8. A 0.40-kg block rests on a level surface and is attached to a horizontally al

Question

8. A 0.40-kg block rests on a level surface and is attached to a horizontally aligned spring with a spring constant of 40 N/m. The block is initially displaced 4.0 cm from the equilibrium point and then released to set up a simple harmonic motion. A frictional force of between the block and surface. What is the speed of the block when it first passes through the equilibrium point after being released from the 4.0-cm displacement point? 0.3 N exists a. 0.020 m/s b. 0.027 m/s. c. 0.032 m/s. d. 0.035 m/s. e. 0.045 m/s.

Explanation / Answer

Work done by spring, W = 0.5 k x2 = 0.5 x 40 x 0.04 x 0.04 = 0.032 J

Work against friction = F x s = 0.3 x 0.04 = 0.012 J

Kinetic energy, KE = 0.5 x m x v2 = 0.032 - 0.012 = 0.02

Velocity, v = [ (2 x 0.02) / 40 ]1/2 = 0.0316 ~ 0.032 m/s Option (c)

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