8/12/2016 - Ballistic Pendulum Lab

PURPOSE:

Determine the firing speed of a ball form a spring-loaded gun.

THEORY:
The ball, mass m, undergoes an inelastic collision with a nylon block, mass M. We assume that the collision happens so quickly that the strings stay vertical throughout the entire collision. This allows us to use conservation of momentum to write an equation for the speed of the system after the collision.

After the collision, the block+ball system rises, losing KE and gaining GPE until it reaches its maximum height. We can use the conservation of energy to write an expression that relates the maximum height to the initial speed of the block.

APPARATUS:
In this lab, the apparatus comes pre-assembled. A spring-loaded gun fires a ball into a nylon block, which is supported by four strings. The ball is absorbed into the block, and the ball and block rise together through some angle, which is measured by the angle indicator.

EXPERIMENTAL PROCEDURE:
Part 1: Initial Velocity

1. Measure/record the mass of the ball and block.
2. Level the block and apparatus.
3. Pull back and lock the spring into one of the notches. (Keep this notch consistent)
4. Fire the ball and record the max angle it travels through.
5. Repeat this 4-5 times to get an average.
6. Calculate the firing speed of the ball.

Part 2: Verification

1. Move nylon block away. 
2. Prepare the apparatus to launch the ball off the table.
3. Place a piece of carbon paper over another piece of paper close to where you expect the ball to land.
4. Determine the actual launch speed of the ball.

DATA:
Part 1:

Part 2:

height of barrel from floor: 0.97 meter

distance traveled by ball: 2.52 meters

ANALYSIS:
Initial Velocity:

Energy and Momentum Approach

Propagated Uncertainty Calculations

Verification:

Kinematics Approach

Propagated Uncertainty Calculations 2

ANALYSIS:

The ballistic pendulum lab is a classic example of an inelastic collision, i.e. a collision between two objects that stick to one another afterwards. Since this collision is inelastic, the momentum of the system is conserved before and after the collision. Energy, on the other hand, is not conserved before and after because there is an inherent loss of KE in the system when the two colliding masses merge with one another. However, since there is presumably no net external force acting on the system after the collision, energy is conserved after the collision, as the bullet+ball system rises with KE and reaches its maximum height with nothing but GPE. After calculating the initial speed of the bullet with our energy and momentum equations, we yielded 6.02 +/- 0.15 m/s. After calculating the initial speed using kinematics, however, we yielded 5.64 +/- 0.00364 m/s. These results have an unacceptable margin between each other because they are not within even the respective upper and lower ends of our propagated uncertainty calculations.

CONCLUSION:

Our results for this experiment were unsatisfactory. After calculating the initial speed of the bullet with our energy and momentum equations, we yielded answers for the initial velocity of the bullet that had an unacceptable margin between each other. There are several factors that could have contributed to this uncertainty. If, for instance, the nylon block remained unbalanced, then our calculations for initial velocity would be inherently flawed because momentum would not have been conserved. Another source of uncertainty is in human error. In our group's case, we had up to twelve different people trying to work together while a handful of people made their own measurements. This chaos increased our chances of miscommunication, potentially leading to imprecise measurements for the whole group. 

GROUP MEMBERS: Xavier C., Billy J., Matthew I.