Question

Problem 2 A block A of 0.5-kg rests on a horizontal, frictionless surface. The block is pressed back against a spring having a constant of k 400 N/m, compressing the spring by 12.0 cm. Then the b sreleased. The incline has a friction coefficient μ-02, and the horizontal surface has no friction. 1. Find the maximum distance d the block travels up the incline if -40 (Position C) 2. How fast is the block moving up when halfway to its maximum height? (Position B)

Answer 1

P.E of compressed spring = 1/2 k x^2 = 1/2 times 400 times (0.12)^2 = 2.88 J This is converted into kinetic energy of block till position B. The block stops at position D Therefore Work done by friction + P.E at D = 2.88 (mu m g cos theta times d + m g h) = 2.88 h = d sin 40 degree (mu m g cos theta) d + (m g sin theta) d = 2.88 d = 2.88/0.5 times 9.81 [0.2 cos 40 degree + sin 40 degree] = 0.7376 m = 73.76 cm rightarrow Ans \r\n 2. Work done by function + P.E of block at distance d/2 i.e. point C = mu m g cos theta d/2 + (m g sin theta) d/2 = m g d/2[mu cos theta + sin theta] = 0.5 times 9.81 times 0.7376/2 [0.2 cos 40 degree + sin 40 degree] = 1.44 J Therefore Kinetic energy = 2.88 - 1.44 = 1.44 J speed is given by 1/2 m nu^2 = 1.44 rightarrow nu = squareroot 2 times 1.44/0.5 = 2.4 m/s