CHAPTER-8

Potential Energy and Conservation of Energy

8-1 Potential Energy

Potential Energy U: energy associated with the configuration of a system of objects that exerts force on one another.

Gravitational Potential Energy Ug: energy associated with the separation between two objects that attracts each other by gravitational force.

Elastic Potential Energy Us: energy associated with the compression or extension of an elastic object.

Ch 8-2 Work and Potential Energy

Kinetic (K) and Gravitational Potential energy (Ug) of tomato-earth system

Negative work Wg done by gravitational force in the rise of tomato in transferring K (decreasing) into Ug (increasing) of tomato

Positive work Wg done by gravitational force in the fall of tomato in transferring Ug (decreasing) into K (increasing) of tomato.

Ug =- Wg or - Ug = Wg

Kinetic (K) and Elastic Potential energy (Us ) of block-spring system

Negative work Ws done by spring force in the rightward motion transferring K (decreasing) of block into Us (increasing) of spring

Positive work Ws done by spring force in the leftward motion transferring Us

(decreasing) of spring into K (increasing) of block.

Us =- Ws or - Us = Ws

Ch 8-2 Work and Potential Energy

Ch 8-2 Conservative and NonconservativeForces

System contains two or more objects including a point-like objects (tomato or block)

A force acts between point-like object and rest of the system

When the configuration change force does work W1, changing kinetic energy K of the object and other type of energy of the system

When the configuration change reversed, force reverse the energy transfer and does work W2

Conservative Force: W1=-W2

Nonconservative Force: W1-W2

Ch 8-3 Path Independence of Conservative

Forces The net work done by a

conservative force on a particle moving around any closed path is zero.U=-W=0Ui=Uf (cylic process)

The work done by a conservative force on a paticle moving between two points does not depends on the path

Wab1=Wab

Ch 8 Check Point 1

• The figure below show three paths connecting points a and b. A single force F does the indicated work on a particle moving along each path in the he indicated direction. On the basis of this information is the force conservative?

• Non-conservative force

Ch 8-4: Determining Potential Energy Values

Work done by a conservative force F

W=xi

xf

F (x) dx but U =- W , then

U =- W =- xi

xf

F (x) dx

Gravitational Potential Energy Ug:

Ug=-yi

yf

-mg dy= mg(yf-yi); Ug(y)= mgy

Elastic Potential Energy Us:

US=-yi

yf

-kx dx= k(xf2-xi

2)/2; Us(y)=(kx2)/2

Ch 8 Check Point 2•A particle to move along an x-axis from x=0 to x=x1., while a conservative force , directed along the x-axis, acts on the particle. The figure shows three situations , in which the x component of that force varies with x. The force has same maximum magnitude F1 in all three situations. Rank the the situation according to the change in the associated potential energy during the particle motion , most positive first

U= -Fxdx

Calculate area under the curve

1) U=-(Fi X1)/2

2) U=-(Fi X1)

3) U=-[-(Fi X1)/2]= FiX1/2

Ans: 3, 1, 2

Ch 8-5: Conservation of Mechanical Energy

Mechanical energy Emec: Emec=K+U

In an isolated system where only conservatives forces cause energy change Emec is conserved

K=W; U =-W then K=-U

Kf-Ki=-(Uf-Ui)=Ui –Uf

Kf+Uf =Ki+Ui

Emec-f = Emec-i

Emec=0

Ch 8-7: Work Done on a System by an External force

Work Wa is energy transfer to or from a system by means of an external force acting on that system

Work done on a system , no friction involved (Ball –Earth system)

Wa=K+U= Emec

Ch 8-7: Work done on a system by an external force

Work done on a system , friction involved (Block–floor system)

F-fk=ma;

v2=v02+2ad; a=(v2-v0

2)/2d

F=fk+ma= fk+m(v2-v02)/2d

Wa =Fd=fkd+m(v2-v02)/2

Wa =fkd +K= Eth + Emec

Eth=fkd

Wa=K+U= Emec

Ch 8-8 Conservation of Energy

Total energy E= Emec+Eth+Eint

The total energy E of a system can change only by amounts of energy W that are transferred to or from the system

W=E= Emec+ Eth+ Eint , W is work done on the system.

Isolated System: The total energy E of an isolated system cannot be changed then

E= Emec+ Eth+ Eint=0

Emec-f-Emec-i + Eth+ Eint=0

Emec-f= Emec-i - Eth- Eint