Work Energy

Energy is Conserved

- Energy is Conserved meaning it can not be

created nor destroyed - Can change form
- Can be transferred
- Total Energy does not change with time.
- This is a BIG deal!

Energy

- Forms
- Kinetic Energy Motion (Today)
- Potential Energy Stored (Wednesday)
- Heat later
- Mass (Emc2) 1161
- Units Joules kg m2 / s2

Work

The definition of work, when the force is

parallel to the displacement

(7-1)

SI work unit newton-meter (Nm) joule, J

Typical Work

Positive Negative Work

Work done may be positive, zero, or negative,

depending on the angle between the force and the

displacement

Force at an Angle Work

If the force is at an angle to the displacement

(7-3)

Only the horizontal component of the force

does any work (horizontal displacement).

Work by Constant Force at Angle

- You pull a 30 N chest 5 meters across the floor

at a constant speed by applying a force of 50 N

at an angle of 30 degrees. How much work is done

by the 50 N force?

W T cos q Dx (50 N) cos (30) (5 m)

217 Joules

Ty

Tx

50 N

30

Where did the energy go?

- You pull a 30 N chest 5 meters across the floor

at a constant speed, by applying a force of 50 N

at an angle of 30o. - How much work did gravity do?
- How much work did friction do?

W Fcos q Dx 30 cos(90) x 5 0

X-Direction SF ma T cos(30) f 0 f

T cos(30) 43.3 N

W f cos(180) Dx (43.3 N) cos(180) x 5

-217 Joules

Perpendicular Force and Work

A car is traveling on a curved highway. The

force due to friction fs points toward the center

of the circular path. How much work does the

frictional force do on the car? Zero!

General Result A force that is everywhere

perpendicular to the motion does no work.

Work Done by Gravity

In lifting an object of weight mg by a height h,

the person doing the lifting does an amount of

work W mgh. If the object is subsequently

allowed to fall a distance h, gravity does work W

mgh on the object.

ACTS Ball Toss

- 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

Work By Gravity

When positive work is done on an object, its

speed increases when negative work is done, its

speed decreases.

Kinetic Energy Motion

- Apply constant net force along x-direction to an

object m. - W Fx Dx
- m a Dx
- ½ m (v2 v02)
- Work changes ½ m v2
- Voila new concept
- Define Kinetic Energy K ½ m v2
- W D K

Work-Energy Theorem

Work-Energy Theorem The total work done on an

object is equal to its change in kinetic energy.

(7-7)

Falling Ball Example

- A ball falls a distance 5 meters, what is

final speed?

Only force/work done by gravity SW DKE Wg ½

m(vf2 vi2) Fg h ½m vf2 mgh ½m vf2 Vf

sqrt( 2 g h ) 10 m/s

mg

Work 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 distance is same in both!

Loading with a Crane

A 3,000 kg truck is to be loaded onto a ship by a

crane that exerts an upward force of 31 kN on the

truck. This force, which is large enough to

overcome the gravitational force and keep the

truck moving upward, is applied over a distance

of 2.0 m. (a) Find the work done on the truck by

the crane. (b) Find the work done on the truck

by gravity. (c) Find the net work done on the

truck.

Preflight 1

V

- 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

T

38 13 50

work done by normal force is 0 because q is 90

and cos 90 0

28

Preflight 2

- 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

0 63 37

The work done on the car by the gravitational

force is negative because it hinders motion up

the hill

Preflight 3

- 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

63 25 12

work done by tension is positive because the

angle of the force is between 0 and 90

KE ACTS

Car 1 has twice the mass of Car 2, but they both

have the same kinetic energy. If the speed of

Car 1 is v, approximately what is the speed of

Car 2?

b) 0.707 v

a) 0.50 v

e) 2.00 v

d) 1.414 v

c) v

Preflight 4

- 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

63 12 25

The total work done is positive because the car

is moving up the hill. (Not quite!)

Total work done on the car is zero because the

forces cancel each other out.

Block w/ friction

- A block is sliding on a surface with an

initial speed of 5 m/s. If the coefficent of

kinetic friction between the block and table is

0.4, how far does the block travel before

stopping?

Y direction SFma N-mg 0 N mg

Work WN 0 Wmg 0 Wf f Dx

cos(180) -mmg Dx

W D K -mmg Dx ½ m (vf2 v02) -mg

Dx ½ (0 v02) mg Dx ½ v02

Dx ½ v02 / mg 3.1 meters

5 m/s

Summary

- Energy is Conserved
- Work transfer of energy using force
- Can be positive, negative or zero
- W F d cos(q)
- Kinetic Energy (Motion)
- K ½ m v2
- Work Change in Kinetic Energy
- S W DK