A mass of 2.2 kilograms is placed on a horizontal frictionless surface against a

Question

A mass of 2.2 kilograms is placed on a horizontal frictionless surface against an uncompressed spring with spring constant 831.5 N/m. The inclined portion of the surface makes at an angle of 30 degrees to the horizontal and has a coefficient of kinetic friction of 0.19 with the mass. The mass is pushed against the spring until it is compressed a distance 0.19 and then released. How high (vertically), in meters, does the mass rise from the original height before it stops (momentarily) on the inclined ramp?

Explanation / Answer

Given

mass m = 2.2 kg, spring constant k = 831.5 N/m

angle theta = 30 degrees

coefficient of kinetic friction mue_k = 0.19

compression of the spring is x = 0.19 m

initial energy Ei = (1/2)*k*x^2

final energy Ef = m*g*h

work done Wf = -uk*m*g*L*costheta

sintheta = h/L=======> L = h/sintheta

work = Ef - Ei

-uk*m*g*h*tantheta = m*g*h - (1/2)*k*x^2

-0.19*2.2*9.8*h*tan30 = 2.2*9.8*h - (1/2)*831.5*0.19^2

h = 0.627 m

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