Question

A force F = (2xî + 4yĵ), where F is in newtons and x and y are in meters, acts on an object as the object moves in the x-direction from the origin to x = 4.99 m. Find the work W = ∫ F · dr done by the force on the object (in J).

Answer 1

Answer:

Work done, W = 24.9001 J

Explanation:

Given that,

Force, F = (2xî + 4yĵ) Where x and y are in meters

This force acts on an object as the object moves in the x-direction from the origin to x = 4.99 m.

We need to find the work done by the force on the object. It is given by :

$W=\int\limits^a_b {F dr} \\\\W=\int\limits^{4.99}_0 {(2xi+4yj)dx} \\\\W=\int\limits^{4.99}_0 {2xi\ dx} \\\\W=x^2|_0^{4.99}\\\\\text{Applying limits}\\\\W=(4.99)^2-0^2\\\\W=24.9001\ J$

So, the work done is 24.9001 J.