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Kinetics of Particles: Work and Energy

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Two blocks A and B, of mass 5 kg and 6kg respectively, are connected by a cord which passes over pulleys as shown. A collar C, of mass 4kg, is placed on block and the system is released from rest. After the blocks have moved through 0.9m, collar C is removed and the blocks continue to move. Determine the velocity of block A just before it strikes the ground.

Numbers in FIG. P13.26 from top to bottom are: 0.3m, 0.6m, and 1.5m.
Letters in FIG. P13.26 from top to bottom are: C, A, and B.

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Given:
m_A = 5 kg
m_B = 6 kg
m_C = 4 kg

The motion is in two parts:

Part (i): Collar C and block A are together and fall height h_1 = 0.9 from rest till collar C is removed.
At this moment the speed of motion of the A and B is v_1

Part (ii): Block A falls
h_2 = 1.5m - 0.3m = 1.2 m
till it hits the ground.
Just before it hits the speed of motion of the A and B is v_2

Solution:

In Part (i), we address the system consisting of all the 3 masses together.
The change in its potential energy ...

Solution Summary

This solution contains step-by-step calculations to determine the velocity of block A just before it strikes the ground using the concepts of potential energy, kinetic energy and the conservation of energy principle.

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