Experiment 6:
Blackwood Ballistic Pendulum
September 18, 2013
Jamal Wright
Zachary Floyd
Christopher Wilson
Experiment 6
Blackwood Ballistic Pendulum
Jamal Wright, Zachary Floyd, Christopher Wilson
Abstract Our goal of this experiment is to determine muzzle velocity by two methods: 1) employing uniform linear motion relations, the kinematic equations; 2) using the principles of conservation of energy and momentum. In this paper, we aim to validate the law of conservation of momentum. We do so by comparing results from two experiments conducted with a single ballistic launcher/pendulum apparatus.
Hypothesis: The initial velocity of a ballistic pendulum can be determined using the law of conservation of momentum. Momentum…show more content… When the ball hits the ground then y = H (since the positive y axis points downward.) By measuring the distance of fall and using that acceleration due to gravity, g, the time of flight t = Tflight, can be calculated with the following transformed kinematic equation:
Tflight = sqrt(2H/g)
The muzzle velocity, vmuzzle, (also the intitial velocity – vx0) of the ball after being fired is horizontal. From a measurement of the range, R, and using the time of flight, the muzzle velocity can be determined
Vmuzzle = Ravg/Tflight
The second method requires the determination of the muzzle velocity from the principle of conservation of momentum. The momentum of the ball just before it collides with the pendulum must equal the momentum of the ball and the pendulum just after the collision, pi = pf. To expand on this we see:
Mvmuzzle + MV = (m + M)V,
Where m is the mass of the ball, M is the mass of the pendulum and V is the velocity of the ball and the pendulum together. Note: the velocity of the ball and the pendulum, v, is initially zero. In order to find the velocity of the ball and the pendulum just after the collision we will use the principle of conservation of energy. Neglecting friction at the point of support of the pendulum, the gravitational potential energy must equal the kinetic energy of the ball and the pendulum at the bottom of the