You are designing a spring-ramp system that will \"catch\" boxes sliding down a

Question

You are designing a spring-ramp system that will "catch" boxes sliding down a ramp, bringing them to a slop by compressing a spring Assume the ramp has a length I. - 6.0 meters, and makes an angle of 25.0 degrees with respect to the horizontal. If a box has weight mg = 1500 N, and initially hits the spring with a speed of v_o = 2.0 m/s, what is the necessary force-constant k of the spring in order to bring the box to a stop after compressing the spring by exactly x = 0.5 meters? (You can assume the frictional fou r is f_s = 550 N and stays constant over the entire length L of the ramp.)

Explanation / Answer

Here, loss in kinetic energy = work done by spring + work done by frictional force

=>   1/2 * 153.061 * 2 * 2 =   1/2 * k * 0.5 * 0.5   + 550 * 0.5

=> k = 249 N/m

=> force constant of spring =   249 N/m

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