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A chain lying on the ground is 19 meters long and its mass is 84 kilograms. The chain is threaded through a pulley, which is fixed to the ground, and pulled directly up so that it forms the shape of an L. How much work is required to raise one end of the chain to a height of 7 meters? Use that the acceleration due to gravity is 9.8 m/s^2. You may assume that the chain slides effortlessly and without friction along the ground as its end is lifted.

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Answer:

Step-by-step explanation:

Given that, the length of the chain is

L= 19m

And the mass of the chain is

M= 84kg

Work to raise the chains to a height of

H = 7m

Acceleration due to gravity

g = 9.8m/s²

Since the chain is 19m long and it has a mass of 84kg

Then, it mass/ length is 84/19

M/L = 4.42kg/m

So, it weight / length is mass / length × gravity

W/L = M/L × g

W/L = 4.42 × 9.8

W/L = 43.33 N/m

So, workdone can be calculated using

Work = ∫F∆x

Work = ∫(W/L)•xdx.

Work = ∫43.33x dx. From x = 0 to 7

Work = 43.33 ∫x dx.

Work = 43.33 x²/2. From x = 0 to 7

Work = 21.66 [x²] from x = 0 to 7

Work = 21.66 ( 7²-0²)

Work = 21.66 × 49

Work = 1061.5 Joule

The workdone to lift the chain to 7m is 1061.5 J

"When work is done to lift the chain to 7m is 1061.5 J. To understand the calculations, check below".

Calculation of Acceleration due to Gravity

Given that, the length of the chain as per the question is:

L= 19m

And also the mass of the chain is

Then M= 84kg

Now Work to raise the chains to a height of

After that H = 7m

Acceleration due to gravity

Then g = 9.8m/s²

Since When the chain is 19m long and it has a mass of 84kg

Then, it mass/ length is 84/19

M/L = [tex]4.42kg/m[/tex]

After that, it weight / length is mass / length × gravity

W/L = M/L × g

W/L = 4.42 × 9.8

W/L = 43.33 N/m

Then, work done can be calculated using

Work is = ∫F∆x

Work is = ∫(W/L)•xdx.

Then Work = ∫43.33x dx. From x = 0 to 7

After that Work = 43.33 ∫x dx.

Now Work = 43.33 x²/2. From x = 0 to 7

Work is = 21.66 [x²] from x = 0 to 7

Work is = 21.66 ( 7²-0²)

Then Work = 21.66 × 49

Hence Work = 1061.5 Joule

Therefore, The work done to lift the chain to 7m is 1061.5 J

Find  more information about Acceleration due to Gravity here:

https://brainly.com/question/88039

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