Download Chapter 2-Mechanical Energy-TFC - Thermal

CHAPTER 2
Mechanical Energy
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Outline
Introduction
Work and Energy
Forms of Mechanical Energy
Kinetic Energy
Potential Energy
The Law of Conservation of Energy
Power
The Golden Rule of Mechanics
Simple Machines
Mechanical Efficiency and Mechanical Advantage
Human Body as a Machine
Summary
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Introduction
Background:
Mechanical energy, in the form of muscle power
First energy source that humans utilized. (to chase and wrestle
animals or escape them)
The use of tools for hunting and agriculture
The bow and arrow was used in hunting and in warfare, and
wind was harnessed to navigate sailboats along rivers and on
seas.
The great civilizations of China, Egypt, Persia, Greece, and
Rome relied on forced labor and animals to plow their farms;
at the same time, their soldiers fought for the acquisition of
more land and slaves.
The work from muscles, the work performed by
windmills and watermills, and the work done by simple
tools are all examples of mechanical energy.
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Work
Work = Force x Displacement
Work is the change in an object’s
state of motion that results from
the application of force.
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FAQ -- Work
Question: If there is no work done, why is
carrying the suitcase not as easy a task as it
appears?
Answer: Although little or no mechanical
work is involved in carrying the suitcase,
energy expended in flexing various muscles
in the body to simply hold the weight above
the ground might not be!
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Torque
Torque = Force x Arm of
force
Torque is a measure of work (energy)
required to rotate an object.
Torque can be interpreted as “force
with a twist”, since it results in
rotation of the object upon which the
force is applied.
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Units (Work & Torque)
In SI system…
Force is given in newtons (N) and distance in
meters (m).
The work (also the Torque) is, therefore,
expressed as newtons-meters (N.m) or
Joules (J).
In the U.S., …
Work is expressed in Btu or lb-ft.
1 Btu = 778 lb-ft = 1055 J
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FAQ -- Work
Question: Which of the following represents the performance of work?
a. An apple falls off an apple tree
b. A horse pulls a carriage
c. A balloon ruptures and air rushes out
d. A woman carries a basket of fruit over her head
e. A boy pushes against a wall until exhausted
Answer:
In each of the first three instances, a force has caused a movement in the direction of
the force.
In case (a), the force of gravity causes the apple to fall.
In case (b), the horse applies a force in the direction of motion.
In case (c), the higher pressure in the balloon forces air out.
Instances (d) and (e), however, do not constitute work.
In case (d), the force that the woman applies to the basket is upward and
perpendicular to the direction of her motion.
Similarly, in case (e), when the boy pushes on a wall, there is no displacement and
he performs no work.
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FAQ -- Work
Question: A boy is moving a heavy box along a hallway. If the boy
wants to move the box with the smallest amount of effort (putting in
the least amount of work), which approach should he choose?
a. Pull the box with a rope parallel to the floor.
b. Push the box parallel to the floor.
c. Pull the box with a rope at an angle.
d. All of the above require the same amount of effort.
Answer: The answer is (d).
Although the boy might be a bit more comfortable in one situation
over another, the work done is exactly the same in all cases.
Work is needed because of friction between the two surfaces; the
amount of work is equal to the magnitude of the friction force,
multiplied by the distance traveled.
The component of force perpendicular to the ground is not doing
any work. The smart thing to do, probably, is to put the box on a
wheeled cart or a dolly to reduce the friction.
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Forms of Mechanical Energy
Kinetic Energy (K.E.)
Energy of motion.
“The K.E. of an object
can be interpreted as the
work required for
accelerating that object
from rest.”
K.E. = ½ mV2
Potential Energy (P.E.)
Energy at rest.
“The P.E. of an object is
equal to the work needed
to lift or deform the
object.”
P.E. = mgh
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Sub-classifications
Kinetic Energy (K.E.)
Linear K.E.: The energy of
motion from one location to
another.
Rotational K.E.: The
energy due to rotational
motion about the center of
mass.
Potential Energy (P.E.)
P.E. of form: It is the
result of twisting,
compressing, stretching,
and bending matter out of
object’s natural shape.
P.E. of position
(gravitational energy): It
is the energy of mass
caused by its higher
elevation relative to its
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FAQ
Question: You inflate a balloon by blowing into it. Do you perform work? By
how much?
Answer: Yes, you do work.
because you are applying a force (moving your diaphragm to push the air
out) through a distance (expanding the balloon outward).
The amount of work is equal to the stored elastic potential energy; that is,
the amount of energy needed to stretch (deform) the balloon.
Question: Which one requires more work in carrying a weight to the second
floor -- using a ramp, stairs, or an elevator?
