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
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