Ballistic Pendulum Essay

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Ballistic Pendulum Objectives: To measure the initial velocity of a projectile in two independent ways: one by treating it as a projectile moving according to the kinematic equations, and the other is by applying the conservation of linear momentum and energy to a ballistic pendulum. Equipment: 1. 2. Ballistic pendulum 3. Meter stick 4. paper 5. Electronic balance 6. Ruler 7. Triple beam balance Theory and Equations: If a projectile is fired horizontally with an initial velocity v0, it will follow a parabolic path. The horizontal range X and vertical displacement Y of the projectile are given by: X = v0T and Y = ½gT2 These equations combined yield v0 = X(g/2Y)1/2. The initial velocity v0 of the projectile an also be determined by using the ballistic pendulum. It consists of a spring gun that fires a metal ball of mass m which is caught by a catcher at the end of a pendulum of mass M. The collision between the ball and pendulum is perfectly inelastic. As a result, the combination swings upward until it stops at the highest point by a ratchet. From conservation of momentum, Mv0 = (m + M)v1 where v1 is the common velocity of the pendulum ball just after collision. If the combination rises through height h, then from conservation of mechanical energy we have ½(m + M)v12 = (m + M)gh Velocity v0 will be v0 = [(m + M)/m](2gh)1/2. Procedure: For the first part of the experiment, our goal was to measure how far a metal ball would travel after it was shot from the spring-loaded gum. We removed the pendulum from the ballistic pendulum set and placed the set at the edge of the lab counter. We measured the height of the gun from the counter top (8 cm) and measured the mass of the ball on the triple beam balance. We placed the ball in the shaft in the uncocked position and determined that the device was level. We

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