Download Chapter 4 Work and Energy

Bruening Work and Energy
Chapter 5 Work and Energy
work:
a measure of the amount of change to which a force
gives rise when it acts on something
the product of the magnitudes of the component of a force
along the direction of displacement and the displacement
W = F*d
a force that causes a displacement of an object does work
on the object
Is Work a scalar or vector quantity?
Work is scalar. A vector multiplied by a scalar results in a scalar
quantity.
This means you do not have to give a direction in an answer, but
direction will be important when figuring out the net force on an object.
Work is done on an object when a force causes a
displacement of the object.
Work is not done on an object unless the object is moved with the
action of a force.
The action of a force alone does not constitute work.
Units of work are the joule (jool) or J .
1 joule = 1J = 1 N*m
in the British system the unit of work is the foot pound (ft*lb). A ft*lb
is a little more than 1⅓ J
1 joule is about the amount of work it takes to lift an apple from your
waist to top of your head.
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Bruening Work and Energy
Work is done only when the component of a force is
parallel to displacement.
When a force on an object and the object’s displacement are in
different directions, only the component of the force that is parallel to
the displacement does work.
Example: A person pulls an 80 kg crate 20 m across a level floor
using a rope that is 30° above the horizontal. The person exerts a
force of 150 N on the rope. How much work is done?
2.6 x 103 J or 2.6 kJ
Another example: How much work is done on a vacuum cleaner
pulled 3.0 m by a force of 50.0 N at 15° above the horizontal?
W = 145 J
Back to example 1. How would we incorporate friction into this
problem. What is the coefficient of kinetic friction was 0.15? How
would this change our problem?
What forces are involved?
Force of the person pulling. Force of friction.
The sign of work is important.
Work is scalar and can be positive or negative.
Work is positive when it is in the same direction as the displacement.
Example: lifting a box, pushing a car
Work is negative when it is in the opposite direction as the
displacement.
Example: force of kinetic friction
Homework:
Read 160-171 probs page 189: 1-4, 7,8,11,68
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Bruening Work and Energy
Energy definitions
 the property that gives something the ability to do work
 The capacity for work or vigorous activity; vigor; power.
 Usable heat or power: Each year Americans consume a
high percentage of the world's energy.
 A source of usable power, such as petroleum or coal.
 Physics. The capacity of a physical system to do work.
When we say that something has energy, we mean it is able
(directly or indirectly) to exert a force on something else and do
work on it.
When we do work on something, we add to it an amount of energy
equal to the work done.
What are the units of energy?
Joules
What are the three types of energy?
Kinetic energy –the energy something possesses by virtue
of its motion
Potential Energy – the energy something possesses by
virtue of its position
Rest energy – the energy something possesses by virtue
of its mass (not really discussed in this class)
What would this be?
Kinetic Energy
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Bruening Work and Energy
Energy of Motion
If I throw a ball with force F a distance of d, what becomes of this
work?
If the ball was starting from rest, then vo = 0 and from the following
equation
vf2 = vo2 + 2ad
then vf2 = 2ad
F = ma or a = F/m
If a is substituted, then vf2 = 2ad = 2 (F/m)d which can be rewritten
as
F∙d = ½ mvf2
So the work done on the ball = the kinetic energy of the ball
symbol for Kinetic Energy = KE, then KE = ½ mv2
Example #1
A 600g hammer strikes a nail at a speed of 4.0 m/s and drives it
5.0mm into a wooden board. What is the average force on the
nail?
F∙d = ½ mvf2
F = (½ mvf2)/d
F = 960 N
Example #2
A 7.00 kg bowling ball moves at 3.00 m/s. How fast must a 2.45 g
ping-pong ball move in order to have the same kinetic energy as
the bowling ball? Is this speed reasonable?
Vping-pong = 1.60 x 102 m/s
How much more energy does a car traveling 100 km/h have then a
car traveling 25 km/h?
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Bruening Work and Energy
Potential Energy
the energy of position
gravitational potential energy – the work something could
do by falling
If we lift a ball to height h and drop it, the work done by
gravity is W = mgh
How is this like W = F∙d?
mg = Fg
and h is the displacement the object fell.
***This height is a relative measure. If I am measuring the height
from the counter top or from the floor, it will still have the same
amount of energy, but fall to different places or heights. 1 meter
falling anywhere will give the same amount of potential energy
If dropping to the desk is 1m and drop to the floor is 2m, then
there is twice as much potential as measured from the floor
Example
Compare the potential energy of a 1200 kg car at the top of
the hill 30 m with its Kinetic Energy when moving 100 km/h.
PE = mgh (1200 kg) (9.8 m/s2) (30 m) = 3.5 x 105 J
KE = 4.6 x 105 J
Homework
P 189 12, 15, 21, 57, 59, 73, 76
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Bruening Work and Energy
Conservation of Energy
** a fundamental law of nature
General conservation principle – in a system of any kind, isolated
from the rest of the universe, a certain quality keeps the same value it
originally had no matter what changes the system undergoes.
do you remember conservation of mass from chemistry?
conservation of energy – the total amount of energy in a system
isolated from the rest of the universe always remains constant,
although energy transformations from one form to another may occur
within the system. THERE HAS NEVER BEEN A VIOLATION OF
THIS LAW FOUND!!!
who can give me an example?
a falling object is a good example. if you have a 1 kg ball 50m above
ground what is its initial Potential energy?
