PHYSICSWork, Power & Energy

How work is done

Energy Force Function

Work is done

Work is the result of force moving an object

W = f • d

{Distance

Force

{Distance

WORKWORK When a force acts on a body in such a way that When a force acts on a body in such a way that

body covers some displacement, it is called work.body covers some displacement, it is called work. *Work(W) is defined as a product of force(F) and *Work(W) is defined as a product of force(F) and

displacement(d)displacement(d)

Work can be defined as transfer of energy. Work can be defined as transfer of energy.

Work is scalar quantity. Work is scalar quantity. InSI unit of work is Joule( J ). J=N×mInSI unit of work is Joule( J ). J=N×m If force makes an angle with the direction of motion, then If force makes an angle with the direction of motion, then

for finding work done, that component of force will be for finding work done, that component of force will be taken which acts in the direction of motion(Fcostaken which acts in the direction of motion(Fcos ) .W=F ) .W=F coscos dd

W=F cosW=F cos dd

dF

F

d

W= F×d

W = F× d

TYPES OF WORKTYPES OF WORK (A) When direction of force and (A) When direction of force and

displacement is same the work done is displacement is same the work done is positivepositive

(B) When direction of force and (B) When direction of force and displacement is opposite the work done is displacement is opposite the work done is negative.negative.

(C) When force and displacement are (C) When force and displacement are mutually perpendicular to each other the mutually perpendicular to each other the work done is zero.work done is zero.

F d

F d

F d

Perpendicular forcePerpendicular force

Since cos Since cos ΘΘ = 0, = 0, F*d* F*d* ΘΘ = 0 = 0No work done!No work done!

REMEMBER!REMEMBER!A vertical force A vertical force

CANNOT cause CANNOT cause horizontal horizontal displacement!displacement!

Cos Θ = 0 when Θ = 90 degrees

• Man does positive work lifting box

• Man does negative work lowering box

• Gravity does positive work when box lowers

• Gravity does negative work when box is raised

Although it takes less force for car A to get the top of the ramp ,but all cars do the same amount of work.

POWERPOWERIn unit time Work performed is termedIn unit time Work performed is termedpowerpower..Power is a measure of how quickly work Power is a measure of how quickly work

can be donecan be doneP=W/t.(P=Power,W=Work,t=Time)P=W/t.(P=Power,W=Work,t=Time)Unit of power is watt (J/s).Unit of power is watt (J/s).Power is scalar quantity.Power is scalar quantity.Other common unit of Power is horse Other common unit of Power is horse

power(hp)power(hp)1hp= 746 watt.1hp= 746 watt.

P = W/ t But W = F . dP = F .d /t But d/t = V Then P = F . VSo power is product of force & velocity.

ENERGY

Mechanical Non- Mechanical

Kinetic Potential

Linear

Rotational

Gravitational

Elastic

Electric

Magnetic

Light

Sound

Heat

ENERGYENERGYCapability of doing work is called EnergyCapability of doing work is called Energy..In SI units energy is measured in Joule(J).In SI units energy is measured in Joule(J).Energy is scalar quantity.Energy is scalar quantity.There are two basic kinds of energy.There are two basic kinds of energy.Kinetic Energy(K.E).Kinetic Energy(K.E).Potential Energy(P.E).Potential Energy(P.E).

Other forms of energy are as under:-Other forms of energy are as under:-

(Electrical,Mechanical,Light,Sound,(Electrical,Mechanical,Light,Sound,

Chemical,Thermal,Nuclear,Geo-Chemical,Thermal,Nuclear,Geo-thermal,Tidal,Magnetic,Solar e.t.c.)thermal,Tidal,Magnetic,Solar e.t.c.)

POTENTIAL ENERGYPOTENTIAL ENERGY Definition=Capacity to perform work by a body due Definition=Capacity to perform work by a body due

to its position or state or condition is termed to its position or state or condition is termed potential energy (P.Epotential energy (P.E))

Examples=Bullet loaded in a gun & water stored in a Examples=Bullet loaded in a gun & water stored in a dam have potential energydam have potential energy

The P.E possessed by a body in the gravitational The P.E possessed by a body in the gravitational fields is called gravitational P.E.fields is called gravitational P.E.

Derivation of equation of Gravitational Potential Derivation of equation of Gravitational Potential energyenergy..

W=FW=Fd. But F=W(Weight) & d=h (Height)d. But F=W(Weight) & d=h (Height) W=wW=wh. But W=mgh. But W=mg W=mgh. ButW(work)=P.EW=mgh. ButW(work)=P.E P.E = mghP.E = mgh P.E=Potential energy( Gravitational)P.E=Potential energy( Gravitational) g=Acceleration due to gravityg=Acceleration due to gravity m= Mass, h= Heightm= Mass, h= Height

B

A

m

m

Height

Elastic Potential EnergyElastic Potential Energy

Definition:-Definition:- It is stored as a result of It is stored as a result of deformation of an elastic object, such as deformation of an elastic object, such as stretching of springstretching of spring..

