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A bullet of mass m B = 0.0153 kg is moving with a speed of 105 m/s when it colli

ID: 2260149 • Letter: A

Question

A bullet of mass mB = 0.0153 kg is moving with a speed of 105 m/s when it collides with a rod of mass mR = 6.61 kg and length L = 1.02 m (shown in the figure). The rod is initially at rest, in a vertical position, and pivots about an axis going through its center of mass. The bullet imbeds itself in the rod at a distance L/4 from the pivot point. As a result, the bullet-rod system starts rotating.

a) Find the angular velocity, ?, of the bullet-rod system after the collision. You can neglect the width of the rod and can treat the bullet as a point mass.




b) How much kinetic energy is lost in the collision?
(Hint: Please enter a positive number for your answer! If ?K < 0, then the amount of kinetic energy lost is a positive number.)


https://media.cheggcdn.com/media/794/7943a7a7-0bac-4663-89a5-c9c9d4b2e175/phpKFQ0XV.png

A bullet of mass mB = 0.0153 kg is moving with a speed of 105 m/s when it collides with a rod of mass mR = 6.61 kg and length L = 1.02 m (shown in the figure). The rod is initially at rest, in a vertical position, and pivots about an axis going through its center of mass. The bullet imbeds itself in the rod at a distance L/4 from the pivot point. As a result, the bullet-rod system starts rotating. Find the angular velocity, ?, of the bullet-rod system after the collision. You can neglect the width of the rod and can treat the bullet as a point mass. How much kinetic energy is lost in the collision? (Hint: Please enter a positive number for your answer! If ?K

Explanation / Answer

L1 = L2
mB*Vb*(L/4) = IR*wR where IR = (1/12)*mR*L