Question

A 4-meter chain with a linear mass density rho(x) = 2x(7 - x) kg/m lies on the ground. Calculate the work required to lift the chain from its front end so that its bottom is 3 m above the ground.

Answer 1

The work required to lift the chain is (28/3)m‌².

Step-by-step explanation:

To calculate the work required to lift the chain, we need to integrate the product of the chain's linear mass density and the distance it is lifted. We are given that the linear mass density, ρ(x), is equal to 2x(7 - x) kg/m and the bottom of the chain needs to be lifted 3 m above the ground. Let's set up the integral to find the work:

Work = ∫032x(7 - x) dx

Simplifying the integral and solving, we get:

Work = (28/3)m2