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# lab 04 - Ballistic Pendulum Lab#4 xxxxxx/13/06...

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Ballistic Pendulum Lab #4 xxxxxx Physics 11 11/13/06

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Introduction/Purpose The purpose of this lab is to find the initial velocity of a ball shot from a spring-loaded gun. For Investigation 1, a ballistic pendulum will be used along with concepts of energy and momentum. Since the ball will be shot into the pendulum and immediately caught, the collision will be perfectly inelastic. This means that momentum is conserved during the collision V m M mv ) ( 0 + = where V is the velocity of the ball and pendulum immediately after the collision. Now that the velocity of the pendulum and ball is known, it is possible to establish a statement that relates the energy at the bottom to the energy at the pendulum’s highest point. Since the total energy is conserved, the potential plus kinetic energy should be the same at the bottom and the top. If the height of the pendulum at its lowest point is said to be zero, it will have only kinetic energy at the bottom and only gravitational potential energy at the top gh m M V m M ) ( ) ( 2 1 2 + = + where h is the distance in the y -direction that the center of mass moves through. Solving for V and then plugging in to the momentum equations yields gh m m M v gh V 2 2 0 + = = Now in Investigation 2, the initial velocity of the ball shot from the spring-loaded gun will again be found. This time, however, concepts of projectile motion will be utilized. One way to find the initial velocity of the ball is to use the equation for range t R v = 0 The range, R , can be determined by measuring the distance in the x -direction that the ball flew. This still leaves the time of flight unaccounted for. Time is related to the height that the ball started. Since there was no initial velocity in the y -direction, the following equations describe the time of the flight g y t gt y 2 2 1 2 = =
where y is the height of the center of mass of the ball above the table. Plugging this value of t into the range equation should give the initial velocity of the ball. The ultimate goal of the lab is to show how two separate methods can be used to find the same quantity, velocity.

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