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

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SUMMARY

The discussion focuses on calculating the work required to raise one end of a 10-meter long chain with a mass of 80 kg to a height of 6 meters. The correct approach involves using the formula W = ∫(mg)dx, where the linear density of the chain is determined to be 8 kg/m. The final calculation yields a total work of 1411.2 Joules, confirming the accuracy of the integration process used to derive this result.

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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
 
Physics news on Phys.org
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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