Need help - ramp problem inclined plane

AI Thread Summary
To minimize the work against gravity and friction while moving crates up an inclined plane with constant velocity, the relationship between the angle of the ramp (θ) and the coefficient of kinetic friction (µ) is crucial. The correct condition for minimizing work is given by the equation tan θ = µ. This ensures that the forces acting on the crates are balanced, allowing for efficient movement. The discussion emphasizes the importance of understanding the physics behind inclined planes and friction in practical applications. Properly setting the ramp angle can significantly reduce the effort required by movers.
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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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