1-May-2017: Lab 16:

Lab: Ballistic Pendulum

Author: Tiancih Jiao

Lab Partners: Nina Song, Roya Bijanpour, Joel Cook, Eric Chong, Kitarou Chen, Lynel Ornedo, Weisheng Zhang

Date: 05/02/2017

Purpose of the lab: The purpose of the lab is to determine the firing speed of a ball from a spring-loaded gun.

Theory/Introduction: A spring-loaded gun fires a ball into a block in this case. The block is supported by four string. The ball is launched so that it "sticks" with the block moving together upward through some angle. Eventually, they will stop at some point. The angle is measured by the angle indicator, where it points at an angle after having a hard contact with the block-ball mass.

Let the mass of the ball be m and the mass of the block be M. The first part of the motion is associated with conservation of momentum. m * V0 + M * 0 = (m+M) * Vf.

Therefore, Vf = m * V0 / (m+M).

For the second part, we should conservation of energy to compute.

(m+M)gh=0.5*(m+M)V^2

then drop (m+M) each side, we will get V=sqr(2gh)

Summary of apparatus/experimental procedure: 

First we need to measure both m and M. Level the base of the apparatus and the block so that the measured angle becomes accurate enough. Pull back the string in order to load the firing ball into position and place the angle indicator to zero degrees. Once the ball is launched, record the maximum angle the indicator reaches. Repeat this process five times to get an average.

Measured data:

m = 7.59 grams

M = 78.9 grams
L = 21 centimeters

1st attempt: 22.5 degrees

2nd attempt: 24.2 degrees

3rd attempt: 27 degrees

4th attempt: 24 degrees

5th attempt: 23.5 degrees 

then V average = 24.24 degrees.

Calculation shown below: 

Then for the second part, we use projectile motion to test the horizontal velocity of the ball which is actually the V0, and compare it with V0 we got in the first part.

V = 5.86 which is not very close to the velocity we calculated in the first part. But it is also possible, because there might some errors in this lab such as air resistance. Also, we did the first part one week ago, so there was one week interval that the spring might have changes in the time period. Those are all the errors that might affect the result.

Conclusion: 

In this lab, we use two different method to find out the initial speed of ball from the gun. Then we compare two results and find that there are still many errors in this lab.