Solving Work Done in Lifting 150ft Cable, 4lb/ft

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In summary, the problem is to find the work done in winding up a 150 ft cable that weighs 4.00 lb/ft, while excluding the gravitational force. The solution involves using the equation W = ∫ py dy from 0 to 150, where p is the density and y is the lifting distance. The final answer is 45000 ft-lb.
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Pruddy
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Homework Statement



Find the work done in winding up a 150 ft cable that weighs 4.00 lb/ft. Assume that the weight includes the gravitational force. In order words exclude the gravitational force g in your calculation.

Homework Equations



W = ∫ pgA(y)D from a ft to b
a = area
P = density
g = gravitational
d= lifting distance


The Attempt at a Solution


The question clearly states that g should be excluded from the equation.
W = ∫A(y) (d) from 150 to zero

But I am not sure of my work.
 
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  • #2
Finally found a solution to the problem.
W= ∫ py dy from 0 to 150
p = 4

W = 4∫ ydy
W = 4[y^2/2]
W = 4 [11250] = 45000

I Think this is the right answer to the problem.
 

What is work done in lifting?

Work done in lifting refers to the amount of energy required to lift an object against the force of gravity. It is calculated by multiplying the weight of the object by the height it is lifted.

How do you calculate the work done in lifting a 150ft cable?

To calculate the work done in lifting a 150ft cable, you would first need to determine the weight of the cable. In this case, it is given that the weight of the cable is 4lb per foot. Therefore, the total weight of the 150ft cable would be 600lbs (4lb/ft x 150ft). Then, you would multiply the weight (600lbs) by the height it is lifted (150ft) to get the work done, which in this case would be 90,000 foot-pounds.

What is the unit of measurement for work done in lifting?

The unit of measurement for work done in lifting is foot-pounds (ft-lb) in the imperial system and joules (J) in the metric system.

How does the weight of the object affect the work done in lifting?

The weight of the object directly affects the amount of work done in lifting it. The heavier the object, the more energy is required to lift it to a certain height. Therefore, the work done in lifting a heavier object would be greater than that of a lighter object, assuming the height lifted remains the same.

Is there a difference in the work done if the cable is lifted straight up versus at an angle?

Yes, there is a difference in the work done if the cable is lifted straight up versus at an angle. When lifting an object at an angle, the force required to lift it is greater due to the component of the force acting against the direction of the lift. Therefore, the work done in lifting an object at an angle would be greater than that of lifting it straight up, even if the height lifted is the same.

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