3. A ullet of mass M 2.59 x 103 kg is moving with a speed of 374.5 m/s when it c

Question

3. A ullet of mass M 2.59 x 103 kg is moving with a speed of 374.5 m/s when it collides with a pole of mass Mi 3 kg and length L 2.0 m. The pole is initially at rest, in a vertical position, and pivots about an axis going through its center of mass. The bullet embeds itself in the pole at a point that is 1/3 the length of the pole above the pivot point. As a result the bullet-pole system starts to rotate. (a) What is the angular velocity of the rod and the bullet immediately after the collision? (b) What is the initial kinetic energy of the system before collision? (c) What is the rotational kinetic energy immediately after the impact? (d) Is the kinetic energy conserved? If not, what is the energy loss? (a) (b)

Explanation / Answer

conservation of angular momentum

before collsion

2.*59*10^-3 * 374.5 * (2/3) = 0.647

aftr collision

0.647 = ([2.59*10^-3 * (4/9)] + [3*4/12] )*w
a)
w = 0.646 rad/sec

b)

initaila kinetic energy = 0.5*m*v*v = 181.624 J

c)

total energy conserved but not kinetic energy

after cloosion

totaional kinetic enery = 0.2088 J

energy loss = 181.624-0.208 = 181.415 J

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