An elevator has mass 600 kg, not including passengers. the elevator is designed to ascend, at constant speed, a vertical distance of 20.0 m (five floors) in 16.0 s, and it is driven by a motor that can provide up to 40 hp to the elevator. what is the maximum number of passengers that can ride in the elevator? assume that an average passenger has mass 65.0 kg

Power = 40 hp (745.7 W / 1 hp) = 29828 W

Power is the rate of energy so,

P = dW/dt = F (v) where F is force and v is velocity

v = d/t = 20 m / 16 s = 1.25 m/s

F = P/v = 29828 W / 1.25 m/s = 23862.4 N

The force calculated is the force that is applied by the elevator to carry all of the weight (itself and the passengers). So,

Weight of the elevator = 600*9.81 = 5886N

Weight of the passengers = 9.81m where m is the mass of the passengers

For this system, in order to hold the maximum number of passengers it should be that the total force applied by the the elevator plus the passengers is equal to the force provided by the motor. Therefore, the elevator should be at rest or acceleration is 0.

F - We - Wp = 0

23862.4 N - 5886 N - 9.81m = 0

m = 1832.5 kg (total mass of the passengers)

No. of passengers = 1832.5 kg / 65 kg = 28.19

Thus, the maximum number of passenger is approximately 28.