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## Homework Statement

A ballistic pendulum is a common device that is designed to measure the speed of small projectiles. As shown in the sketch on the right, it is composed of an initially stationary metal "cage" which traps the projectile and is suspended vertically by a very light weight rod attached to a low friction pivot. The bottom of the cage is usually equipped with a "pawl" (not shown) which prevents it from slipping backward after reaching it's maximum height. In a particular experiment, the projectile is a steel ball with a mass of 50.0 grams, the cage assembly has a mass of 250. grams, and the length L from the pivot to the center of mass of the entrapped ball + cage = 25.0 cm. After firing, the ball + cage reach a maximum angle from the vertical of 35.0. What was the initial speed 0o of the ball?

## Homework Equations

Conservation of Angular Momentum

L = r x p

L = Iw

I = MR

^{2}for a thin cylindrical shell

w = v/r

1/2 Iw

^{2}= mgh

## The Attempt at a Solution

L of ball = r x p = .25m * .05kg * v

_{0}= .0125m * kg v

_{0}

L of ballistic pendulum + ball = Iw = (.3kg)(.25m)

^{2}w = .01875kg * m

^{2}w

.0125m * kg v

_{0}= .01875kg * m

^{2}w

v

_{0}= 1.5m * w

v

_{0}/1.5m = w

1/2 * MR

^{2}* v

_{0}

^{2}/2.25m

^{2}= (.300kg)(9.8 m/s

^{2})(.25m sin35)

1/2 * (.300kg)(.0625 m

^{2})* v

_{0}

^{2}/2.25m

^{2}= .42 kg* m

^{2}/s

^{2}

.0041 kg v

_{0}

^{2}= .42 kg* m

^{2}/s

^{2}

v

_{0}

^{2}= 102.43 m

^{2}/s

^{2}

v

_{0}= 10.1 m/s

The correct answer is 5.65, so I'm not sure where I messed up.