A 250 g block slides on a rough horizontal table. Determine the work done by the frictional force in bringing the block to rest if it is initially travelling at a speed of 40 cm/s . If the friction coefficient between the table and the block is 0.1 , determine how far the block moves before coming to rest.

Step-by-step solution

Given mass of the block, m = 250 g = 0.25 kg Initial velocity, v = 40 cm/s = 0.4 m/s Final velocity, v_f = 0 m/s By the work-energy theorem, the work done by the frictional force is equal to the change in kinetic energy of the block: W = K = K_f - K_i W = 0 - 1 2 m v^2 W = - 1 2 0.25 (0.4)^2 = -0.02 J The frictional force acting on the block is given by f = m g . Taking g = 9.8 m/s ^2 , f = 0.1 0.25 9.8 = 0.245 N The work done by friction is also given by W = -f d , where d is the distance moved before coming to re