An Introduction to Work and Energy

Unit 4 Presentation 1

What is Work?

Work is defined as a force applied over a distance

Work is a scalar

Note that the distance must be parallel to the applied force

SI Unit: Joule

lldFW

2

2

s

mkgJ

Work Examples

Calculate the work it takes to lift a 50N box 3 meters.

Calculate the work it takes to lift a 20 kg box 5 meters.

md

NF

W

3

50

?

JmNdFW 150)3(50

md

NsmkgF

W

5

196)/8.9(20

?2

JmNdFW 980)5(196

Non-aligned forces

Remember, the applied force MUST be in the same direction of the motion to calculate work. If not, consider the following:

F

Force applied, through tension in a rope

Motion of the block

Consider the applied force vector:

llF

apF

cosapll FF

Therefore, work can also be described as:

llap dFW

)cos(

What is Energy?

Energy is defined as the ability to do work.

If an object has energy, it has an ability to do work, which is a force applied over a distance.

6 Main Types of Energy

Heat Sound Light Chemical Electrical Mechanical (Kinetic & Potential)

Mechanical Energy

Mechanical Energy is divided into Kinetic Energy and Potential Energy

Kinetic Energy: The Energy of Motion

Potential Energy: Stored Energy that can be converted into other types of energy

Work – Kinetic Energy Theorem

Theorem: The net work done on an object is equal to the change in the object’s kinetic energy.

Kinetic energy is the energy of motion of an object:

SI Unit for Energy: Joule

KEKEKEW of

2

2

1mvKE

Kinetic Energy Example

The driver of a 1000 kg car traveling on the interstate at 35.0 m/s (nearly 80 mph) slams on his breaks to avoid hitting a second vehicle in front of him, which had come to rest because of congestion ahead. After the breaks are applied, a constant friction force of 8000 N acts on the car. Ignore air resistance.

(a) At what minimum distance should the breaks be applied to avoid a collision with the other vehicle?(b) If the distance between the vehicles is initially only 30 m, at what speed would the collision occur?

Kinetic Energy Example

Lets apply the Work-Kinetic Energy theorem:

Now, consider that the only work being done is by kinetic friction, and the force and direction of motion are opposite of each other:

22

2

1

2

1of mvmvW

22

2

1

2

1ofk mvmvdf

smv

smv

kgm

d

Nf

f

o

k

/0

/35

1000

?

8000

k

of

f

mvmvd

22

21

21

md 6.768000

)35)(1000(21

)0)(1000(21 22

Kinetic Energy Example

Now, find the speed at impact if the distance is only 30 m.

?

/35

1000

30

8000

f

o

k

v

smv

kgm

md

Nf 22

2

1

2

1ofk mvmvdf

f

ok

vm

mvdf

2121 2

smv f /3.27)1000(

21

)35)(1000(21

308000 2

Conservative and Nonconservative Forces

Conservative Force: A force that allows a user to recover their work, as kinetic energy, completely and with very little dissipation.

Nonconservative Force: A force that does not allow a user to recover their work, as kinetic energy, very well. In fact, much of the work is dissipated as various other forms of energy (heat, sound, etc.)

Gravitational Potential Energy

Work can be done on a system to raise its level of energy without giving it kinetic energy.

Ex: Lifting a brick from the floor to a tabletop.

Work was done against the force of gravity, and the brick is said to have gravitational potential energy.

Gravitational Potential Energy

heighth

hmgU

U = Potential Energy

SI Units: Joule

Gravitational Potential Energy Example

Calculate the change in gravitational potential energy when a 5 kg brick is lifted 20 meters above ground level.

?

20

/8.9

52

U

mh

smg

kgm

JmsmkgU

mghU

980)20)(/8.9(5 2

Conservation of Energy

Energy can be neither created nor destroyed in any type of reaction, physical or chemical. Rather, energy simply changes form.

Conservation of Mechanical Energy

In any isolated system of objects interacting only through conservative forces, the total mechanical energy E = KE + GPE, of the system, remains the same at all times.

Conservation of Mechanical Energy Mathematically

ffoo

ffoo

fo

mghmvmghmv

GPEKEGPEKE

EE

22

2

1

2

1