Physics 2215: The Ballistic Pendulum
Purpose
 Solve a problem by using
• Kinematics (Newton’s Laws, Equations of Motion)
• Energy/Momentum Conservation.
 Use techniques learned in earlier labs:
• Measuring techniques
• Error calculation
• Statistics
Physics 2215: The Ballistic Pendulum
A simple example of kinematic versus
energy conservation approaches.
Dropping a ball from a height of 1m. Calculate the velocity just
before the impact on the floor.
vo= 0
y=0
h=1m
y
vf= ?
Physics 2215: The Ballistic Pendulum
Kinematic Approach
1 2
y (t )  g t
2
1
2
y (t f )  g t f  h
2
v(t )  g t
m
g  9 .8
s
tf 
2h
g
y=0
2h
v(t f )  g t f  g
 2 gh
g
y
v(t f )  2 gh
Physics 2215: The Ballistic Pendulum
Energy Approach
y=0
Ei  mgh  0
Potential
Energy
Kinetic
Energy
y
1
2
E f  0  mv f
2
1
2
E f  Ei 
 mv f  mgh 

2
v f  2 gh
Physics 2215: The Ballistic Pendulum
Ballistic Pendulum Apparatus
Pendulum that
catches the ball
and is able to swing
after the impact.
Spring loaded apparatus
that “shoots” metal ball.
Physics 2215: The Ballistic Pendulum
A. Determine the Speed of the Metal Ball Using a Kinematic
Approach
Idea:
1) Remove the pendulum part and simply shoot the ball horizontally off the table
2) Measure the horizontal and vertical distances from launch to impact on the floor.
3) Calculate vo.
vo
y
x
Physics 2215: The Ballistic Pendulum
B. Determine the Speed of the Metal Ball Using a Momentum
Conservation and Energy Conservation Approach
Idea:
1) Shoot the metal ball into the pendulum so that the metal ball gets stuck in it.
2) Measure the maximum angle the pendulum will swing up after the impact.
3) Use conservation of angular momentum and conservation of energy to
determine vo.
L conserved
vo
Before impact:
Lball  I ball ball
vo
 ml
 mvol
l
2
v
After impact:
Lsystem  I system  system
Physics 2215: The Ballistic Pendulum
Energy conserved
v
After impact:
1 2
E1  I
2
Qmax
At maximum of the swing:
E2  M tot g h 
M tot g lcm  1  cos Q max
lcm  distance between pivot point and the center
of mass of the pendulum with the ball in it.

Physics 2215: The Ballistic Pendulum
Determining the Moment of Inertia of Pendulum with Ball
(Isystem)
1) Disconnect the pendulum and reattach it on the other side
so that it can swing freely.
2) Let the pendulum swing (with the ball in it) and measure
the period of oscillation.
3) Determine the moment of inertia I using this formula:
I
T  2
M tot g lcm
Hint: You can get lcm by balancing the pendulum on the center of mass:
lcm