PE = mgh = (1kg) (9.8m/s2)(50m) = 490 J
This means that for this system there is ALWAYS 490 J of total
energy.
What is the amount of PE after the ball has fallen 10m? How much
KE is there?
PE = mgh = (1kg) (9.8m/s2)(40m) = 392
KE = Total Energy – PE = 490J – 392J = 98 J
as it falls this potential energy is converted to kinetic energy
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Bruening Work and Energy
Work-Energy Theorem
work energy theorem: the net work done by all of the forces
acting on an object is equal to the change in the object’s
kinetic energy
Wnet = ΔKE
net work = change in kinetic energy
Wnet = ½ mvf2 – ½mvi2
When using this formula you must include all forces that do work on
the object in calculating net work.
From this formula if the object’s speed increases, then positive work
was done on the object. If the speed decreases, then negative work
is done on the object.
Another way to think about the work-energy theorem
work done ON an object = change in object’s KE
+ change in object’s PE
+ work done BY object
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Bruening Work and Energy
Example
A 25 kg box is pulled up a ramp 20m long and 3.0 m high by a
constant force of 120 N. If the box starts from rest and has a speed of
2.0m/s at the top, what is the force of friction between the box and the
ramp?
total work W = Wf + ΔKE + ΔPE
or Wf = W- ΔKE - ΔPE
total work W = Fd = (120 N) (20M) = 2400 J
ΔKE = ½ mv2 = ½ (25 kg)(2.0 m/s)2 = 50 J
ΔPE = mgh = (25 kg) (9.8 m/s2)(3.0 m) = 735 J
Wf = W- ΔKE - ΔPE
=2400 J – 50 J -735 J
=1615 J
W f = Ff d
Ff = Wf / d = 1615 J / 20m
= 81 N
PE = mgh = (1kg) (9.8m/s2)(50m) = 490 J
This means that for this system there is ALWAYS 490 J of total
energy.
]
Total Energyi = Total Energyf
ΔKEi + ΔPEi = ΔKEf + ΔPEf
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Bruening Work and Energy
Does conservation of energy apply to friction as well?
Where does the work done by friction go to? PE? KE? what?
Rub your hands together. What do you feel?
The work of friction is converted to heat.
Friction is a non-conservative force
conservative force:
1) a force is conservative when the work it does on a moving
object is independent of the path between the object’s final
and initial positions
2) A force is conservative when it does no net work on an
object moving around a closed path, starting and finishing at
the same point
Examples: gravitational force, elastic spring force, electric force
non-conservative force: anthing that is not a conservative
force
Examples: Friction, air resistance, tension, normal, propulsion
of a rocket
This energy can be calculated and included into the
conservation of energy equation:
ΔKEi + ΔPEi = ΔKEf + ΔPEf +Wf
Homework
Page 190 25, 28, 30-33
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Bruening Work and Energy
Example
Starting from rest a 25.0 kg child slides down a frictionless slide from
an initial height of 3.00 m. What is her speed at the bottom of the
slide?
Wf = 0
ΔKEi + ΔPEi = ΔKEf + ΔPEf
ΔKEi = 0 since vi = 0
ΔPEi = mgh
ΔKEf = ½mvf2
ΔPEi = mgh = 0 since h = 0
So
ΔPEi = ΔKEf
mgh = ½mvf2
gh = ½vf2
vf = √(2gh)
vf = 7.67 m/s
Why would the final velocity be less than 7.67 m/s?
If there is friction then the velocity would be less.
What would the work done by friction be if the final velocity was 5
m/s?
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Bruening Work and Energy
Power: Rate of Energy Transfer
power: a quantity that measures the rate at which
work is done or energy is transformed
or
power: the rate at which work is being done
the more powerful something is, the faster is can do work
P=W/t
Power = work done / time interval
1 watt (W) = 1 J/s
This is the same watt that rates light bulbs.
Another more common unit for Power in America is Horsepower (hp).
1 hp = 746 W.
kilowatt-hour (kWh) is a unit of work since it is Power x time
An alternate equation to find Power
P = W/t and since W = F∙d then P = (F∙d)/t or P = F(d/t) or
Power = Force x speed
1 W = 1 N∙m/s
An often used unit when discussing energy consumption is the kWh
(kilowatt-hour)
1 kWh = 1000 W (1hr) = (1000 J/s)(3600s) = 3600000 J or 3.6 MJ
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Bruening Work and Energy
Example #1
An electric motor with an output of 15 kW provides power for the
elevator of 6 story building. If the total mass of the loaded elevator is
1000 kg, what is the minimum time needed for it to rise the 30m from
the ground floor to the top floor?
W =mgh
P = W/t or t = W/P = mgh/P = (1000 kg) (9.8m/s2) (30m) / 15kw
t = 20s
Example #2
A 193 kg crate needs to be raised 7.5m, at constant speed, in as
close to 5.0s as possible. The power ratings for three motors are
listed as 1.0 kW, 3.5 kW, and 5.5 kW. Which motor is best for the job
and how fast will it raise the crate?
P = W/t = F(d/t)= (mgd)/t
= (193 kg∙9.8 m/s∙7.5m)/5.0s
= 2800 W or 2.8 kw
So the 3.5 kW should be used, if it is used then how long will it take
P = mgd/t
then t = mgd/P
3500 W = (193 kg∙9.8 m/s∙7.5m)/ t
then t = (193 kg∙9.8 m/s∙7.5m) / 3500
t = 4.1 s
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