Question

​​A cable of length 50 meters and density 4 kilograms per meter hangs over the edge of a skyscraper. What work is needed to pull the whole cable to the top of the building?​

Answer 1

W = 49000 J

Step-by-step explanation:

Given that,

Length of the cable, l = 50 m

Density of the cable,
`d=4\ kg/m`

The force acting on the cable is variable and it is equal to,

`F=4l\ g`

Let W is the work is needed to pull the whole cable to the top of the building. It is given by :

`W=\int\limits^(50)_0 {4lg\ dl}`

`W=39.2\int\limits^(50)_0 {l.dl}`

`W=(39.2l^2)/(2)|_0^(50)`

W = 49000 J

So, the work needed to pull the whole cable to the top of the building is 49000 J. Hence, this is the required solution.