Question

1. A 40 kg piece of muck starting from rest is sliding down a 35°, 45 m long orepass     If the coefficient of friction µ_k =   0.32 what will be the speed of the piece of muck at the end of the orepass?   (5 points)

Please write your answer, Please do not write on the paper and paste it.

Answer 1

R = normal force on the body by the surface of incline

m = mass of the body

θ = angle of incline

μ = coefficient of kinetic friction

a = acceleration of the body

F = kinetic frictional force

perpendicular to incline surface , force equation can be given as

R = mg Cosθ                                  eq-1

kinetic frictional force is given as

F = μ * R

using eq-1

F = μ mg Cosθ                              eq-2

parallel to incline , force equation is given as

mg Sinθ - F= ma

using eq-2

mg Sinθ - μ mg Cosθ = ma

a = g (Sinθ - μ Cosθ )

NOW using given data in question

a = 9.8(sin35 - 0.32cos35) = 3.05 m/s²

Now use kinematic equation

V² - U² = 2aS

S = 45m

U = 0

V = sqrt(2aS) = sqrt(2*3.05*45) = 16.57 m/s²

Hence this is the final speed of muck

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