Download Unit 7 Work, Power, and Energy

WORK AND
ENERGY
WORK
• Work is done when an object is
moved through a distance. It is
defined as the product of the
component of force applied along
the direction of displacement and the
magnitude of the displacement.
• W = F • d cosq
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Units of Work
• Look at the equation:
• W = F • d cosq, the units are the
units of force times displacement.
• So, Newton • meter
• A Newton • meter is called a Joule
• 1 Joule = 1 Newton • meter
•1 J = 1 N • m
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Units of Work
• SI or MKS Newton•meter
Joule
• CGS
Dyne•centimeter Erg
• English
Pound•foot
ft•lb
• The unit is named after the English
physicist James P. Joule
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• Not formally trained
as a physicist.
• He ran experiments
during his
honeymoon.
• He later found the
mechanical
equivalent of heat.
• Heat is energy not a
substance.
James Joule
(1818-1889)
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Work: positive or negative?
• Work is a scalar quantity
• Work is positive when the
component of force and the
displacement are in the same
direction.
• Work is negative when the
component of force and the
displacement are in the
opposite directions.
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Force
Area under Curve is Work
Displacement
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Can you determine the work
done?
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Who’s Doing Work?
A
B
C
D
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Try this problem
• A horse pulls a stationary 300 kg cart for 55 m.
The horse pulls on the cart at an angle of 35o with a
450 N constant force.
– Find the force along the direction of motion.
– Find the work done by the horse.
– Find the acceleration of the cart.
– Find the total time this takes.
– Find the weight of the cart.
– What would the d-t, v-t, a-t, F-d graphs look 16
like?
POWER !
• Power is the rate of doing work.
W Fd
P

 Fv
t
t
Power is measured in units called Watts
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Units of Power
• The units of power are:
Joules
 Watt
sec ond
J
W
s
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The Inclined Plane
A Simple Machine
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Independence of Path
Work is the
same
mg
Height
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Forms of
Energy
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Chemical Energy
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Solar Energy
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Electrical Energy
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Wind Energy
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Sound Energy
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Nuclear Energy
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Heat Energy
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Kinetic Energy
Kinetic Energy is energy of motion.
1 2
KE  mv
2
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Work-Energy Theorem
The result of work is that there is a
change of speed, or an acceleration.
W=F•d
W=ma•d
vf2 = vi2 + 2ad and solve for ad
ad = (vf2 – vi2)/2
Insert into W=mad
W=m(vf2 – vi2)/2
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Work-Energy Theorem
1
1
2
2
W  mv f  mvi
2
2
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Work-Energy Theorem
W  K f  Ki
W  K
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Gravitational Potential Energy
The force of gravity does work. It
accelerates objects.
W = Fg • d
W = mg • d
W = mg • h
(h = height above a reference
point)
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Gravitational Potential Energy
PE  mgh
Note: AP Physics uses the
symbol U for potential
energy
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Potential Energy and Work
When work is done by gravity or
against it, the change in PE is equal
to the work done.
W  PE
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Work and Gravity
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Work and Friction
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Conservation of Energy
Energy is conserved in all systems.
This means that in the Universe,
all the energy that was at the
beginning of time is still in the
Universe today.
As we isolate systems, we find that
the total energy before is equal to
the total energy after.
The energy just changes form.
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Mechanical Energy
KE i  PE i  KE f  PE f
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1
2
2
mvi  mghi  mv f  mgh f
2
2
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Try this Problem
Find the final speed
of the object as it
hits the pavement.
35m
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The Roller Coaster
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Conservation of EnergyThe Roller Coaster
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A
The Roller Coaster
Problem
E
40 m
C
25 m
30 m
20 m
B
F
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Find the Speeds at points A-F
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Atwood’s Machine Revisited
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Spring Potential Energy
• Springs possess potential energy if
they are elongated or compressed
from their rest positions.
• This is called spring (or elastic)
potential energy.
• The formula is derived from Hooke’s
Law:
F  kx
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Spring Potential Energy
1 2
PE s  kx
2
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Conservative Force
• A conservative force is such that the work
done on the object is independent of the
path.
OR
The force does NO work as the object
moves around a closed path from start to
finish.
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Conservative vs. Non-conservative
Force
• Conservative
– Gravity
– Elastic Spring
– Electric
• Non-conservative
– Friction
– Air resistance
– Tension
– Normal force
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Conservative Force
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Non-Conservative Force
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Internal Energy
• The total energy contained within a
thermodynamic system.
• Basically we are talking about heat when we
use the term internal energy
• Usually in mechanical systems, heat is
created because of friction, air resistance, or
water resistance
• Energy in this form is typically wasted
energy
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Non-Conservative Forces
• A force is non-conservative if the work
done on an object is dependent upon the
path of travel.
W nc  KE  PE
W nc  (KE f  KE i )  (PE f  PE i )
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Review Questions


Write responses to each question on a separate
sheet of paper to be handed in.
There are 6 questions.

Some are equations, some require written responses
and deep thought, while some are graphical.
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Question 1
What is the definition of
Work in Physics?
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Question 2
• Name two ways in which Work and Energy
are related.
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Question 3
What equation equates
Work with Kinetic Energy?
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Question 4
• Explain how this
picture shows that:
W  PE
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Question 5
How does the statement, “the Earth gets
all its energy from the Sun,” explain how
you can be awake here today?
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Question 6
• Draw a graph that shows how PE and KE
change while riding this roller coaster.
Label points W, X, and Y on the graph.
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In Summary
• Work is Force times a displacement.
• Kinetic Energy is 1/2 mv2.
• Gravitational Potential Energy
is mgh.
• The work-energy theorem is
W=  K.
• Conservation of energy
• Spring potential energy is 1/2 kx2
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