures 1 and 2.
Apply the proper conservation principles in the two events—the collision between
ball and pendulum and the swing upward of the pendulum with ball--to derive an
expression for v in terms of:
 the mass of the ball, m,
 the combined mass of the pendulum and ball, M,
 the length of the pendulum pivot point to the center of mass, Rcm,
 the strength of the gravitational field, g,
 and the maximum angle of the pendulum’s swing, θ.
3 The Experiment
1. Load and cock the launcher to medium range (2 clicks)
2. Let the pendulum hang at its vertical position and move the angle indicator to
zero degrees.
3. Fire the launcher and note and record the angle reached.
4. Load the launcher, then set the angle indicator to an angle of 5o less than that
reached in step 3. This will nearly eliminate the drag on the pendulum caused
by the indicator, since the pendulum will only move the indicator the last few
degrees.
5. Fire the launcher and record the angle reached by the pendulum. Try to
estimate the angle to the nearest 1/2 degree.
6. Repeat steps 4 and 5, recording the angle each time, to get ten angle
measurements.
7. Determine the average angle, the standard deviation of the angles, and the
standard error (the standard deviation divided by the square root of the
number of points). Record the result as θ +Δθ.
8. Remove the pendulum from the base by unscrewing and removing the pivot
axle.
9. Measure the mass of the pendulum and ball together, estimate the uncertainty,
and record the result as M+ΔM.
10. Measure the mass of the ball, estimate the uncertainty, and record the result
as m +Δm.
11. Determine the center of mass of the pendulum with the ball in it by balancing
it on the edge of a ruler. Measure the distance from the pivot point to this
balance point, estimate the uncertainty, and record it as Rcm +ΔRcm.
12. Perform the calculations discussed on the next page.
4. The Muzzle Speed and its Uncertainty
Using the expression you derived in Section 2 and the data you obtained in 3,
calculate the muzzle speed of the launcher. (Hints are provided in WebAssign).
Also, determine the uncertainty in v from the uncertainties of your measurements
and record the result as v+ Δv.