Answer:
As long as frictional forces are neglected, all three require the same amount
of work, equal to the change in potential energies of the weight between
the first and second floors.
When riding an elevator, the work is being done by the electric motor, but
when walking upstairs, the same work must be provided by our muscles.
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The Law of Conservation of Energy
The principle of conservation of energy
implies that the amount of energy in
a system does not change; only its
form does.
Conservation of Mechanical Energy
P.E. + K.E. = Constant (Ideal Condition)
P.E. + K.E. + Heat losses= Constant
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FAQ
Question: As you walk, it is the static frictional
force between your shoes and the ground that
propels you. How much work is done by this
force on your shoes?
Answer: None.
At the point of contact, your shoes do not
move. The ground does work on you as a
whole, and you do work on your shoes.
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Power
Power = Work / Time
Power = Force x Velocity
Power is a measure of rate of
change of work; or the rate of
energy consumption.
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Units (Power)
In SI system…
The power is expressed in Joules per second
(J/s), commonly called a watt (W) in honor of
James Watt, the inventor of the steam engine.
However, as a watt (W) is relatively small unit of
power, a kilowatt (1 kW = 1000 W) is often
used.
In the U.S., …
Power is customarily expressed in horsepower.
1 hp = 746 W = 0.746 kW
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Power Outputs
of Few Basic Machines
Laptop Computer
Man
Horse
Automobiles
Water/Gas Turbines
Power Plants
Space Shuttle Main Engine
10 W
100 W
746 W
(1 horsepower)
100 kW
1 MW
1 GW
30 GW
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FAQ -- Power
Question: Two identical cars are leaving Los Angeles at the
same time. The first car arrives in San Francisco in five hours,
while it takes ten hours for the second car to reach the same
destination. Which car consumes more energy? Which car puts
out more power?
Answer:
Assuming that the cars’ efficiencies are equal at all speeds
[in reality, cars are designed to give better gas mileage at
about 80-100 km/h (50-60 mph)], both cars use the same
amount of fuel (energy), i.e., work the same amount.
The first car, however, uses up fuel twice as fast, therefore
putting out twice the power of the second car.
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FAQ -- Power
Question: Suppose a small passenger sedan with
a power rating of 80 hp can accelerate from 0-60
mph in twelve seconds. How long would it take a
sports car with a power rating of 240 hp to
accelerate by the same amount? Which car
performs more work?
Answer:
Both cars accelerate to the same speed (and gain the
same amount of kinetic energy), therefore they
perform the same amount of work.
The second car uses three times the power—which
means it does the same work in one third of the time,
or four seconds.
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FAQ - Power
Question: A cart filled with bricks is to be loaded onto a truck.
Three ramps of different lengths are available (see figure on the
right).
1. Which situation requires the least amount of force?
2. Which situation requires the least amount of work?
3. Which situation requires the least amount of power?
Answer:
Situation (a) requires the least amount of force, but the force
must be applied over the longest distance.
The product of force times distance, or work, is the same in
all cases.
The power expenditure depends on how long it takes to
perform this work.
If you pull faster, the time is shorter and more power is
needed.
Assuming speeds are the same in all cases, it takes longest
for the cart to move up the longest ramp (a), and the least
power is consumed.
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The “Golden Rule” of Mechanics
“Whatever you lose in power you
gain in displacement.”
Although the output work is less than the
input work, output force does not have to be
small than input force.
This is exactly what a machine is supposed to
do – transform a part of the energy (work)
into a form most convenient – that which
requires less force.
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FAQ
Question: Consider a bottle opener. In lifting the handle, you do work
on the opener which, in turn, does work on the cap it is lifting. Which
one is greater, your work or the work of the bottle opener?
Answer:
Because the opener cannot be a source of energy, the output work
(work of opener) can never exceed the input work (your work).
The opener simply aids in the transfer of energy from you to the
bottle cap.
In fact, nearly all of your work will go into deforming, rather than
into lifting, the bottle cap.
Of course, energy was not really lost; it was just not used in the
way you intended.
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FAQ
Question: A transmission gearbox transmits power from the
engine to the axle through a number of interlocking gears. To
get more power, we need to put the transmission into a lower
gear. Speed, at the same time, decreases. Can we design
transmissions that increase the power without reducing the
speed?
Answer: No.
A machine can increase the magnitude of the effort (input)
force, or increase the velocity of the object to be moved, but
not both.
If a machine increased the power without a corresponding
decrease in velocity, the output work would exceed the
input work, which is impossible.
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Simple Machines
They are designed to perform one simple
task.
Types:
A.
B.
C.
D.
E.
F.
Inclined Plane (ramp)
Wedge
Screw
Lever
Wheel and Axle
Pulley
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A. Inclined Plane – Ramp
Inclined plane: any slanted surface used to raise a load
from a lower level to a higher level.
