A particle moves along a straight path through displacement while force acts on it. (Other forces also act on the particle.) What is the value of c if the work done by on the particle is (a) zero, (b) 4.0 J, and (c) -1.8 J

a) c = 1.85

b) c = 0.8

c) c = 2.33

Explanation:

a)

The displacement of the particle is given by

While the force applied on the particle is

So we have a problem in 2-dimensions.

The work done on the particle is given by the scalar product between force and displacement:

(1)

Here the work done on the particle is zero, so

W = 0

Therefore from eq(1) we find:

b)

In this problem, the work done on the particle is

The force and displacement are still

(displacement)

(force)

Therefore, by calculting the scalar product between force and displacement and equating it to the work done (4.0 J), we find:

c)

In this problem instead, the work done on the particle is negative:

As before, the force and displacement are

(displacement)

(force)

And so again, we calculate the scalar product between  force and displacement and we equate it to the work done on the particle, -1.8 J.

Doing so, we find:

c) up

hope this