Work, Energy & Power

Worked: a crate down a ramp

A 200 lb crate starts from rest and slides 20 ft down a 30° ramp with μₖ = 0.20. It drops 20 sin 30° = 10 ft, so gravity does 200 × 10 = 2,000 ft-lb. The normal force is 200 cos 30° = 173.2 lb, so friction takes 0.20 × 173.2 × 20 = 693 ft-lb. What is left is kinetic energy: 1,307 ft-lb.

The mass is 200/32.2 = 6.21 slugs, so v = √(2 × 1,307/6.21) = 20.5 ft/s at the bottom.

Power: a hoist raising 2,000 lb at 3 ft/s delivers 6,000 ft-lb/s = 10.9 hp. With an 85% efficient drive, the motor must supply 10.9/0.85 = 12.8 hp.