Work is carried out using less effort by moving a smaller
force over greater distances.
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B. Wedge
Two back-to-back ramps turned on
their sides.
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C. Screw
The circular version of the inclined
plane.
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D. Lever
A bar or a rigid object that rests and rotates about a point called
fulcrum.
Depending upon the position where force and weight apply
relatively to the pivot, there are three kind of levers:
First class lever
Second class lever
Third class lever
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D1. First Class Levers
Fulcrum is between the force and weight.
• Pliers
• Seesaw
• Scissors
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D2. Second Class Levers
Weight is between the fulcrum and the force.
• Nutcracker
• Wheelbarrow
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D3. Third Class Levers
Force is between the fulcrum and weight.
• Baseball bat
• Shovel
• Tongs
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E. Wheel and Axle
A wheel or spoke attached to an axle or a lever.
A smaller force applied to the longer motion at the
wheel results in a shorter, more powerful motion at
the axle.
Examples: Windmills, Gears, Doorknobs, Steering
wheels etc.
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F. Pulley
A chain, belt, or rope wrapped around a
wheel.
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FAQ – Simple Machines
Question: Which of the six simple
machines reduce the amount of work
needed to raise a load?
Answer: None of them.
Machines do not change the amount of
work required.
They merely make the work easier.
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Mechanical Efficiency (M.E.)
M.E. is a measure of losses that may be
included while performing a certain
work.
It is given by a fraction of the input
work that is available for carrying out
the desired output work.
M.E. = Desired Work Output / Necessary Work Input
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FAQ -- M.E.
Question: Suppose you hook two machines
together, one with an efficiency of 40% and the
other with an efficiency of 60%. What is the
efficiency of the two machines operating together?
Answer:
If you are tempted to say 100%, try to resist.
The first machine will feed only 40% of the original input
energy into the second machine, which then puts out 60%
of the 40%.
In other words, each machine loses some energy and the
net efficiency is 0.40 X 0.60= 0.24 (or 24%).
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Mechanical Advantage (M.A.)
M.E. is the factor by which the machine
multiplies the force.
It is given by a ration of the force
exerted by a machine to the force
exerted up on the machines.
M.E. = Resistance force (load) / Effort Force
= Force exerted by machine / Applied Force
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FAQ -- M.A.
Question: What is the mechanical advantage of a hammer
driving a nail through a block of wood?
Answer:
The energy used to carry the hammer through its flight
(from the time of raising your hand until the time that the
hammer hits the nail) is used to push the nail only a few
millimeters into the wood.
For example, if we lower our hand by 50 cm, but the nail is
pushed down only by 0.5 cm, then we have reduced the
displacement by 100 times and, at the same time, multiplied
the force by a factor of 100.
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FAQ -- M.A.
Question: What is the mechanical
advantage of the system of pulleys shown
here?
Answer: The mechanical advantage of a
pulley system is approximately equal to the
number of supporting ropes or strands.
A single, fixed pulley can only change the
direction of the pull to lift a load; it does not
multiply the force. Therefore, the pulley
shown in (a) has a mechanical advantage of
one (MA = 1).
The pulley system in (b) has two ropes that
are supporting the moving pulleys and,
therefore, has a mechanical advantage of
two (MA = 2).
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FAQ -- M.A.
Question: How does a car jack
allow you to raise a 2,000-lb car,
when you can only lift a weight of
50 pounds?
Answer: The jack is a lever
allowing a much smaller force
applied over a longer distance.
In this particular case, you must
lower the jack handle 40 cm just
to raise the car by 1 cm.
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Human Body as a Machine
Human Body = A machine that
consumes food and converts it to
mechanical work and heat.
Power Transmission through the
action of forces on the muscles, bones
and joints.
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A Human Elbow
(Third class Lever during Weight Lifting)
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FAQ
Question: A man is lifting a heavy weight by contracting the biceps muscle
and, at the same time, relaxing his triceps muscle. The elbow acts as the
fulcrum. What is the force needed to lift a 10-pound weight?
Answer: The force needed is higher by ratio of the arms (40 to 4); we
need ten times the weight of the object to support the weight when
assumed that there are no losses involved.
When losses are present, mechanical advantage will be reduced by a factor
equal to the mechanical efficiency.
Question: Our muscles are much stronger than they seem. For instance, the
biceps is attached to the forearm about eight times closer to the fulcrum (the
elbow) than one’s hand is, when lifting a weight. What is the advantage of this
seemingly inefficient arrangement?
Answer: The advantage is speed (also a factor of eight), which is
frequently more important in the animal world.
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Summary
Add the summary notes as per your
convenient.
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