1. 0/1 points I PrevicuS Answers Tipler6 10.P.064. My Notes Ask Your Te The figu

Question

1. 0/1 points I PrevicuS Answers Tipler6 10.P.064. My Notes Ask Your Te The figure below shows a thin, uniform bar of length D = 1.43 m and mass M = 0.85 kg pivoted at the top. The rod, which is initially at rest, is struck by a particle whose mass is m = 0.30 kg at a point x = 0 80d below the pivot Assume that the particle sticks to the rod. I the maximum angle between the rod and the vertical o owing the collision is S find the speed o the particle before impact. 9.2 X m/s Because the net external torque acting on the system is zero, angular momentum is conserved in this perfectly inelastic collision. You can also use conservation of mechanical energy to relate the initial kinetic energy of the system after the collision to its potential energy at the top of its swing. Draw a sketch showing the bar and particle just before the collision, and whern the bar is at its maximum angle. eBook

Explanation / Answer

Given,

d = 1.43 m ; M = 0.85 kg ; m = 0.3 kg ; x = 0.8 d ; theta = 60 deg

The moment of inertia of the system after collision:

I = 1/3 M d^2 + m x^2

I = 1/3 x 0.85 x 1.43^2 + 0.3 x (0.8 x 1.43)^2 = 0.97 kg-m^2

from conservation of enery

1/2 I w^2 = (m g x + M g d/2)(1 - cos60)

0.5 x 0.97 w^2= (0.3 x 9.81 x 0.8 x 1.43 + 0.85 x 9.81 x 1.43/2)(1 - 0.5) = 4.66

w = 3.1 rad/s

from conservation of angular momentun

m v x = I w

v = I w/ mx = 0.97 x 3.1/0.3 x 0.8 x 1.43 = 8.76 m/s

Hence, v = 8.76 m/s

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