Question

(1 point) A chain 64 meters long whose mass is 24 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 13 meters of the chain to the top of the building

Answer 1

Answer:

W = 2747,1 [J]

Step-by-step explanation:

Chain is 64 meters long with mass 24 Kg

Then weight of the chain is p = 24 * 9.8

p = 235.2 [N]         N = kg*m/s²

And by meter is 235,2 / 64    = 3.675

Total work has two component

- work to lift the 13 top meters of chain  W₁

W₁ = ∫₀ᵇ F(y) dy

- work to lift last ( 64 - 13 ) meters  51   W₂

W₂ = 3.675 * 51 * 13      Kg m² /s²   [J]

W₂ =  2436,53 [J]

We need to calculate  W₁

W₁  = ∫¹³₀ mgy dy    ⇒     W₁  = ∫¹³₀ 3,675 ydy

W₁  = 3,675* ∫¹³₀ ydy     W₁  = 3,675* y²/2  |₀¹³

W₁  = 3,675* 84,5 [J]

W₁  = 310,54 [J]

And total work W

W = W₁ + W₂

W = 310,54  + 2436,53 [J]

W = 2747,1 [J]