Physics 211: Lecture 9, Pg 1

Physics 111: Lecture 9

Today’s Agenda

Work & Energy

Discussion

Definition

Work of a constant force

Work/kinetic energy theorem

Work of multiple constant forces

Comments

Physics 211: Lecture 9, Pg 2

Work & Energy

One of the most important concepts in physics

Alternative approach to mechanics

Many applications beyond mechanics

Thermodynamics (movement of heat)

Quantum mechanics...

Very useful tools

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

Physics 211: Lecture 9, Pg 3

Forms of Energy

Kinetic: Energy of motion.

A car on the highway has kinetic energy.

We have to remove this energy to stop it.

The brakes of a car get HOT!

This is an example of turning one form of energy into another (thermal energy).

Physics 211: Lecture 9, Pg 5

Energy Conservation

Energy cannot be destroyed or created.

Just changed from one form to another.

We say energy is conserved!

True for any closed system.

i.e. when we put on the brakes, the kinetic energy of the car is turned into heat using friction in the brakes. The total energy of the “car-brakes-road-atmosphere” system is the same.

The energy of the car “alone” is not conserved...

» It is reduced by the braking.

Doing “work” on an isolated system will change its “energy”...

Returning

Can

Physics 211: Lecture 9, Pg 6

Definition of Work:

Ingredients: Force (F), displacement (r)

Work, W, of a constant force F

acting through a displacement r

is:

W = F r = F r cos = Fr r

F

r Fr

“Dot Product”

Physics 211: Lecture 9, Pg 7

Definition of Work...

Only the component of F along the displacement is doing work.

Example: Train on a track.

F

r

F cos

Hairdryer

Physics 211: Lecture 9, Pg 12

Back to the definition of Work:

Work, W, of a force F acting

through a displacement r is:

W = F r F

r

Inclined Plane

Physics 211: Lecture 9, Pg 13

Lecture 9, Act 1 Work & Energy

A box is pulled up a rough (m > 0) incline by a rope-pulley-weight arrangement as shown below.

How many forces are doing work on the box?

(a) 2

(b) 3

(c) 4

Physics 211: Lecture 9, Pg 14

Lecture 9, Act 1 Solution

Physics 211: Lecture 9, Pg 15

Work: 1-D Example (constant force)

A force F = 10 N pushes a box across a frictionless floor for a distance x = 5 m.

x

F

Work done by F on box :

Physics 211: Lecture 9, Pg 16

Units:

N-m (Joule) Dyne-cm (erg)

= 10-7 J

BTU = 1054 J

calorie = 4.184 J

foot-lb = 1.356 J

eV = 1.6x10-19 J

cgs other mks

Force x Distance = Work

Newton x

[M][L] / [T]2

Meter = Joule

[L] [M][L]2 / [T]2

Physics 211: Lecture 9, Pg 17

Work & Kinetic Energy:

A force F pushes a box across a frictionless floor for a distance x. The speed of the box is v1 before the push and v2 after the push.

x

F

v1 v2

i

m

Physics 211: Lecture 9, Pg 18

Work & Kinetic Energy...

Since the force F is constant, acceleration a will be constant. We have shown that for constant a:

v22 - v1

2 = 2a(x2-x1) = 2ax.

multiply by 1/2m: 1/2mv22 - 1/2mv1

2 = max

But F = ma 1/2mv22 - 1/2mv1

2 = Fx

x

F

v1 v2

a

i

m

Physics 211: Lecture 9, Pg 19

Work & Kinetic Energy...

So we find that

1/2mv2

2 - 1/2mv12 = Fx = WF

Define Kinetic Energy K: K = 1/2mv2

K2 - K1 = WF

WF = K (Work/kinetic energy theorem)

x

F a

i

m

v2 v1

Physics 211: Lecture 9, Pg 20

Work/Kinetic Energy Theorem:

{Net Work done on object}

=

{change in kinetic energy of object}

KWnet

12 KK

2

1

2

2 mv2

1mv

2

1

We’ll prove this for a variable force later.

Physics 211: Lecture 9, Pg 21

Lecture 9, Act 2 Work & Energy

Two blocks have masses m1 and m2, where m1 > m2. They are sliding on a frictionless floor and have the same kinetic energy when they encounter a long rough stretch (i.e. m > 0) which slows them down to a stop. Which one will go farther before stopping?

(a) m1 (b) m2 (c) they will go the same distance

m1

m2

Physics 211: Lecture 9, Pg 22

Lecture 9, Act 2 Solution

m

Physics 211: Lecture 9, Pg 23

Lecture 9, Act 2 Solution

m

Physics 211: Lecture 9, Pg 24

Lecture 9, Act 2 Solution

m

Physics 211: Lecture 9, Pg 25

A simple application: Work done by gravity on a falling object

What is the speed of an object after falling a distance H, assuming it starts at rest?

H

v0 = 0

Physics 211: Lecture 9, Pg 26

What about multiple forces?

Suppose FNET = F1 + F2 and the

displacement is r.

The work done by each force is:

W1 = F1 r W2 = F2 r

WTOT = W1 + W2

= F1 r + F2 r

= (F1 + F2 ) r

WTOT = FTOT r It’s the total force that matters!!

FNET

r F1

F2

Physics 211: Lecture 9, Pg 27

Comments:

Time interval not relevant

Run up the stairs quickly or slowly...same W

Since W = F r

No work is done if:

F = 0 or

r = 0 or

= 90o

Physics 211: Lecture 9, Pg 28

Comments...

W = F r

No work done if = 90o.

No work done by T.

No work done by N.

T

v

v

N

Physics 211: Lecture 9, Pg 29

Lecture 9, Act 3 Work & Energy

An inclined plane is accelerating with constant acceleration a. A box resting on the plane is held in place by static friction. How many forces are doing work on the block?

a

(a) 1 (b) 2 (c) 3

Physics 211: Lecture 9, Pg 30

Lecture 9, Act 3 Solution

a

Physics 211: Lecture 9, Pg 31

Lecture 9, Act 3 Solution

a

Physics 211: Lecture 9, Pg 32

EXTRA EXAMPLE 1

Return to ACT 2:

m

Physics 211: Lecture 9, Pg 33

EXTRA EXAMPLE 2a

Consider an inclined plane with no friction:

Physics 211: Lecture 9, Pg 34

EXTRA EXAMPLE 2a

Consider an inclined plane with no friction:

Physics 211: Lecture 9, Pg 35

EXTRA EXAMPLE 2b

Consider an inclined plane with friction:

Physics 211: Lecture 9, Pg 36

EXTRA EXAMPLE 2b

Consider an inclined plane with friction:

Physics 211: Lecture 9, Pg 37

EXTRA EXAMPLE 2c

Consider an inclined plane with friction:

Physics 211: Lecture 9, Pg 38

EXTRA EXAMPLE 2c

Consider an inclined plane with friction:

Physics 211: Lecture 9, Pg 39

Recap of today’s lecture

Work & Energy (Text: 6-1 and 7-4)

Discussion

Definition (Text: 6-1)

Work of a constant force (Text: 7-1 and 7-2)

Work/kinetic energy theorem (Text: 6-1)

Properties (units, time independence, etc.)

Work of a multiple forces

Comments