Calculating Work Done by a Variable Force in an Electric Elevator

Thus: W = Force(X) X distance.In summary, the work done by the motor in lifting the cable from the first floor to the top floor is 72900 lb-ft. This is calculated by finding the force needed to lift the cable, which is 40x, and then integrating it from 0 to 180 ft. However, the correct answer is actually 72900 lb-ft, which can be found by using the formula W = Force(X) X distance and taking into account the variable force.
  • #1
birdec
5
0
An electric elevator with a motor at the top has a cable weight 4.5 lb/ft. When the car is at the first floor, 198 ft of cable are paid out, and effectively 0 ft are out when the car is at the top floor. How much work does the motor do just lifting the cable when it takes the car from the first floor the to the top?

This is what I've done:

180=4.5k
k=40
force=40x

work = integral from 0 to 180 40x dx
then I took the anti derivative and it was (40x^2)/2 which ends up 20x^2
I then plugged in 180 for x
20(180)^2 = 648000

The correct answer is 72900. Any thoughts?
 
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  • #2
Check your units. The work done in lifting against gravity is: W = Force X Distance = mass X g X distance. And you need to acount for the variable force as you have noticed.
 

1. What is work done by a variable force?

The work done by a variable force is the product of the force and the displacement of an object in the direction of the force. It is a measure of the energy transferred to or from an object by the force.

2. How is work done by a variable force calculated?

The work done by a variable force can be calculated by taking the integral of the force with respect to displacement. This means that the force must be a function of the displacement for the work to be calculated.

3. What is the difference between work done by a variable force and constant force?

The main difference is that the force in variable force is changing, while the force in constant force remains the same. This means that the work done by a variable force will vary depending on the displacement, while the work done by a constant force will remain constant.

4. Can work done by a variable force be negative?

Yes, work done by a variable force can be negative. This occurs when the force and displacement are in opposite directions, causing the energy to be transferred away from the object.

5. What are some real-life examples of work done by a variable force?

Examples of work done by a variable force include pushing a shopping cart, lifting a weight with a pulley system, and pedaling a bicycle. In all of these cases, the force applied varies depending on the displacement of the object.

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