Download Work, Energy, Power, and Machines

Energy, Work and Power
Energy
Energy: the currency of the universe.
Just like money, it comes in many
forms!
Everything that is accomplished has to
be “paid for” with some form of energy.
Energy can’t be created or destroyed, but
it can be transformed from one kind
into another and it can be transferred
from one object to another.
• Doing WORK is one way to transfer
energy from one object to another.
Work = Force x displacement
W = F∙d
• Unit for work is Newton x meter. One
Newton-meter is also called a Joule, J.
Work- the transfer of
energy
Work = Force x displacement
• Work is not done unless there is a displacement.
• If you hold an object a long time, you may get tired,
but NO work was done on the object.
• If you push against a solid wall for hours, there is
still NO work done on the wall.
• For work to be done, the displacement
of the object must be along the same
direction as the applied force. They
must be parallel.
• If the force and the displacement are
perpendicular to each other, NO work is
done by the force.
• For example, in lifting a book, the force
exerted by your hands is upward and the
displacement is upward- work is done. F
d
• Similarly, in lowering a book, the force
exerted by your hands is still upward, and
F
the displacement is downward.
d
• The force and the displacement are STILL
parallel, so work is still done.
• But since they are in opposite directions,
now it is NEGATIVE work.
• On the other hand, while carrying a
book down the hallway, the force
from your hands is vertical, and the
displacement of the book is
horizontal.
• Therefore, NO work is done by
your hands.
• Since the book is obviously moving,
what force IS doing work???
The static friction force between your
hands and the book is acting
parallel to the displacement and IS
doing work!
F
d
Example
How much work is done to push a 5 kg
cat with a force of 25 N to the top of
a ramp that is 7 meters long and 3
meters tall?
W = Force x displacement
Which measurement is parallel to the
force- the length of the ramp or the
height of the ramp?
W = 25 N x 7 m
W = 175 J
3m
Example
How much work is done to carry a 5 kg
cat to the top of a ramp that is
7 meters long and 3 meters tall?
W = Force x displacement
What force is required to carry the cat?
Force = weight of the cat
Which is parallel to the weight vectorthe length of the ramp or the height?
d = height NOT length
W = mg x h
W = 5 x 10 x 3
W = 150 J
3m
Your Force
Vertical component of d
• And,….while
carrying yourself
when climbing
stairs or walking
up an incline, only
the height is used
to calculate the
work you do to get
yourself to the
top!
• The force required
is your weight!
Horizontal component of d
How much work do you do on a
30 kg cat to carry it from one
side of the room to the other
if the room is 10 meters
long?
ZERO, because your Force is
vertical, but the displacement
is horizontal.
Pre-AP only…
Example
Displacement = 20 m
A boy pushes a
lawnmower 20 meters
across the yard. If he
pushed with a force of
200 N and the angle
between the handle
and the ground was
50 degrees, how
much work did he do?
F cos q
q
F
W = (F cos q )d
W = (200 cos 50˚) 20 m
W = 2571 J
A 5.0 kg box is pulled 6 m across a rough horizontal floor
(m = 0.4) with a force of 80 N at an angle of 35 degrees
above the horizontal. What is the work done by EACH
force exerted on it? What is the NET work done?
●Does the gravitational force do any work?
Normal
NO! It is perpendicular to the displacement.
● Does the Normal force do any work?
FA
No! It is perpendicular to the displacement.
q
f
● Does the applied Force do any work?
Yes, but ONLY its horizontal component!
WF = FAcosq x d = 80cos 35˚ x 6 m = 393.19 J
mg
● Does friction do any work?
Yes, but first, what is the normal force? It’s NOT mg!
Normal = mg – FAsinq
Wf = -f x d = -mN∙d = -m(mg – FAsinq)∙d = -7.47 J
● What is the NET work done?
393.19 J – 7.47 J = 385.72 J
Watch for those “key words”
NOTE: If while pushing an object, it is
moving at a constant velocity,
the NET force must be zero.
So….. Your applied force must be exactly
equal to any resistant forces like friction.
• Energy and Work have no direction
associated with them and are therefore
scalar quantities, not vectors.
YEAH!!
• Power is the rate at which
work is done- how fast you
do work.
Power = work / time
P=W/t
• You may be able to do a lot
of work, but if it takes you a
long time, you are not very
powerful.
• The faster you can do work,
the more powerful you are.
• The unit for power is Joule / seconds
which is also called a Watt, W
(just like the rating for light bulbs)
In the US, we usually measure power
developed in motors in “horsepower”
1 hp = 746 W
Example
A power lifter picks up a 80 kg barbell above his
head a distance of 2 meters in 0.5 seconds.
How powerful was he?
P=W/t
W = Fd
W = mg x h
W = 80 kg x 10 m/s2 x 2 m = 1600 J
P = 1600 J / 0.5 s
P = 3200 W
Another way of looking at Power:
work
power 
time
(force x displacement)
power =
time
 displacement 
power  force x 



time
power  force x velocity
Power = Force x velocity