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Chapter 5
Energy
Work
Work is the transfer of energy through motion.
In order for work to occur, a force must be exerted
through a distance.
Work depends on:
the amount of force exerted.
the distance over which the force is applied.
Work
When force is applied in the direction of
motion, work can be calculated:
W=Fxd
Work = Force x distance
Work is measured in Joules ( J )
1 Joule = 1 Newton • meter
Work continued
There are two factors that determine if work
is being done:
something has to move
motion must be in the direction of the
applied force
(even when you carry books across a
level floor no work is done on the books
b/c the force is holding the books up and
the movement is horizontal)
Solve Practice Problems
WORK
• Work is only done when components of a force are parallel
to displacement
• Components of the force perpendicular do not do work.
NET WORK DONE BY A NET
CONSTANT
•
•
• There are three key ingredients to WORK
• work
• Force
• Displacement
• cause
• In order for a force to qualify as having done work on an object
• there must be a displacement
• the force must cause the displacement.
WORK BY A WAITER
• Calculating the Amount of Work Done by Forces Problems
5-1 Energy & Work
Kinetic and Potential Energy
Energy can’t be smelled or heard, but you
can smell, see, and hear the effects of energy.
Therefore, energy is the ability to cause
change.
Energy has many forms: radiant, electrical,
chemical, thermal, and nuclear.
The basic unit of energy is the joule (J),
named for the British scientist James Prescott
Joule.
KINETIC ENERGY EQUATION
• Kinetic energy = ½ x mass x (speed) 2
• KE=1/2 mv2
• Kinetic energy is the energy of motion. An object that has
motion - whether it is vertical or horizontal motion - has
kinetic energy.
• There are many forms of kinetic energy - vibrational (the
energy due to vibrational motion), rotational (the energy
due to rotational motion), and translational (the energy due
to motion from one location to another).
TRANSLATIONAL KINETIC
ENERGY
• The amount of translational kinetic energy that an object
has depends upon two variables:
• the mass (m) of the object
• the speed (v) of the object
The kinetic energy is dependent upon the
s q u a re o f t h e s p e e d .
• The following equation is used to represent the kinetic energy
(KE) of an object.
• KE = 0.5 • m • v2
• This equation reveals that the kinetic energy of an object is
directly proportional to the square of its speed. That means
that for a twofold increase in speed, the kinetic energy will
increase by a factor of four, etc...
KINETIC ENERGY
• is a scalar quantity
• the kinetic energy of an object is completely described by
magnitude alone.
• the standard metric unit of measurement for kinetic energy
is the Joule.
PROBLEM
• 1. Determine the kinetic energy of a 625-kg roller coaster
car that is moving with a speed of 18.3 m/s.
• 2. If the roller coaster car in the above problem were
moving with twice the speed, then what would be its new
kinetic energy?
• 3. Missy Diwater, the former platform diver for the Ringling
Brother's Circus, had a kinetic energy of 12 000 J just prior
to hitting the bucket of water. If Missy's mass is 40 kg, then
what is her speed?
• 4. A 900-kg compact car moving at 60 mi/hr has
approximately 320 000 Joules of kinetic energy. Estimate its
new kinetic energy if it is moving at 30 mi/hr. (HINT: use
the kinetic energy equation as a "guide to thinking.")
Kinetic & Potential Energy
Kinetic energy is energy in the form of
motion. KE depends upon the mass and
velocity of the moving object.
The greater the mass or the greater the
velocity, the greater the KE, assuming the
other components remains the same.
Potential energy is stored energy.
Gravitation PE depends on height.
Elastic PE depends on stretching/
compression.
POTENTIAL ENERGY
• An object can store energy as the result of its position.
• Potential energy is the stored energy of position possessed
by an object.
EX: POTENTIAL ENERGY
• The heavy ball of a demolition machine is storing energy
when it is held at an elevated position.
EX: CONTINUED
• A drawn bow is able to store energy as the result of its
position. When assuming its usual position (i.e., when not
drawn), there is no energy stored in the bow.Yet when its
position is altered from its usual equilibrium position, the
bow is able to store energy by virtue of its position.
