2. A rod of mass \"10m\" and length \"L\" is hangin g through a pivot at one end
ID: 1770749 • Letter: 2
Question
2. A rod of mass "10m" and length "L" is hangin g through a pivot at one end. The rod is pulled up 90 and released from rest. When the rod swings through its lowest point it collides with a lump of clay of mass "m moving to the right at a velocity The collision occurs at the far end of the stick. Tbe clay as it continues to swing up to an angle "8". The angular speed of the rod just before the collision is "a" and the angular speed of the rod just after the collision is " a. Write out the energy equation from release to just before the collision in terms of the parameters given. out the angular momentum equation for the collision in terms of the parameters given. b. Write te out the energy equation after the collision in terms of the parameters givern. L ces e u)Explanation / Answer
a] By energy conservation,
10mgL/2 = 0.5 i w1^2
10mgL/2 = 0.5*10mL^2/3 w1^2
b] initial momentum = final momentum
iw1 - mvL = (i+ mL^2) w2
10 m L^2/3 w1 - mvL = (10mL^2/3 + mL^2) w2
c] 0.5 (10 mL^2/3 + mL^2) w2^2 = mgL(1-cos theta) + 10mgL/2 (1-cos theta)
0.5 (10 mL^2/3 + mL^2) w2^2 = 6mgL(1-cos theta)
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