Explanation:-Explanation:-The force that is applied on object is stored as its The force that is applied on object is stored as its elastic potential energy, which helps the object to restore its initial elastic potential energy, which helps the object to restore its initial position.position.

According to Hooke’s law F = k XAccording to Hooke’s law F = k X

Average force required for displacement( X ) is F/2.Average force required for displacement( X ) is F/2.

Hence work done for displacement isHence work done for displacement is

W (work ) = F/2 × X But F = kXW (work ) = F/2 × X But F = kX

EP = W = kX/2 × X = ½ kX2EP = W = kX/2 × X = ½ kX2

EP = ½ k X2EP = ½ k X2

EP= Elastic P.E, K= Spring constant, X= Extension of spring.EP= Elastic P.E, K= Spring constant, X= Extension of spring.

KINETIC ENERGYKINETIC ENERGY Definition=Energy produced by a body due to its motion is called Definition=Energy produced by a body due to its motion is called

Kinetic energy(K.EKinetic energy(K.E)) Examples=Bullet fired from a gun& Water flowing from dam have Examples=Bullet fired from a gun& Water flowing from dam have

Kinetic energy.Kinetic energy. Derivation of equation of kinetic energy.Derivation of equation of kinetic energy.

As 2as=VAs 2as=Vff22 – V – VII

22 .But V .But VI I = o m/s & V= o m/s & Vf f = V= V

Then 2as =V Then 2as =V 22

Or ” S” = V Or ” S” = V 2 2 As ” F “= m a As ” F “= m a 2a2a Put value of “S” & “F “ in below equation.Put value of “S” & “F “ in below equation. As W = F × SAs W = F × S W = m. a × V W = m. a × V 2 2 = m V = m V 22 . But W = K.E So K.E = mV . But W = K.E So K.E = mV22

2a 2 22a 2 2

FSm m

V i V f

LAW OF CONSERVATION OF LAW OF CONSERVATION OF ENERGYENERGY

Statement=Energy is neither created nor destroyed, but one Statement=Energy is neither created nor destroyed, but one form of energy is converted into an other form of energy, so form of energy is converted into an other form of energy, so total energy of the system remains constant.total energy of the system remains constant.

ExplanationExplanation= In an isolated system from the motion of the = In an isolated system from the motion of the pendulum above law of conservation of energy is proved in pendulum above law of conservation of energy is proved in following way.following way.

P.E=100J

K.E= OJ

P.E= O JK.E = 100 J

A

B

Ch

At point AAt point A Suppose: m=2Kg , g=10m/ sSuppose: m=2Kg , g=10m/ s22 ,h= 5m ,h= 5m As P.E = mgh As P.E = mgh P.E = 2P.E = 210 10 5 = 100 5 = 100 P.E = 100 J(At point A )P.E = 100 J(At point A ) Suppose: V = O m/ s Suppose: V = O m/ s 22

As K.E = mV As K.E = mV 22 = 2 = 2 0 0 0 = 0 0 = 0 2 22 2 K.E = 0 J ( At point A )K.E = 0 J ( At point A )

Total energy at point A = 100 J(P.E ) + 0 J ( K.E )= 100 JTotal energy at point A = 100 J(P.E ) + 0 J ( K.E )= 100 J

At point BAt point B

Suppose: m = 2mg , g = 10 m / s Suppose: m = 2mg , g = 10 m / s 22 ,h = 0m. ,h = 0m. As P.E = mghAs P.E = mgh P .E = 2 P .E = 2 10 10 0 = 0 0 = 0 P.E = 0JP.E = 0J Suppose: m = 2 Kg , V = 10 m/ s Suppose: m = 2 Kg , V = 10 m/ s 22

K.E = m V K.E = m V 22 = 2 = 2 10 10 10 = 100 J 10 = 100 J 2 22 2 K .E = 100 JK .E = 100 J Total energy at point B = 0J (P.E )+ 100 J ( K .E )= 100JTotal energy at point B = 0J (P.E )+ 100 J ( K .E )= 100J

Hence it is proved that at point A and B total energy Hence it is proved that at point A and B total energy is 100J (Remains constant)is 100J (Remains constant)

though energy from one form to another though energy from one form to another changes(P.E toK.E )changes(P.E toK.E )

KE=Kinetic Energy, EE= Energy Efficiency, GP= Gravitational potential Energy.

Thanks *****