What is the Work Required to Raise a Chain to a Given Height?

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To calculate the work required to raise one end of a 10 m long, 80 kg chain to a height of 6 m, the linear density is determined to be 8 kg/m. The work is calculated using the integral of the weight of the chain segment raised, which is expressed as W = integral of (8 * change in x * 9.8) dx from 0 to 6. The final result of this calculation yields 1411.2 Joules. The integration variable represents the length of the chain that is lifted, confirming the approach taken is correct. The solution effectively demonstrates the application of physics principles to solve the problem.
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Homework Statement



A chain lyinh on the ground is 10 m long and its mass 80 kg. How much work is required to raise one end of the chain to a height of 6m.

Homework Equations



W = F x d
= mg x d
W = integral of mg dx from 1 to 6

The Attempt at a Solution


since mass is 80 kg and length is 10 m, linear density is 8kg/m

therefore m = 8 * change in distance
put it together

w = integrel of 8*change in x * 9.8 * dx from 0 to 6
= 78.4 * change in x * dx from 0 to 6
= 1411.2 Joules

AM i right?

p.s. sorry i am new at this i don't know how to get the actual functions for this
 
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The result is correct. That "change of x" is the length of chain in air, and it is "x", the integration variable.

ehild
 
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