Question

An object, with mass M, is located on a frictionless table. A massless string is attached to this mass and is attached to another mass, with mass m, hanging over the edge of the table by a massless, frictionless pulley. Find the tension in the string, T, and the acceleration of the system, a, in terms of M, m, and g.

Answer 1

Let a be the acceleration with which the blocks move. As they are attached a will be same for both.

Let g be acceleration due to gravity.

M is mass of object on table

m is mass hanging

T is tension in string

For mass M

We see that the forces acting on it are

T = M a -----(1)

For mass m

m g - T = m a -----(2)

Add (1) and (2)

m g = (m+M)a

a= g m/(m+M)

This is the acceleration of the system.

Substituting a in (1)

T = g m M/(m+M)