In a simple Atwood machine, two unequal masses m₁ and m₂ are connected by a string going over a clamped light smooth pulley. In an arrangement as shown in the figure, m₁ = 300 g and m₂ = 600 g . The system is released from rest. Determine the distance travelled by the first block in the first two seconds.

Step-by-step solution

The acceleration of the blocks in a simple Atwood machine is given by: a = m₂ - m₁ m₁ + m₂ g Substituting the given values m₁ = 300 g and m₂ = 600 g : a = 600 - 300 600 + 300 g = 300 900 g = g 3 Taking g = 9.8 m/s ^2 : a = 9.8 3 m/s ^2 The system is released from rest, so the initial velocity u = 0 . The distance travelled by the first block in time t = 2 s is: s = ut + 1 2 a t^2 s = 0 + 1 2 ( 9.8 3 ) (2)^2 s = 1 2 9.8 3 4 s = 19.6 3 6.5 m