Page 5 - LN

For example, when we push hard against a wall, the force we are
exerting on the wall does no work, because in this case the
displacement of the wall is d = 0. However, in this process, our muscles
are using our internal energy and as a result we get tired.

o If the force and displacement are perpendicular to each other, the work
done is zero.

Displacement at an angle to the force

o To understand this let us consider a block of mass m sliding on an
inclined surface as shown below in the figure.

o Now the object moves along the inclined surface from point P to Q. So,
its displacement would be PQ. The force acting on this block due to
force of gravity would be
F=mg
which acts in vertically downwards direction.
o Now here our problem is to find the work done by the gravitational
force in moving the block from point P to point Q.
o When the block moves from point P to Q, it comes down through a
height PR. So here we can also say that the object is displaced in the
vertically downwards direction through a distance PR and at the same
time it is also displaced horizontally through a distance RQ. Since the
displacement in the direction of force is PR, the work done would be
W=mg(PR)=mg(PQcosθ)
o If displacement d of any object makes an angle θ with the force F
o F acting on it as shown below in the figure, then the work done by the
force is