A coiled spring with a spring constant of 500 N/m is compressed some distance, \

Question

A coiled spring with a spring constant of 500 N/m is compressed some distance, "x". When the spring uncoils, it releases a ball of mass 0.5 kg. THe ball travels through a flat surface that is 2.1 m long and has a coefficient of friction of 0.2. At the end of this flat surface is a frictionless ramp which makes an incline of 25 deg. If the goal is to have the ball come to a complete stop at the top of the ramp (0.35 m from the base, what distance "x" should the spring be compressed?

Please be as specific as possible and showw all of your work.

Explanation / Answer

chnage in kinetic energy is equal to work done .

first we compress the spring by distance x after release energy in spring is equal to spring force

and here friction also so it will in opposote direction and at ramp it working against gravity

1/2*kx^2 = kd - mu*mg - mghsintheta

d = 2.1 m

u = 0.2

0.5*500*x^2 = 500*2.1 - 0.2*0.5*9.8*2.1 - 0.5 x 9.8 x 0.35 sin25

x = 2.05 m

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