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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?

  • physics -

    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.

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