Need help - ramp problem inclined plane

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SUMMARY

The discussion centers on optimizing the angle of a truck ramp to minimize the work done against gravity and friction when moving crates at constant velocity. The correct relationship to achieve this is established as tan θ = µ, where µ represents the coefficient of kinetic friction. This conclusion is crucial for movers to efficiently load and unload crates without excessive effort. The forum emphasizes the importance of understanding the physics behind inclined planes and frictional forces.

PREREQUISITES
  • Understanding of basic physics principles, particularly forces and motion.
  • Knowledge of inclined planes and their mechanics.
  • Familiarity with the coefficient of kinetic friction (µ).
  • Basic trigonometry, specifically the tangent function.
NEXT STEPS
  • Study the principles of inclined planes in classical mechanics.
  • Learn about the calculations involving frictional forces and their impact on motion.
  • Explore the relationship between angles and forces in physics using trigonometric functions.
  • Investigate real-world applications of minimizing work in mechanical systems.
USEFUL FOR

This discussion is beneficial for physics students, movers, logistics professionals, and anyone involved in the design or operation of loading ramps and inclined surfaces.

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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