Ramp angle for minimum work against gravity and friction

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tricky_tick
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Movers want to set the ramp of their truck so that the work they do against the combination of gravity and friction is a minimum for crates moving up the ramp with constant velocity. µ is the coefficient of kinetic friction and θ is the angle between the ramp and the ground. For the work to be a minimum, they must choose:

a. tan θ = µ

b. tan θ = -µ

c. tan θ = -1/µ

d. tan θ = 1/µ

e. tan θ = 1 - µ
 
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