Lab Activity:
Conservation of Energy and Conservation of Momentum:
the Ballistic Pendulum
Introduction: In this lab you will use a ballistic pendulum to determine the initial
velocity of the ball (at the launch point) by two different methods. The first method will
involve concepts studied in class: conservation of momentum and conservation of
mechanical energy. The second method involves simple kinematics and will serve as a
check for the first.
Experiment 1 (Method 1):
Never aim the apparatus at a person and avoid pinching your fingers when loading the
ball . When loading the ball you are compressing a spring. The apparatus has three
settings; make sure you use the same setting for all of your measurements.
In this experiment you will find the initial velocity of the ball using the conservation of
momentum and conservation of energy.
1. Load the ball and fire it into the pendulum a few times to get an idea of what’s going
on.
2. Where do you choose the gravitational potential energy to be zero and where you
choose the elastic potential energy to be zero?
3. Sketch your setup. Indicate in your diagram where your gravitational and elastic
potential are zero.
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Lab Activity:
Conservation of Energy and Conservation of Momentum:
the Ballistic Pendulum
4. During the collision there are so-called non-conservative forces acting and mechanical
energy is not conserved. However, just for question 4, pretend that mechanical energy is
conserved during both collision and swing. Then you could easily calculate the initial
kinetic energy from the final potential energy. Then you could solve for the initial
velocity of the ball as it exited the gun. Do this here, showing all steps of your algebra
(in symbols, since we have no numbers yet).
5. Unfortunately, we do not know whether a significant amount of mechanical energy is
lost when the ball collides with the pendulum, so the above method may not work.
However, we can use the principle of conservation of momentum instead. Write the
conservation of momentum equation here with the given variables and call it Equation 1:
(Eq. 1)
where
m = mass of the ball
M = mass of the pendulum
v = velocity of the ball before it enters the pendulum
V = velocity of the ball + pendulum
6. Write the expression for the total kinetic energy just after the ball has entered the
pendulum. Write the expression for the total gravitational potential energy when the
ball/pendulum system is at the top of the swing. Set them equal to each other; this is (Eq.
2).
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Lab Activity:
Conservation of Energy and Conservation of Momentum:
the Ballistic Pendulum
7. Solve Eq. 1 for V and substitute it into Eq. 2. Solve for the original velocity of the ball
alone, v. Show all your steps.
8. What quantities do you need to measure in order to calculate the initial speed of the
ball?
9. Run the experiment several times (at least six times) to get an accurate average for
each measurement.
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Lab Activity:
Conservation of Energy and Conservation of Momentum:
the Ballistic Pendulum
10. How much mechanical energy was lost? To do this, Calculate/Fill in
a. the velocity of the ball just before it enters the pendulum:
b. the kinetic energy of the ball just before it enters the pendulum:
c. the total final energy of the ball+pendulum:
d. the energy lost during the collision of the ball with the pendulum:
Calculate what percentage of the initial energy was lost when the ball entered the
pendulum   KEball pendulum  KEball  :


KEball


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Lab Activity:
Conservation of Energy and Conservation of Momentum:
the Ballistic Pendulum
Experiment 2 (Method 2):
In this part of the lab we will try to check the accuracy of the result obtained from method
1. To do this, we find the initial speed using kinematics. Place the apparatus on your table
and fire the ball horizontally. Use a piece of paper on top of a piece of carbon paper to
record where the ball lands on the floor and measure the horizontal distance traveled by
the ball. Recall your projectile motion equations, make relevant measurements several
times to get an accurate average, be careful not to shoot anyone, and find the initial speed
of the ball as it exits the spring gun.
Vertical height the ball falls through (y = ½gt2):
Horizontal distance the ball travels (x = vt):
Calculations:
Initial velocity of the ball:
 v
v
Percentage error:   Method 1 Method 2
vMethod 2


:

Are your two results in agreement? If not, list possible reasons.
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