Question

Two blocks are connected by a rope that passes over a set of pulleys. One block has a weight of 412 N, and the other has a weight of 908 N. The rope and the pulleys are massless and there is no friction.
(a) What is the acceleration of the lighter block?
(b) Suppose that the heavier block is removed, and a downward force of 908 N is provided by someone pulling on the rope, as part b of the drawing shows. Find the acceleration of the remaining block.
(c) Explain why the answers in (a) and (b) are different.

Answer 1

Answer

given,

Weight of one block = m₁ = 412 N

Weight of other block = m₂ = 908 N

pulley is mass less and have no friction

a) acceleration of lighter block

    T - m₁g = m₁a

    T - 412 = m₁a..............(1)

    m₂g - T  = m₂a

    908 - T  = m₂a..............(2)

adding equating equation (1) and (2)

   496 = (m₁ + m₂)a

     $a = \dfrac{496}{\dfrac{412}{9.8}+\dfrac{908}{9.8}}$

     $a = \dfrac{496}{134.69}$

          a = 3.68 m/s²

b) downward force of 908 N is provided need to calculate acceleration of remaining block

 now,

   F - mg = ma

   $908 - 412 = \dfrac{412}{9.8}\ a$

   a = 11.79 m/s²

c) there is difference in the result because in part b force is applied to move   the smaller weight.

 but in part a,  both of the masses are independent to move.