Challenge Problem (Extra Credit) A bullet with a mass m = 4.83 g and initial spe

Question

Challenge Problem (Extra Credit) A bullet with a mass m = 4.83 g and initial speed of 330 m/s passes through a wheel which is initially at rest as in the figure. The wheel is a solid disk with mass M = 2.29 kg and radius R = 18.6 cm. The wheel rotates freely about an axis through its center and out of the plane shown in the figure. The bullet passes through the wheel at a perpendicular distance 14.8 cm from the center. After passing through the wheel it has a speed of 225 m/s. What is the angular speed (rad/s) of the wheel just after the bullet leaves it? How much kinetic energy (J) was lost in the collision?

Explanation / Answer

Initial angular momentum

= I w = m r^2 w = m r v

= .00483 * .148 * 330 = .2359

Final angular momentum

= .00483 * .148 * 225 = .16083

change in angular momentum

= .2359 - .16083 = .07507

that is the angular momentum for wheel
I w = .07507
I = (1/2) M R^2 =

.5*2.29*.186^2 = .03961

so
w = .07507/.03961 = 1.911 rad/s

Ke (o) = (1/2) m v^2 of bullet

Ke (f) =(1/2)mvfinal^2 of bullet + (1/2)I w^2 of wheel

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