• • One of the most important concepts in physics One of the most important concepts in physics

Chapter 7. Kinetic Energy and Chapter 7. Kinetic Energy and

Work Work

• • One of the most important concepts in physics One of the most important concepts in physics

– Alternative approach to mechanics

• • Many applications beyond mechanics Many applications beyond mechanics

– Thermodynamics (movement of heat) – Quantum mechanics...

• • Very useful tools Very useful tools

– You will learn new (sometimes much easier) ways to solve problems

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

Question

Question

Example:

Example:

S f F

W F_N

Find work done by each force. Answers:

F: FS f: -fS F_N: 0 W: 0

You are towing a car up a hill with constant velocity.

The work done on the car by the normal force is:

1. positive 2. negative 3. zero

W

T F

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

Question

Question

You are towing a car up a hill with constant velocity.

The work done on the car by the gravitational force is:

1. positive 2. negative 3. 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

W

T F

Question

Question

Question Question

You are towing a car up a hill with constant velocity.

The work done on the car by the tension force is:

1. positive 2. negative 3. 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

F

You are towing a car up a hill with constant velocity.

The total work done on the car by all forces is:

1. positive 2. negative

3. 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 F

Question

Question

Work and Kinetic Energy Work and Kinetic Energy

F r

d x

F r force Constant

x

x

ma

F =

d F d

ma mv

mv d

a v

v

−

=

⇒

−

=

=

2

1 2

2 1

State functions !

Energy Energy

• Forms

– Kinetic Energy (운동에너지) – Potential Energy (위치에너지) : 8장 – Heat : 18장

– Mass (E=mc

) : 37장

• Units Joules = kg m

/ s

운동에너지

운동에너지 (Kinetic Energy) (Kinetic Energy)

단위 : Joules = kg m² / s²

(보기문제 7-1)

Definition of Work Definition of Work

Ingredients:

Ingredients: Force (FF), displacement (S)

•• Work, WWork, W, done on object by a constant force FF acting through a

displacement S is: θ

FF

S

displacement F_s

• Units:

[W] = [F][L] = N-m = Joules (J) 1 Joule = 1 Newton-meter (N-m)

θ

cos Fs

s F

W = r r ⋅ =

Work: Energy Transfer due to Force Work: Energy Transfer due to Force

• Force to lift trunk at constant speed

–Case a T

– mg = 0 T = mg

–Case b 2T

- 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!

T

T

T

W = FScos θ

Work by Constant Force Work by Constant Force

• Only component of force parallel to direction of motion does work!

¾ W = F Δr cos θ

F θ

Δr

F

Δr

W

> 0: 0< θ < 90 : cos(θ) > 0

F

Δr

W

= 0: θ =90 : cos(θ) =0

F

Δr

W

< 0: 90< θ < 270 : cos(θ) < 0

W>0 W=0 W<0

Δr

> 0: 0> θ > -90 : cos(θ) > 0

1)

2) 3) 4)

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?

0 1 2 3 4

Question Question

N does no work (perp. to v) T does positive work

f does negative work mg does negative work v

T

N

f correct

Four forces are on the box.

일 일 (Work) (Work)

일 W 이란

물체에 가해진 힘을 통해서

외부에서 물체(의 에너지)로 (W > 0),

또는, 물체(의 에너지)에서 외부로 (W < 0) 전달되는 에너지이다.

x cos x

F = F φ = ma

힘이 한일 운동에너지

변화

Δ = K W

일과

일과

운동에너지

변화

일

일 -운동에너지

정리

물체의 운동에너지 변화량은 물체에 행해진 알짜일과 같다.

Falling Ball Example Falling Ball Example

• Ball falls a distance 5 meters.

What is final speed? (g = 10 m/s

)

Only force/work done by gravity

W

= F

h = m ½ (v

– v

) F

h = ½m v

mgh = ½m v

V

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

mg

(보기문제 7-2)

(보기문제 7-5)

d

cos( 90 ) sin

Wg =mgur urd = mgd θ + ^o = −mgd θ = mgh

장력이 한 일

d g m

W

= r⋅ r

Work by Variable Force Work by Variable Force

• W = F

Δx : constant force

– Work is area under F-x plot

– Spring F ~ k x : variable force

• Area = ½ k x

= W

Force

Distance

Work

Force

Distance F~ kx

Work

변하는 변하는 힘이 힘이 한 한 일 일

변하는 힘

용수철 용수철 힘 힘 (복원력 ( 복원력 )이 ) 이 한 한 일 일

F

= − k d

ur ur

( k : 용수철 상수)

복원력이 (물체에) 한 일이란 복원력 증가 할 때

물체의 (운동)에너지가 감소, 즉, 물체에서 외부(용수철)로 에너지가 전달되므로,

W < 0

(보기문제 7-7)

(

)

6.9

a s

F = − =F N ur uur

a s 59

W = −W = mJ

-12mm 까지 이동하는 동안 물체에 한 일

W > 0 :

물체가 에너지를 받음

변하는 변하는 힘에 힘에 대한 대한 일 일 -운동에너지 - 운동에너지 정리 정리

(보기문제 7-8)

m 1.2

d v cm

= k =

일률 일률 (Power) (Power)

(보기문제 7-11)

• Work = transfer of energy using force

¾Can be positive, negative, or zero

¾W = F d cos(θ)

• Kinetic Energy (Motion)

¾K = ½ m v

• Work = Change in Kinetic Energy

¾Σ W = ΔK

Summary

Summary