# Mechanics HelpWatch

#1
A rough slope is inclined at an angle θ to the horizontal, θ < 45°. A small parcel of mass M is at rest on the slope, and the coefficient of friction between the parcel and the slope is µ. A force of magnitude kMg, where k is a constant, is applied to the parcel in a direction making an angle θ with a line of greatest slope(Diagram in Heinemann M1 Book, Page 153, Question 38. :-)) The line of action of the force is in the same vertical plane as the line of greatest slope.

Given that the parcel is on the point of moving down the slope, show that:

k = (µ cos θ - sin θ ) / ( cos θ - µ sin θ )

Any help is greatly appreciated.. I am VERY stuck

Tut
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13 years ago
#2
N2L:
Mgsinθ + kMgcosθ = f = uR (1)
R = Mgcosθ + kMgsinθ (2)

Combining (1) and (2):
Mgsinθ + kMgcosθ = uMgcosθ + ukMgsinθ
kMgcosθ - ukMgsinθ = uMgcosθ - Mgsinθ
k(cosθ - usinθ) = ucosθ - sinθ
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