**Work Energy And Power Concept** is an important topic in Physics. Because this chapter deals with new concept. Through which some mechanics difficult problem is easy to solve. So learn here easy mechanics concept. Because you have studies in mechanics, these equations v = dx/dt, a = dv/dt and F= ma so far. And these equation are very powerful to solve any mechanics problems. But it is important to note.

Some mechanics problem is difficult to solve using above equations. Because it is complicated and become long derivation. And using work energy and power new concept it is easy to solve the problems. Therefore work energy and power concept is very important to understand.

## Work power and Energy definition

Hence I like to tell you the one fact about this topic. Do You know scientist Newton ? Well i hope you know. He was a great scientist. He had discovered many laws in Physics and invented calculus. What do you think ? Which equations Newton use to solve mechanics problems ?.

Well he was using equations v = dx/dt, a = dv/dt and F= ma, to solve each mechanics problem. Because that time new equation was not derived. Therefore later on after Newton, other scientist derived a new equation. By using these v = dx/dt, a = dv/dt and F= ma equations.

Hence the new equation is very powerful equation, to solve mechanics problem. And that equation you learn in this chapter. So this is very good chapter for you. Because after study this new equation concept. You will be able to solve, some difficult problem in one line easily. So now lets start.

### Why work done is dot product of force and displacement ?

Well first i like to explain work definition. “Work is done, When force is applied and displacement takes place”. This is the simple definition of work. Hence important point is, how force is applied on the body. So there are two method to apply force on any body. Which is explained below.

**Contact force** (Which is directly apply on body by touching the body. like you are pushing or pulling body touching it by your hand). And this is called contact force.

**Field force** (It is non touching force, which is applied by the fields. For example gravitational, electrostatic, and magnetic field ). So this type of force is called field force.

So any method can apply force on body. Now next important point is, its point of application. In other words, at what point force is applied. Hence from that point, you need to calculate displacement. Therefore mathematical work done formula is W = F.S = Fscosθ.

#### Work done by different forces

Which is called dot product of force and displacement. And θ is angle between force and displacement. Hence work is a scalar quantity. And work is a form of energy.

When work is done by an object, then it losses energy. And when work is done on an object, then it gains energy. Therefore work is transformation of energy. So work unit is joule. Which is same unit of energy. Now i hope, you know energy is conserved. And it can neither be created nor be destroy. So what, it can only be transfer one form to other form.

Hence energy transformation does’t depend upon the frame of reference. If you change the frame of reference. But actual energy transfer, can be observed from any frame of reference. And energy is also a scalar quantity. So this is reason, why work is dot product of force and displacement.

### Why work done is not cross product ?

If work is cross product of force and displacement. Then work will be a vector quantity. And energy transfer is observed different from different frame of reference. Which is contradiction of energy transfer and work done. So work done is not cross product of force and displacement.

**How many Type of forces ? **There are two types of forces. And these two type of forces, are very important concept about force. Hence you must know the difference between these two forces. So that you can better understand work done concept. Therefore see the below two types of forces and their difference.

**What is conservative force ?**

The work done by such force, Which does’t depend upon the path, but only depend upon the initial and final point, Such forces are called conservative forces. So for example gravitational force, spring force and electrostatic force are conservative forces. Because work done by these forces does’t depend upon the path. Therefore see the gravitational force picture.

#### Work done example conservative and non conservative force

Suppose a mass m is bring through path A to C, Then how much work done by gravitational force. Work done Wac = Fscos(90+θ) = -mglsin(θ). Now again calculate work done by gravitational force by path AB to BC. So in this case work done during AB path is zero. Because mg force and displacement

are perpendicular.

And work done during path BC is -mglsin(θ). So in this case force and displacement are anti-parallel. Hence work done is negative. Therefore work done by gravitation force is equal in both the path A to C and AB to BC. So it is clear that, gravitational force work done is not depending upon path.

Hence it is called Conservative force.

#### What is work done by conservative force ?

So one important conclusion. Work done by conservative force in a closed path is always zero. But can you think why ? well it is because of, initial and final position is same in closed path. And you know Conservative force depend upon initial and final point. So work done is always zero in closed path by conservative force.

Now i want to ask a question. If displacement is zero, What is work done ? Do you know ? Well you study in Physics if anywhere displacement is zero. Then work done is always zero.

But this is not always true. So you must know this is only true, in case of conservative force. And it is not true in case of non conservative force.

**What is work done by non conservative force ?**

A force which is not conservative is non conservative force. So a non conservative force does’t depend upon initial and final point. But its depend upon the path taken. See the picture of non conservative friction force.

