Answer

Verified

403.2k+ views

**Hint:**We know that integrating a curve in an x-y plane within the prescribed limits of x can give us the area under that curve. An integration can sum up the small area elements over the given limits to provide the final resultant area.

**Complete step by step answer:**

The force acting on the system is constant, for example, when a force of gravity and friction moves with the constant speed, therefore the force-displacement graph is just a horizontal line because force can’t change.

In this case, the area under the graph is triangular, with base length (S) that is displacement height (H). So, the area of the triangle is 0.5×base×height.

Now here in the above figure, the area under the line that is blue represents the work done by force.

Since we can say that force is a function of x, let’s say F(x) then the work is given by,

Here W is the work done, and dx is the differential distance, and when we integrate the sum of F(x)dx continually with integration, then we will get the required work done. Here 0 to x is the range of displacement within which the work is calculated.

From this formula, we calculate the mechanical work done by a constant force.

We can also use this method to calculate the work done when an object accelerates from rest to final speed (v), using a constant force F. For a constant acceleration from rest, the distance travelled can be written in terms of the average rate (V

_{av})

$\therefore {\rm{S = }}{{\rm{V}}_{{\rm{av}}}} \times {\rm{t = }}\dfrac{{{\rm{Vt}}}}{2}$

And the acceleration (a) becomes,

${\rm{a = }}\dfrac{{\rm{v}}}{{\rm{t}}}$ (Here v is velocity and t is time.)

So, the work is done, ${\rm{W = F}}{\rm{.S}}$

$ \Rightarrow {\rm{W = m}} \times {\rm{a}} \times {\rm{S = m}} \times \dfrac{{\rm{v}}}{{\rm{t}}} \times \dfrac{{{\rm{vt}}}}{2} = \dfrac{1}{2}{\rm{m}}{{\rm{v}}^2}$

So the work is done, when objects accelerate to a constant speed from rest is equal to the energy stored as kinetic energy by the conservation of energy.

**Note:**When we talk about the graph of force-displacement, it means the force is a function of some displacement. Therefore the nature of the graph and its slope will depend upon the nature of the function. No work is done along the direction of the motion if the force is perpendicular.

Recently Updated Pages

Draw a labelled diagram of DC motor class 10 physics CBSE

A rod flies with constant velocity past a mark which class 10 physics CBSE

Why are spaceships provided with heat shields class 10 physics CBSE

What is reflection Write the laws of reflection class 10 physics CBSE

What is the magnetic energy density in terms of standard class 10 physics CBSE

Write any two differences between a binocular and a class 10 physics CBSE

Trending doubts

Difference Between Plant Cell and Animal Cell

Give 10 examples for herbs , shrubs , climbers , creepers

Name 10 Living and Non living things class 9 biology CBSE

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Change the following sentences into negative and interrogative class 10 english CBSE

Write a letter to the principal requesting him to grant class 10 english CBSE

Fill the blanks with proper collective nouns 1 A of class 10 english CBSE

Write the 6 fundamental rights of India and explain in detail