Physics, Page 1

Chapter 7. Kinetic Energy andChapter 7. Kinetic Energy andWorkWork

•• One of the most important concepts in physicsOne of the most important concepts in physics– Alternative approach to mechanics

•• Many applications beyond mechanicsMany applications beyond mechanics– Thermodynamics (movement of heat)– Quantum mechanics...

•• Very useful toolsVery useful tools– You will learn new (sometimes much easier) ways to solve

problems

Physics, Page 2

You toss a ball in the air. What is the work done by gravity as

the ball goes up?A) Positive B) Negative C) Zero

What is the work done by gravity as the ball goes down?A) Positive B) Negative C) Zero

QuestionQuestion

Physics, Page 3

Example:Example:

S

Ff

W

FN

Find work done by each force. Answers:

F: FS

f: -fS

FN: 0

W: 0

Physics, Page 4

You are towing a car up a hill with constant velocity. The work done on the car by the normal force is:

1. positive2. negative3. zero

W

T

FN V

correct

because it's pointing in a positive direction

The normal force is perpendicular to the surface and because of this it points in the negative x direction

force is perpendicular to displacement

QuestionQuestion

Physics, Page 5

You are towing a car up a hill with constant velocity. The work done on the car by the gravitational force is:1. positive2. negative3. zero

It'll be positive because Fg=mg, 9.8m/s^2 will always be positive

When the car is heading up the hill the weight or gravitational force points opposite to that of the displacement, producing and angle greater than 90 degrees, producing a negative number, and negative work.

there is no displacement by gravity, so no work.

W

T

FN V

correct

QuestionQuestion

Physics, Page 6

QuestionQuestionYou are towing a car up a hill with constant velocity. The work done on the car by the tension force is:1. positive2. negative3. zero

correct

The force T is going in the direction of the displacement, so it has to be positive.

The force of the rope is going the opposite direction, in order to pull the car.

Since the car is traveling at a constant velocity it has no acceleration

W

T

FN V

Physics, Page 7

You are towing a car up a hill with constant velocity. The total work done on the car by all forces is:1. positive2. negative3. zero correct

The car is going up, is it not?Because the car wants to go in the opposite direction of the way in which it is being pulled up the hill.

W

T

FN V

QuestionQuestion

Physics, Page 8

Work and Kinetic EnergyWork and Kinetic Energy

Fr

d x

Fr

forceConstant

xx maF =

dFdmamvmvdavv xxx ==−⇒=− 20

220

2

21

212

State functions !

Physics, Page 9

EnergyEnergy

• Forms– Kinetic Energy (운동에너지) – Potential Energy (위치에너지) : 8장– Heat : 18장– Mass (E=mc2) : 37장

• Units Joules = kg m2 / s2

Physics, Page 10

운동에너지운동에너지 (Kinetic Energy) (Kinetic Energy)

단위 : Joules = kg m2 / s2

(보기문제 7-1)

Physics, Page 11

Definition of Work Definition of Work Ingredients:Ingredients: Force (FF), displacement (S)

•• Work, Work, WW, done on object by aconstant force FF acting through adisplacement S is: θ

FF

S

displace

ment

Fs

• Units:

[W] = [F][L] = N-m = Joules (J)

1 Joule = 1 Newton-meter (N-m)

θcosFssFW =⋅=rr

Physics, Page 12

Work: Energy Transfer due to ForceWork: Energy Transfer due to Force• Force to lift trunk at constant speed

–Case a Ta – mg = 0 T = mg–Case b 2Tb - mg =0 or T = ½ mg

• But in case b, trunk only moves ½ distance you pull rope.

• (F x distance) is same in both!

Ta

mg

Tb

mg

Tb

15

W = FScosθ

Physics, Page 13

Work by Constant ForceWork by Constant Force• Only component of force parallel to

direction of motion does work!W = F Δr cos θ

Fθ

Δr

F

Δr

WF > 0: 0< θ < 90 : cos(θ) > 0F

Δr

WF = 0: θ =90 : cos(θ) =0

F

Δr

WF < 0: 90< θ < 270 : cos(θ) < 0

F

W>0 W=0 W<0

Δr

WF > 0: 0> θ > -90 : cos(θ) > 018

1)

2)

3)

4)

Physics, Page 14

A box is pulled up a rough (μ > 0) incline by a rope-pulley-weight arrangement as shown below. How many forces are doing (non-zero) work on the box?

01234

QuestionQuestion

N does no work (perp. to v)

T does positive work

f does negative work

mg does negative work

vT

mg

N

f

correct

Four forces are on the box.

Physics, Page 15

일일 (Work) (Work) 일W이란물체에가해진힘을통해서외부에서물체(의에너지)로 (W > 0), 또는, 물체(의에너지)에서외부로 (W < 0) 전달되는에너지이다.

cosx xF F maφ= =

힘이한일운동에너지변화 K WΔ =

일과일과운동에너지운동에너지변화변화

일일--운동에너지운동에너지정리정리

f iK K K WΔ = − = f iK K W= +

물체의운동에너지변화량은물체에행해진알짜일과같다.

Physics, Page 16

Falling Ball ExampleFalling Ball Example• Ball falls a distance 5 meters.

What is final speed? (g = 10 m/s2)

Only force/work done by gravity

Wg = Fg h = m ½ (vf2 – vi

2)

Fg h = ½m vf2

mgh = ½m vf2

Vf = sqrt( 2 g h ) = 10 m/s

mg

Physics, Page 17

(보기문제 7-2)

Physics, Page 18

(보기문제 7-5) 중력이한일

d

cos( 90 ) singW mg d mgd mgd mghθ θ= = + = − =our ur

장력이한일

dgmWg

rr⋅=

Physics, Page 19

Work by Variable ForceWork by Variable Force• W = Fx Δx : constant force

– Work is area under F-x plot

– Spring F ~ k x : variable force• Area = ½ k x2 = Wspring

Force

Distance

Work

Force

Distance

F~kx

Work

48

Physics, Page 20

변하는변하는힘이힘이한한일일

변하는힘

Physics, Page 21

용수철용수철힘힘((복원력복원력))이이한한일일

sF kd= −ur ur

( k : 용수철상수)

복원력이 (물체에) 한일이란복원력증가할때물체의 (운동)에너지가감소,즉, 물체에서외부(용수철)로에너지가전달되므로, W < 0

Physics, Page 22

(보기문제 7-7)

( )s aF F= −ur uur

6.9a sF F N= − =ur uur

59a sW W mJ= − =

-12mm 까지이동하는동안물체에한일

W > 0 :물체가에너지를받음

Physics, Page 23

변하는변하는힘에힘에대한대한일일--운동에너지운동에너지정리정리

(일정한힘의경우와동일하게성립)f iW K K K= − = Δ

Physics, Page 24

(보기문제 7-8)

1.2md v cmk

= =

Physics, Page 25

일률일률 (Power) (Power)

P F v=ur r

Physics, Page 26

(보기문제 7-11)

Physics, Page 27

• Work = transfer of energy using force Can be positive, negative, or zeroW = F d cos(θ)

• Kinetic Energy (Motion)K = ½ m v2

• Work = Change in Kinetic EnergyΣ W = ΔK

SummarySummary