1. The 50-lb load is hoisted by the pulley system and motor M. If the crate starts from rest and by constant acceleration attains a speed of 15 ft/s after rising 6 ft, determine the power that must be applied to the motor at this instant. The motor has an efficiency ε = 0.76. Neglect the mass of the pulleys and cable.
2. Roller coasters are designed so that riders will not experience more than 3.5 times their weight (i.e. normal force + weight = 3.5*weight) as a normal force against the seat of the car. Determine the smallest radius of curvature ρ of the track at its lowest point if the car has a speed of 5 ft/s at the crest of the drop. Neglect friction.
See attached file for full problem description.
The solution calculates power applied by a motor and the smallest radius of curvature of a roller coast track.