mID 93541135 CHw6-Ch06 Exercise 6.56 ?) 4015 Constants Part A An elevator has ma

Question

mID 93541135 CHw6-Ch06 Exercise 6.56 ?) 4015 Constants Part A 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. Express your answer using two significant figures. Submit Request Answer Provide Feedback Next >

Explanation / Answer

Answer (A): The force that the motor must exert on the elevator is equal to the weight of
the elevator since it is moving at a constant speed. Since P Fv = the force exerted by the
motor and hence the weight of the elevator is

W = F = P/v = (34302.2W)/(20m/16s) = 27441.76N

The mass of the elevator is thus m = W/g = (27441.76N) /(9.8 m/s^2 ) = 2800.17kg

From the problem, the number of passengers n is

n = (m-600kg)/(65kg) = (2800.17kg-600kg)/65kg = 33.848

The limit is thus 34 passengers.

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