Question

A force F with arrow= (5xî+ 4yĵ), where F with arrow 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 = 5.01 m. Find the work W = F with arrow · dr with arrow done by the force on the object.

Answer 1

Answer:

w= 62.75 J

Explanation:

Given that

Force vector F= 5 x i + 4 y j

Space vector or displacement vector d= 5.01 i

We know that work (w)

w=∫ F.ds

w= ∫(5 x i + 4 y j) .dx            ( only object is moving in x- direction)

$w=\int_{0}^{5.01}5xi.dxi$

$w=\int_{0}^{5.01}5x.dx$

$w=\left [\dfrac{5}{2}x^2\right ]_0^{5.01}$

w= 2.5 x 5.01² J

w= 62.75 J