Page 3 - 11-phy-4 Work and Energy

4. Work and Energy eLearn.Punjab

The force displaces the object from position A to B through a displacement d (Fig. 4.1).
We define work W done by the force F as the scalar product of
F and d.

W = F.d = Fd cos q .......... (4.1)

= (F cos q ) d

The quantity (F cos q ) is the component of the force in the
direction of the displacement d.

Fig.4.1

The work done on a body by a constant force is defined as
the product of the magnitudes of the displacement and the
component of the force in the direction of the displacement.

Can you tell how much work is being done? Fig.4.2(a)
Fig.4.2(b)
(i) On the pail when a person holding the pail by the force F is
moving forward (Fig. 4.2 a).

(ii) On the wall (Fig. 4.2 b)?

When a constant force acts through a distance d, the event can
be plotted on a simple graph (Fig. 4.3). The distance is normally
plotted along x-axis and the force along y-axis. In this case as
the force does not vary, the graph will be a horizontal straight
line. lf the constant force F (newton) and the displacement
d (metre) are in the same direction then the work done is Fd
(joule). Clearly shaded area in Fig. 4.3 is also Fd. Hence the area
under a force- displacement curve can be taken to represent
the work done by the force. In case the force F is not in the
direction of displacement, the graph is plotted between F cosq
and d.

Fig.4.3

3 v: 1.1