A 100 kg block is started with a speed of 2.0 m s ⁻¹ on a long, rough belt fixed in a horizontal position. The coefficient of kinetic friction between the block and the belt is 0.20 . Consider the scenario from a reference frame moving at 2.0 m s ⁻¹ along the initial velocity of the block. As observed from this frame, the block is gently set on a moving belt and eventually starts moving with the belt at 2.0 m s ⁻¹ .

Step-by-step solution

Let the initial velocity of the block be in the positive x -direction. The ground frame is S and the moving frame is S' , which moves with velocity V = 2.0 m s ⁻¹ in the positive x -direction. In the frame S' , the initial velocity of the block is v'₀ = 2.0 - 2.0 = 0 m s ⁻¹ . The belt moves with a constant velocity v'_b = 0 - 2.0 = -2.0 m s ⁻¹ . The block experiences a kinetic friction force f_k = _k m g in the negative x -direction (the direction of the belt's motion relative to the block). The acceleration of the