a m=2.00 kg is pushed against a spring with negligible mass and force constant k

Question

a m=2.00 kg is pushed against a spring with negligible mass and force constant k=300 N/m, compressing it d=.250 m. When the block is released, it moves along a frictionless, horizontal surface and then up an incline with slope 37.0 (degrees) and a coefficient of kinetic friction of .320.

A. What is the speed of the block as it slides along the horizontal surface after having left the spring.

I know this answer, the speed is 3.06 m/s.

B. How far does the object travel up the incline before starting to slide back down?

This is where my group and I are running into problems. If it were a frictionless ramp, we could solve it, but its not. Our question is, do we need to include the kinetic friction, and if we do, how would we do that?

Please only serious answers with explanations. Do not just copy and paste work from another question. Thanks.

Explanation / Answer

use energy Ei + W = Ef Ei = 1/2 k d^2 Let x be the distance up the slope W = - fx = - u N x = - u m g x cos theta Ef = m g h = m g x sin theta so 1/2 k d^2 - u m g x cos theta = m g x sin theta solve for x x = 1/2 kd^2/ ( m g sin theta + u m g cos theta) x = 0.5*300*.25^2/(2*9.81*sin(37)+.32*2*9.81*cos(37))=0.557 m

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