12-Oct-2016: Lab Ballistic Pendulum

1. Title: Lab Ballistic Pendulum

    Name: Qiwen Ye (Sherry)
    Lab partners names: Jae Yoo, Chandler
    Date: 12-Oct-2016

2. Purpose
We determined the firing speed of a ball from a spring-loaded gun by using the theorem of conservation of momentum and conservation of energy. Then, we found the distance where the ball hit the ground in order to get the launch speed of the ball by the Newton's Law measurement.

3. Introduction
In this lab, we found the launch speed of the ball by using a spring-loaded "gun" fires a ball into a nylon block, which is supported by four vertical strings. The ball was "absorbed" into the block, and the ball and block together rise through some angle, which measured by the angle indicator shown, on a scale marked in halves of a degree. Through the angle and the length of the string, we found the final velocity both of ball and block that we got the initial velocity of the ball while it was launching.

Assumed that the collision happened so quickly that the strings stay essentially. That way there was no net force on the ball and block system, we used conservation of momentum to write an equation for the speed of the system immediately after the collision. After the collision, the ball and block system rises, losing the kinetic energy and gaining potential energy. At the system's maximum height, its kinetic energy will be zero. Used conservation of energy to relate the maximum height the block reached to the initial speed of the block in order to find the launch speed of the ball.

In order to verify the experimental launch speed, moved the nylon block out of the way and launched the ball with the apparatus on the lab table. Without using the nylon block, we launched the ball from the apparatus outside the lab table, and we verified the distance where the ball hit the ground. Put a piece of carbon paper onto another piece of paper on the ground, close to where we expected the ball to land. Measured the height from the lab table to the ground and the distance, then used below formula to find the how long the ball hit the ground in order to the actual launch speed.

4. Apparatus/Experimental Procedure
Set up the apparatus as shown. Measured the mass of the ball and block and the length of the string; leveled the base of the apparatus. Placed the ball into position and put the angle indicator to zero degrees. Fired the ball into the block and record the maximum angle to which the block rises. Repeated the same progress of four or five time to get an average values.

After this part, we removed the block and launched the ball to the ground from the lab table in order to find the distance that the ball landed. Measured the height of the table and tried to launch the ball in order to place the carbon paper on the ground where close to the distance.

5. Measured Data
m=the mass of the ball
M=the mass of the block
L=the length of the string
Theta=the angle between the string and the origin after collision
H=the height of the table
X=the distance of the ball where the ball hit the ground

6. Calculated Data/Analysis
Used the uncertainties in measurements for the masses and the angle to determine the experimental uncertainty in the launch speed of the ball.

After we verified the launch speed of the ball, we got the actual launch speed is 5.63 m/s. However, our experimental launch speed is 4.73 m/s.

8. Conclusion
In this experiment, we determined the launch speed by two different measurements. One of using conservation of momentum and conservation of energy to find the initial speed. Another one is using the Newton's Law to find the time of  the ball landed and the height of lab table in order to get the initial speed. The different percent of the launch speed is 15.99%. The reason causes the different is the air-resistance, the friction of the string, and the angle indicator not exactly to zero degree.