A 10kg mass slides 15 meters down a 30 degree incline. The coefficients of frict

Question

A 10kg mass slides 15 meters down a 30 degree incline. The coefficients of friction between the sliding mass and the inclined slope are 0.30 and 0.45for the kinetic and static, respectively.

Use the Modified Conservation of Energy equation to determine the final speed of the mass after it has slid 15 m down the slope (in the x-direction)

Modified Conservation of Energy: E1+Wapp+Wf=E2, where:

E1-initial mechanical energy of the system

Wapp-work done by applied force

Wf-work done by friction force

Explanation / Answer

height at the start of the motion = H

H = L*sin(tehta)

H = 15*sin30 = 7.5 m

N = mgcos(theta)

PE = KE + Work done by friction

mgh = 0.5*mv^2 + u*N*d

m*9.8*H = 0.5*m*v^2 + u*mgcos30*15

9.8*7.5 = 0.5*v^2 + 0.3*9.8*cos30*15

35.3 = 0.5*v^2

v = 8.4 m/s

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