Lifting an Elevator 3000lbs with a 12ft Cable: Calculating Work

In summary, the conversation discusses calculating the work required to lift a freight elevator using a winch and a cable. The solution involves setting up an integral and taking into account the weight of the cable. The final answer is 27,945ft*lb, which differs from the book's answer of 36,945ft*lb.
  • #1
turdferguson
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0

Homework Statement


A freight elevator weighing 3000 pounds is supported by a 12 foot long cable that weighs 14 pounds per linear foot. Approximate the work required to lift the elevator 9 feet by winding the cable onto a winch

Homework Equations


W = int(f)dy

The Attempt at a Solution


The work lifting the elevator is 3000lb(9ft)=27000ft*lb

The winch is lifting a piece of rope dy a distance 12-y from 0 to 9
Each section dy weighs 14dy

(sorry for the lack of latex)
W = int0-9[14(12-y)]dy = 14int0-9[(12-y)]dy
W = 14[12y-.5y2]0-9
W = 945 ft*lb

Total work = 27000+945 = 27,945ft*lb
But the book has an answer of 36,945. The 945 leads me to think I set up the integral correctly, but where did the extra 900 come from?
 
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  • #2
The book's answer is clearly wrong. You knew that, right?
 

1. How much work is required to lift an elevator weighing 3000lbs using a 12ft cable?

To calculate the work required, we need to use the formula W = F x d, where W is work, F is the force applied, and d is the distance moved. In this case, F = 3000lbs (mass) x 9.8m/s^2 (acceleration due to gravity) = 29,400N. Since the elevator is being lifted 12ft or 3.66m, d = 3.66m. Therefore, W = 29,400N x 3.66m = 107,544J or 107.54kJ.

2. How does the weight of the elevator affect the amount of work required to lift it?

The weight of the elevator directly affects the amount of work required to lift it. The heavier the elevator, the more force is required to lift it against the force of gravity. This means that a heavier elevator will require more work to be done to lift it to the same height as a lighter elevator.

3. What is the role of the cable in lifting the elevator?

The cable is responsible for transferring the force applied to the elevator from the lifting mechanism to the elevator itself. It also helps to distribute the weight of the elevator evenly, allowing it to be lifted smoothly and safely.

4. How does the length of the cable affect the amount of work required to lift the elevator?

The length of the cable does not directly affect the amount of work required to lift the elevator. However, a longer cable may require more force to be applied to lift the elevator the same distance compared to a shorter cable, as the weight of the cable itself may add additional load to the lifting mechanism.

5. Is it possible to calculate the amount of work required to lift an elevator without knowing the weight of the elevator?

No, it is not possible to calculate the work required without knowing the weight of the elevator. The force required to lift an object is directly proportional to its weight, so without knowing the weight of the elevator, we cannot accurately calculate the work required.

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