speed of bullet = Sb
speed of pendulum at bottom = Sp
m = bullet mass = 0.010 Kg
initial angular momentum about ceiling hook = m v R
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mass at end after collision = 0.010 + 4.30 = 4.31 Kg
It = total moment of inertia after collision = 4.31(2.9^2)+(1/3)(1.9)(2.9)^2
w is angular velocity after collision
angular momentum after collision
It w = original ang momentum = m v R
so v = It w/ Rm
now
potential energy at top = total mass * g *height of center of mass
= (1/2) It (v^2/R^2)
height of center of mass = (1-cos25.5)(distance of center of mass from ceiling hook)
To test the speed of a bullet, you create a pendulum by attaching a 4.30 kg wooden block to the bottom of a 2.90 m long, 1.90 kg rod. The top of the rod is attached to a frictionless axle and is free to rotate about that point.
You fire a 10 g bullet into the block, where it sticks, and the pendulum swings out to an angle of 25.5°. What was the speed of the bullet?
(Treat the wooden block as a particle.)
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