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A chain 72 meters long whose mass is 29 kilograms is hanging over the edge of a tall building and does not touch the ground. How much work is required to lift the top 14 meters of the chain to the top of the building?
Use that the acceleration due to gravity is 9.8 meters per second squared. Your answer must include the correct units.

Respuesta :

Answer:

Work done required is 3567.2 J

Explanation:

Given :

Length of chain, l = 72 m

Mass of chain, M = 29 kg

Linear mass density of chain, μ = [tex]\frac{Mass\ of\ chain }{Length\ of\ chain}[/tex] = [tex]\frac{29}{72}[/tex]  = 0.40 kg/m

Let x be the length of the chain which lift to the top of the building.

Work done required to lift the chain is equal to the potential energy of the chain.

W = ∫μg (72 - x ) dx

Here g is acceleration due to gravity.

The limit of integration is from 0 to 14.

W = μg ( 72x - x²/2)

Substitute 0.40 kg/m for μ, 9.8 m/s² for g and 14 m for x in the above equation.

W = [tex]0.40\times9.8\times(72\times14\ - \frac{14^{2} }{2})[/tex]

W = 3567.2 J

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