Your engineering firm is asked to specify the maximum load for the elevators in a new building. Each elevator has mass 500 kg when empty and maximum acceleration 2.25 m/s^2. The elevator cables can withstand a maximum tension of 19.6 kN before breaking. For safety, you need to ensure that the tension never exceeds two-thirds of that value. What do you specify for the maximum load?How many 75.0-\rm kg people is that?

Answer 1

Maximum elevator load = M*g, where M is the mass of passengers and/or freight.

Require that
(500 + M)*(g + a) = 1.5 * Tmax

(500 + M)*12.05 = 29.4*10^3 N

Solve for M.

M = 2440 kg

Divide M by 75 kg for the maximum number of people.

Answer 2

a.)588.88 kg
b.) 7