Question

A particle moving on the x-axis experiences a force given by Fx=qx2, where q is a constant. How much work is done on the particle as it moves from x=0 to x=d?

Answer 1

The work done on a particle experiencing a force Fx=qx^2 as it moves from x=0 to x=d is calculated by integrating the force over the distance, resulting in a work done equal to qd^3/3 joules.

Step-by-step explanation:

To calculate the work done by a force represented by Fx=qx2 where q is a constant, as it moves a particle from x=0 to x=d along the x-axis, we need to integrate the force over the displacement. According to the work-energy principle:

W = ∫ Fx dx

So, the work done by the force from x=0 to x=d is:

W = ∫ q x2 dx from x=0 to x=d

Upon integrating, we find:

W = q ∫ x2 dx = q [ x3/3 ] from 0 to d

Therefore, the work done W = q(d3/3 - 0) = qd3/3.

This gives us a result that the work done on the particle as it moves from x=0 to x=d on the x-axis is qd3/3 joules.