Question

A force f=fx fyj acts on a particle that undergoes a displacement of a=sx syj where fx= 1 n fy= -2n, sx= 2 m and sy= 2 m. Find the work done by the force on the particle.

Answer 1

The work done by the force is 0 J.

Step-by-step explanation:

To find the work done by a force, you can use the formula:

work = force x displacement x cos(theta)

where theta is the angle between the force and displacement vectors. In this case, the force vector is given as f = (1 N)i - (2 N)j and the displacement vector is given as a = (2 m)i + (2 m)j. The angle between the force and displacement vectors can be found using the dot product:

cos(theta) = (f.a) / (||f|| ||a||)

Substituting the values, we get:

cos(theta) = (1*2 + (-2*2)) / (sqrt(1^2 + (-2)^2) * sqrt(2^2 + 2^2))

cos(theta) = 0 / (sqrt(5) * sqrt(8))

cos(theta) = 0

Since cos(theta) = 0, the angle theta is 90 degrees or pi/2 radians. Therefore, the work done by the force is:

work = (1 N * 2 m) * cos(pi/2) + (-2 N * 2 m) * cos(pi/2) = 0 J