Q65 of 149 Page 195

Two blocks of masses 400 g and 200 g are connected through a tight string going over a pulley which is free to rotate about its axis. The pulley has a moment of inertia 1.6 × 10-4kg-m2 and a radius 2.0 cm. Find (a) the kinetic energy of the system as the 400 g block falls through 50 cm, (b) the speed of the blocks at this instant.

Given:


Radius of the pulley = 2.0cm


Moment of inertia of pulley= 1.6 × 10-4kg-m2


Masses of the block, m1= 400g and m2= 200g



Using the free body diagram





Using the above equations,



Velocity of the system v



A) total kinetic energy of the system




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(a) the linear speeds of the balls A and B after the collision, (b) the velocity of the center of mass C of the system A + B + P and (c) the angular speed of the system about C after the collision.



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Suppose the rod with the balls A and B of the previous problem is clamped at the center in such a way that it can rotate freely about a horizontal axis through the clamp. The system is kept at rest in the horizontal position. A particle P of the same mass m is dropped from a height h on the ball B. The particle collides with B and sticks to it. (a) Find the angular momentum and the angular speed of the system just after the collision. (b) What should be the minimum value of h so that the system makes a full rotation after the collision.

 66

The pulley shown in figure (10-E11) has a radius of 20 cm and moment of inertia 0.2 kg-m2. The string going over it is attached at one end to a vertical spring of spring constant 50 N/m fixed from below, and supports a 1 kg mass at the other end, the system is released from rest with the spring at its natural length. Find the speed of the block when it has descended through 10 cm. Take g= 10 m/s2.


 67

A meter stick is held vertically with one end on a rough horizontal floor. It is gently allowed to fall on the floor. Assuming that the end at the floor does not slip, find the angular speed of the rod when it hits the floor.