27-Apr-2015: Ballistic Pendulum

Purpose: To measure the velocity of a metal ball shot into a ballistic pendulum using our knowledge of conservation of momentum and conservation of energy.

Procedure: We were given a device which had a spring loaded gun, a metal ball, and a ballistic pendulum. Firing the metal ball out of the gun and into the pendulum causes the pendulum to swing back in order to absorb the impact. The angle at which the pendulum recoils is recorded by a bar behind the pendulum. The idea was to measure certain variables in order to be able to solve for the velocity of the ball as it left the gun.

Ballistic Pendulum

So to begin the lab, we measured the mass of the ball (m), the pendulum (M), the length of the pendulum from its pivot (L), and the angle theta recorded by the bar after we shot the ball.

ballistic pendulum angle reading

m = 0.00763 kg +/- 0.0001
M = 0.0809 kg +/- 0.0001
L = 0.2000 m +/- 0.001
theta = 16.5 degrees +/- 0.00873 rad







Using our measurements and the conservation of momentum theory we then calculated for the velocity of the ball as it left the gun by using our equation. We understood that this was a elastic collision so we knew that momentum and energy was being conserved so by solving for the component of the distance the pendulum traveled and using our other known values, we could come up with the initial velocity of the ball. We also used the propagated uncertainty from our measuring devices by finding the partial derivative of each variable in relation to our equation to find a range of values for the velocity of the ball.

calculations for v +/- dv

Results: Our calculations gave us a velocity of 4.66 m/s +/- 0.2131, which sounds very reasonable. 

Conclusion/Uncertainty: By understanding the conservation of momentum in a collision from a ball and ballistic pendulum, we were able to solve for the initial velocity of the ball before hitting the pendulum. This was an elastic collision where momentum and energy were conserved. We did solve for uncertainty in our velocity but there still may be other errors that are unaccounted for. Things such as heat from friction from the ball and even the integrity of the pendulum can slightly effect the results. But overall the results do seem fairly reasonable.