October 12, 2016: Ballistic Pendulum

Anthony Betancourt
Lab Partners: Josh Fofrich, Christine, Jarrod , Alex Reyes
Lab Performed: Oct. 12, 2016

Lab Activity: Ballistic Pendulum

Purpose:

The main objective of this lab activity is to provide a real world example of the conservation of energy and also conservation of momentum.  These concepts are used in order to relate the max height the ball and nylon block reach to the initial speed of the ball before the collision.  

Theory:

In order to determine the balls velocity before the collision we must relate the balls kinetic energy to the momentum transferred into the block that leads it to rise upward a certain angle.  

Procedure:

1. Measure and record the mass of the ball and block.  Tilt apparatus on its side over the scale in order to weight block.
2. Make sure the block is in line and level with the ball exiting from the spring loaded canon.  
3. Pull back on the plunger until its in the "locked and loaded" position. Be sure to take note on the locking position and continue using the same for the remainder of the lab.
4. Place the angle indicator at the 0 position.
5. Fire ball into the block.  Record the angle the block rises up to.
6. Repeat four or five times and get the average.  
7. Next, Setup ballistic apparatus on the edge of the lab table.  
8. Measure the distance from the barrel to the top of the lab table.  Measure the height of the lab table, Record measurements.
9. Fire the ball out away from the table's edge and note where it lands.  Place a carbon paper and white sheet in the area where it lands.  
10. Fire the ball several times until a cluster forms where the ball has landed.  Measure the distance from the table's edge to the cluster area where the ball landed. Record measurement.   

Measures Data:

(Measured Data)

(Ballistic Pendulum Apparatus)

(Calclations for initial velocity of ball)

(distance ball traveled from table top; 2.65m)

(cluster formed from impact of the steel ball; 2 near bottom are insignificant, practice shots)

(calculations for verifying launch speed)

(Calculation for uncertainty)

(Updated uncertainties calculations including the length of the string)

Analysis:

In order to find the initial launch speed of the ball we must relate the movement of the ball and block swing upward to some height, h, and the collision that occurs with the ball and block after the ball is fired.  We first use the conservation of momentum to derive an equation for the balls initial velocity. After we can use the energy of the system to transfer of kinetic energy into gravitational potential energy through some angle the block and ball rise.  The balls initial kinetic velocity derived and solved for, then this value input into the first equation for the momentum and finally solved for the initial speed the ball was launched at. In order to verify our initial speed, the ball is shot out from the table edge and measured the distance the ball traveled.  We can use kinematics to find the time for the balls decent in the y-direction. Once we have time, we use it for finding the velocity of the ball in the x-direction dividing the distance over the time.  Lastly, we find the uncertainties in the lab to account for any discrepancies in our values for the initial velocity.   

Conclusion:

The launch speed calculated using conservation of momentum and energy was slightly higher than the value using kinematics.  If we take into account for the uncertainties in measurements, the values are closer to the same.  The measurements from lab could be off from the length of the string, the apparatus being completely level on the table top, and accuracy of the measurements on the pendulum itself.  There are also uncertainties in the verification of the speed of the ball from firing off the lab table.  The measurement for the distance traveled could be off due to using two measuring sticks, the cannon itself being completely horizontal before firing, and the measurement for the cluster where the ball lands.