Question

Show that work done by varying force is given by area under fs graph ?​

Answer 1

Answer:

Example: A force acts on a body and displaces it in it's direction. The graph

shows the relation between the force and displacement. The work done by the force is:

Work done by force =∫F.ds =Area under F.s graph=Area of △

=

2

1

×base×height

=

2

1

×(14−2)×60

=360

Answer 2

Explanation:

Work done by a force is given by the formula = $F.S$

where, $F$ represents the force

and $S$ represents the displacement.

Now, For a varying force, Let's say we get a curve as shown in the figure.

Then, for an infinitesimal displacement, we can take the force to be constant.

So, small work done by the force to vary the distance of the object from $s$ to $s+ds$ is, $dW = \int\limits^{s+ds}_s {F}. \, ds$

Now, Integrating force over the whole curve will give us the total work done, i.e,

$\int dW =\int{F} \, ds$

$W=\int \limits^a_b {F} \, ds$

We know, from the mathematics that, right-hand side of the equation is the ara under the curve.

So, work done = Area under the Force-displacement curve.

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