Question

Suppose a box of mass m is being pulled across the ground with a horizontal force fpull=ax2 , where a is a constant, from the position x=0 to x=d . Find an expression for the work done by fpull on the box. express your answer in terms of some, all, or none of the variables a and d .

Answer 1

The work done by the force Fpull=ax2 on a box pulled from x=0 to x=d is W = ⅓ad3, which is obtained by integrating the force over the distance.

Step-by-step explanation:

When a box of mass m is pulled across the ground with a horizontal force, Fpull=ax2, from the position x=0 to x=d, the work done by Fpull on the box can be found by integrating the force over the distance covered. Work is defined as the integral of force over distance, so the work done W is:

W = ∫ Fpull dx

Since Fpull varies with x2, we can express the work done as:

W = ∫ ax2 dx from 0 to d

Integrating, we get:

W = a[⅓x3] from 0 to d

When evaluated from 0 to d we find:

W = a[⅓d3 - 0]

Therefore, the expression for the work done by Fpull on the box is:

W = ⅓ad3