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