Calculate Power of Cable Force Moving Elevator Cab: 3.0x103 kg, 191 m, 23 s

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In summary, the power of the force from the cable on the elevator cab can be calculated by taking the dot product of the force and velocity. Since the cab moves at constant speed, the cable's force must be equal in magnitude to the gravitational force on the cab. Therefore, the power of the force from the cable can be calculated by multiplying the force (tension) by the velocity (191/23 m/s) and converting the result from W to kW.
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themanofosu
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Question: The loaded cab of an elevator has a mass of 3.0 103 kg and moves 191 m up the shaft in 23 s at constant speed. At what average rate does the force from the cable do work on the cab? answer is in kW

hint provided : Power is the rate at which work is done. The power of a force is the dot product of the force and the velocity. If the cab moves at constant speed, how does the cable's force compare with the gravitational force on the cab?

So I am guessing tension which equals mg is our force, and so that force times velocity, which is 191/23 m/s is our power. what did i do wrong? how do you solve this properly? thank you! :D
 
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Welcome to PF!

Hi themanofosu ! Welcome to PF! :smile:

(try using the X2 tag just above the Reply box :wink:)

You haven't actually shown us your final figures, but your method looks correct …

did you remember to convert from W to kW ? :smile:​
 

1. What is the formula for calculating power?

The formula for calculating power is power = work / time. Power is measured in watts (W), work is measured in joules (J), and time is measured in seconds (s).

2. How do you calculate the work done by the cable force?

The work done by the cable force can be calculated using the formula work = force x distance. In this scenario, the force is the weight of the elevator cab, which is equal to its mass (3.0x103 kg) multiplied by the gravitational acceleration (9.8 m/s2). The distance is the height the elevator cab moves, which is given as 191 m in the question. Therefore, the work done by the cable force is equal to (3.0x103 kg x 9.8 m/s2) x 191 m = 5.5x106 J.

3. What is the unit of power?

The unit of power is watts (W). This unit is equivalent to one joule per second (J/s).

4. How do you calculate the time taken for the elevator cab to move?

The time taken for the elevator cab to move can be calculated using the formula time = distance / speed. In this scenario, the distance is given as 191 m and the speed is not given. However, we can calculate the speed using the formula speed = distance / time, which is rearranged to time = distance / speed. Since the speed is not given, we can assume it to be constant and equal to the average speed of the elevator cab, which is equal to the distance (191 m) divided by the time taken (23 s). Therefore, the time taken for the elevator cab to move is equal to 191 m / (191 m / 23 s) = 23 s.

5. How do you calculate the power of the cable force in this scenario?

The power of the cable force can be calculated using the formula power = work / time. In this scenario, we have calculated the work done by the cable force to be 5.5x106 J and the time taken for the elevator cab to move to be 23 s. Therefore, the power of the cable force is equal to 5.5x106 J / 23 s = 2.4x105 W.

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