# Kinetics of Particles: Work and Energy

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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#### Solution Preview

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.

angular velocity of the particle and work done

A particle of mass m is moving on a frictionless horizontal table and is attached to a massless string, whose other end passes through a hole in the table, where I'm holding it. Initially, the particle is moving in a circle of radius r0 with angular velocity w0, but I now pull the string down through the whole until at length r remains between the hole in the particle.

(a) What is angular velocity of the particle now?

(b) Assuming that I pull the string so slowly that we can approximate the particles that my circle of slowly shrinking the radius, calculate the work I did pulling the string.

(c) Compare your answer with part (b) with the particles gain in kinetic energy.