Answer:
28190 pounds-mass
Step-by-step explanation:
To solve this problem, we need to use several physical principles, such as work, power, energy, and force.
First, we can calculate the work done by the elevator to lift the people and itself to the top of the building. This is given by:
Work = Force x Distance
where the force is equal to the weight of the elevator and the people, and the distance is the height of the building. We can calculate the force as:
Force = (Mass of elevator + Mass of people) x Gravity
where the mass of the elevator is given as 500 kg, the mass of people is unknown, and the gravity is 9.81 m/s^2. We can convert the height of the building to meters as well:
Height = 100 ft x 0.3048 m/ft = 30.48 m
Therefore, the work done by the elevator is:
Work = Force x Distance = (500 kg + 6 x Mass of people) x 9.81 m/s^2 x 30.48 m
Work = (5000 + 58.86 x Mass of people) joules [J]
Next, we can use the power rating of the motor and its efficiency to calculate the energy consumed by the motor during the 55 seconds it takes to lift the elevator. The energy consumed is given by:
Energy = Power x Time / Efficiency
where the power is 8.5 kW, the time is 55 s, and the efficiency is 0.62. We can convert the units of power to joules per second (J/s) as well:
Power = 8.5 kW x 1000 W/kW = 8500 J/s
Therefore, the energy consumed by the motor is:
Energy = Power x Time / Efficiency = 8500 J/s x 55 s / 0.62
Energy = 763709 J
Finally, we can use the conservation of energy to relate the work done by the elevator to the energy consumed by the motor:
Work = Energy
Therefore, we can set the two expressions for work equal to each other and solve for the mass of people:
5000 + 58.86 x Mass of people = 763709 J
Mass of people = (763709 J - 5000) / 58.86 kg = 12778 kg
To convert this mass to pounds-mass, we can use the conversion factor:
1 kg = 2.20462 lbm
Therefore, the average mass of a person on the elevator is:
Mass of people = 12778 kg x 2.20462 lbm/kg = 28190 lbm
So the average mass of a person on the elevator is 28190 pounds-mass.