Question

A wooden block A of mass m1 slides on a frictionless table when pulled using a massless string and pulley array by a hanging box B of mass m2, as shown in the figure. What is the acceleration of block A as it slides on the frictionless table? Hint: Think carefully about the acceleration constraint.

Answer 1

The block A(mass m1) is being pulled by the block B(mass m2) which is hanging from the table over a pulley.

As the table is frictionless, the table will not have a frictional force which can oppose the movement of A.

Now from the free body diagram(FBD) of m1, we can see that the block A is experiencing the following forces-

• Normal force by the surface of the table(N),
• tension by hanging block B through the massless string (T), and these is the force for the movement of the Block A. Hence T = m1a, where a is the acceleration of the block
• and the gravitational force (G=m1g)

From the FBD of m1,

1. N = m1g------------------------------------------------------------------------------1
2. T = m1a------------------------------------------------------------------------------2

and from the FBD of m2,

1. m2g-T = m2a---------------------------------------------------------------------------3

Now equation 2 + equation 3 will give us-

m2g = (m1 + m2)a

or, a = m2g/(m1 + m2)