A block of mass 20 kg initially at rest on a rough horizontal surface is pulled by a horizontal rope with a constant acceleration of 2 m s ⁻² . If the coefficient of kinetic friction between the block and the surface is 0.4 , the power delivered by the rope at t = 4 s from the start is _____ W . [Take g = 10 m s ⁻² ]

Step-by-step solution

Let the tension in the rope be T . Using Newton's second law for the block in the horizontal direction: T - _k mg = ma T = m(a + _k g) Substituting the given values: T = 20(2 + 0.4 10) T = 20(2 + 4) = 120 N The velocity of the block at t = 4 s is: v = u + at v = 0 + 2 4 = 8 m s ⁻¹ The power delivered by the rope at t = 4 s is: P = T v P = 120 8 = 960 W Answer: 960