Hence a block of mass m is moving from A to B. Then work done by friction force is (-frs). Here negative sign is because of friction force and displacement are in opposite direction. Now again block is moving from B to C, which is same distance in close path. Hence work done by friction force is (-frs).

So total work done is (-2frs) by friction force . Therefore in close path non conservative force work done is not zero. Whereas its initial and final point is same. And block displacement is zero. But work done is not zero by friction .

Therefore this is confirm that, if displacement is zero. But it is not necessary work done is zero. Because friction force is non conservative force. Now i hope that, your concept is clear for conservative and non conservative force .

**How do you find given force is conservative or non conservative ?**

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Suppose a force F = xi^ +yj^ is given, Then can you tell me this force is conservative or non conservative. So to check this force, you need to apply some method. Which is given below.

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First you write the force in this form F = Fxi^ + Fyj^ +Fzk^ . Then check the partial differentiation like this.

- ∂Fx/∂y = ∂Fy/∂x
- ∂Fx/∂z = ∂Fz/∂x
- ∂Fy/∂z = ∂Fz/∂y

If above all three condition is satisfied. Then given force is a conservative force. And if above any one condition is not satisfy. Then it is a non conservative force . I hope you know the partial differentiation . If you take Fx component then other Fy and Fz is treated as constant.

Hence lets check F = xi^ + yj^ . Now compare with above equation Fx = x , Fy = y and Fz = 0

∂Fx/∂y = ∂x/∂y = 0 ( Because x will look like constant with respect to y).

∂Fy/∂x = ∂y/∂x = 0 ( Here y will look like constant with respect to x ).

So similarly you can check .

∂Fx/∂z = ∂Fz/∂x = 0 and ∂Fy/∂z = ∂Fz/∂y = 0 . Therefore all three equation is satisfying . Hence given force

F = xi^ + yj^ is a conservative force.

Q A force F = 5i^ + 8yj^ acts on a body and follows the path coordinate O(0,0), A(0,a), B(a,a) and C(a,0). Then calculate the net work done .

This question is for you . Solve yourself what do you think to take first step. Hints first you should check this is a closed path. So check about force conservative or non conservative and proceed further.

#### Work Energy theorem

Work Energy theorem is states that, “Work done by all the forces on a body, is equal to change in kinetic energy of the body”. This is simple definition of work energy theorem. Hence in this theorem all the forces are included . Whether it is internal, external, conservative or non conservative forces. But you are required to include all the forces.

Therefore if work done is positive, Then kinetic energy of the body is increases. Suppose any body is moving slowly. And then you apply a force on the body in the moving direction. After that velocity of body is increases. Therefore kinetic energy is also increases.

And If work done is negative. Then kinetic energy is decreases. Because you are applying force in opposite direction of motion, So velocity of body is decreases and therefore kinetic energy is decreases.

Hence in mathematical form. work energy theorem is written like this.

(Wc + Wnc + We + Wi + ……..) = ΔKE or ( Work done by all forces ) = (KEf – KEi ) . Now it is also written the equation in differential form .

(dW by all forces ) = d(KE) ( for very small work done and change in kinetic energy ). So this is new equation ,through which you are able to calculate work done.

Hence now you have two formula for work done calculation. Which is given below.

F = Fscosθ and ( Work by all forces ) = ΔKE.

##### How to Solve Work Energy And Power Questions

See the above question. Here force is not given. But you are ask to find the work done. So how you calculate work done ? Well you are having second equation for work energy theorem . So apply this formula and easily find out work done.

Hence Work (w) = ( Change in kinetic energy ) or W = ΔKE .

Therefore W = (KEf – KEi ) so here Initial velocity is vi = 10m/s and final velocity is vf = 0m/s. Now use the equation W = 1/2mvf² – 1/2mvi² = 0 – 1/2 (5×10²) = 0- 500/2 = -250J .

So work done W = -250J ( here work done is negative because velocity is decreasing ) . Hence you see how powerful is work energy theorem. And numerical problem is easily solved by this equation.

###### Relation between Work Energy And Power formulas

Work energy and power formula is very important. So here is relation between work and energy formula. Which is given by W = ΔKE .

**What is power** ?

Power is rate of doing work. Hence in other words, how fast work is done that is called power of the system . So mathematically, it is define as power P = Δw/Δt or dw/dt or W = Pt .

- Δw/Δt ( Average power)
- dw/dt ( Small variable power)
- W = Pt ( Constant power )

Therefore relation between work energy and power is W = pt = ΔKE .

If you want to learn more about work energy and Telecom technology. So you refer my previous post. link is given below.

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I will continue with more hidden concept of Physics topic. You feedback is important . If you have any doubt can ask through mail .And hope that you enjoyed learning **Work Energy And Power. **Thanks for like and share in social media.