Figure (10-E4) shows two blocks of masses m and M connected by a string passing over a pulley. The horizontal table over which the mass m slides is smooth. The pulley has a radius r and moment of inertia I about its axis and it can freely rotate about this axis. Find the acceleration of the mass M assuming that the string does not slip on the pulley.

Question

Figure (10-E4) shows two blocks of masses m and M connected by a string passing over a pulley. The horizontal table over which the mass m slides is smooth. The pulley has a radius r and moment of inertia I about its axis and it can freely rotate about this axis. Find the acceleration of the mass M assuming that the string does not slip on the pulley.

Philoid · Accepted Answer

The acceleration of the mass M is

Given

The blocks are of “m” and “M” masses, with radius of r pulley and moment of Inertia “I”

Formula Used

The formula used to find the acceleration of the mass pulled/pushed is determined by the second law of Newton when the Force/Tension applied is equivalent to the product of mass and acceleration

where

is the force of the mass in terms of tension, is the acceleration and m is the mass of the block.

Explanation

The diagram 10.E4.1 is drawn below for better understanding of the kinematics of the blocks

The tension applied on the first block is

The tension applied on the block of mass “m” is

The torque applied on the pulley is derived as

The angular acceleration is changed into normal linear acceleration.