Question

Two identical bodies of mass M are joined by a string passing over a pulley with a fixed axis. An additional mass m is placed on one of the masses (Fig.). (a) What will be the acceleration of the masses? (b) What will be the tension in the string during the motion of the masses? (c) What is the force exerted on the axis of the pulley during the motion of the masses? (d) What will be the force exerted be the mass m on mass M? The mass of the pulley, the weight of the string, and the air resistance may be neglected.

Answer 1

Explanation:

All the bodies of the system move with the same acceleration.

On the mass M on the left act the force Mg due to its weight and the tension T in the string; on the mass on the right act the force Mg due to its weight, the force f of the additional mass and the tension T in the string. Acting on the additional mass m are the force mg due to its weight and the force f from the mass M. The equations for Newton's second law for each of the three masses are

T— Mg = Ma, 

Mg+f—T= Ma, 

mg — f = ma.

The solution of these equations determines the values of a, T, and f. 

The force on the pulley axis is double the tension in the string: F = 2T