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.
Solution 56E Step 1 of 3: Here in the given problem we need to calculate the number of passengers(n) can be lift using elevator with average weight of one such passenger m=65 kg in a elevator of mass M= 600 kg moving a distance h=20 meter for t=16 seconds driving a power of P=40 hp. Given data, Mass of elevator, M= 600 kg Mass of one person, m= 65kg Mass of n number of passenger,=n m=n 65 kg Total mass , M t total mass of passengers + mass of elevator M t nm + M= (n 65 + 600)kg Power, P= 40 hp Using 1hp = 746 W P=40×746 W = 29840 W Height, h= 20 m Time taken , t= 16 s To find, Number of passengers, n= Step 2 of 3: The work done by the given power will be equal to the work done on the elevator with passenger against the gravity to move to a height h. That is, Work done against gravity, W =gM ght Similarly work done due to applied power, W P P t Since both are equal, W =gW P Using above equations, M th = P t