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.
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)
wherem = 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).
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.
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 :
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:
Percentage error: :
Are your two results in agreement? If not, list possible reasons.
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