An elevator operates by cables, pulleys, an electric motor and controls. This elevator is driven by an 8-kW motor.
Calculate the maximum rate of ascent of the elevator.
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An elevator operates by cables, pulleys, an electric motor and controls. This elevator is driven by an 8-kW motor.
Calculate the maximum rate of ascent of the elevator.
♦ We start with the rate form of the energy equation with the elevator modeled as a BODY.
| (1) 1 |
Addressing terms, left to right. U: as the elevator moves (or waits at a floor) there is no motive for its internal energy to change. (It is not exposed to high temperatures nor is it bent, twisted... etc.) KE:The elevator moves at constant speed hence dKE/dt = 0. dPE/dt for the elevator is not zero; we will return to this term. Rightward, across the equality... V:, the volume of the elevator (system) does not change; hence the "system-volume-change-work" is zero. Bypass ΣW for now. The the sum of heats for the event will be zero at the state of the event and have no motive for change thereafter; ΣQ = 0.
| (2) 2 |
Rewrite the equation to omit the zero or negligible terms:
| (3) 3 |
To proceed, write dPE/dt explicitly:
 | (4) 4 |
About the derivative of the product of terms; mass (m) and gravity (go) are constant. The derivative is then:
 | (5) 5 |
A solution is at hand:
 | (6) 6 |
Obviously this is the maximum rate of ascent this motor could accomplish. All aspects of friction were assumed equal to zero.