The situation of Prob. 2/53 is repeated here. This time, use the values m = 5 kg, k = 150 N /m, μ = 0.40, and x₀ = 500 mm and determine the final spring stretch (or compression) x_ƒ when the block comes to a complete stop. The sign on the μg term is dictated by the direction of motion for the block and always acts in the direction opposite velocity.

Data from Prob. 2/53

A block of mass m rests on a rough horizontal surface and is attached to a spring of stiffness k. The coefficients of both static and kinetic friction are μ. The block is displaced a distance x₀ to the right of the un stretched position of the spring and released from rest. If the value of x₀ is large enough, the spring force will overcome the maximum available static friction force and the block will slide toward the un stretched position of the spring with an acceleration a = μg − k/m x, where x represents the amount of stretch (or compression) in the spring at any given location in the motion. Use the values m = 5 kg, k = 150 N /m, μ = 0.40, and x₀ = 200 mm and determine the final spring stretch (or compression) x_ƒ when the block comes to a complete stop.

Transcribed Image Text:

Unstretched spring position a Problem 2/53