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.

Question

Mathematics

Lucian Schultz

29 March, 06:04

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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Answers (1)

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Luz Prince · Answer 1

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