2 TYPES OF POTENTIAL ENERGY
• gravitational potential energy
• elastic potential energy.
GRAVITATIONAL POTENTIAL
ENERGY
• is the energy stored in an object as the result of its vertical
position or height.
• The energy is stored as the result of the gravitational
attraction of the Earth for the object.
EX: GRAVITATIONAL POTENTIAL
ENERGY
• The gravitational potential energy of the massive ball of a
demolition machine is dependent on two variables - the
mass of the ball and the height to which it is raised.
MASS AND GRAVITATIONAL PE
• There is a direct relation between gravitational potential
energy and the mass of an object.
• More massive objects have greater gravitational potential
energy.
GRAVITATIONAL PE AND
HEIGHT
• There is also a direct relation between gravitational
potential energy and the height of an object.
• The higher that an object is elevated, the greater the
gravitational potential energy.
Gravitational PE equation:
• PEgrav = mass • g • height
•
• PEgrav = m *• g • h
• In the above equation, m represents the mass of the object,
h represents the height of the object and g represents the
gravitational field strength (9.8 N/kg on Earth) - sometimes
referred to as the acceleration of gravity.
WHAT IS POWER
POWER
• The standard metric unit of power is the Watt.
• Rate at which work is done
POWER FORMULAS
• Two physics students, Will N. Andable and Ben Pumpiniron,
are in the weightlifting room. Will lifts the 100-pound
barbell over his head 10 times in one minute; Ben lifts the
100-pound barbell over his head 10 times in 10 seconds.
Which student does the most work? ______________
Which student delivers the most power?
______________ Explain your answers.
ANSWER
• Ben and Will do the same amount of work. They apply the
same force to lift the same barbell the same distance above
their heads.
• Yet, Ben is the most "power-full" since he does the same
work in less time. Power and time are inversely
proportional.
• During a physics lab, Jack and Jill ran up a hill. Jack is twice
as massive as Jill; yet Jill ascends the same distance in half
the time. Who did the most work? ______________ Who
delivered the most power? ______________ Explain your
answers.
ANSWER
• Jack does more work than Jill. Jack must apply twice the
force to lift his twice-as-massive body up the same flight of
stairs.Yet, Jill is just as "power-full" as Jack. Jill does one-half
the work yet does it one-half the time. The reduction in
work done is compensated for by the reduction in time.
• 3. A tired squirrel (mass of approximately 1 kg) does pushups by applying a force to elevate its center-of-mass by 5
cm in order to do a mere 0.50 Joule of work. If the tired
squirrel does all this work in 2 seconds, then determine its
power.
ANSWER
• The tired squirrel does 0.50 Joule of work in 2.0 seconds.
The power rating of this squirrel is found by
• P = W / t = (0.50 J) / (2.0 s) = 0.25 Watts
POWER AND ENERGY
CONSUMPTION
• It is easy to estimate the cost of energy for an electrical
appliance if its power consumption rate and time used are
known. The higher the power consumption rate and the
longer the appliance is used, the greater the cost of that
appliance.
• The power consumption rate is P = W / t = E / t , where E
is the energy supplied by the electricity company. So the
energy consumed over a time t is
• E = Pt
• Electricity bills state the energy used in units of kilowatthours (kW ⋅ h), which is the product of power in kilowatts
and time in hours. This unit is convenient because electrical
power consumption at the kilowatt level for hours at a
time is typical.
• What is the cost of running a 0.200-kW computer 6.00 h
per day for 30.0 d if the cost of electricity is $0.120 per
kW ⋅ h ?
STRATEGY
• Cost is based on energy consumed; thus, we must find E
from E = Pt and then calculate the cost. Because electrical
energy is expressed in kW ⋅ h , at the start of a problem
such as this it is convenient to convert the units into kW
and hours.
SOLUTION
• The energy consumed in kW ⋅ h is
• E = Pt = (0.200 kW)(6.00 h/d)(30.0 d) (7.73)
• = 36.0 kW ⋅ h,
• cost = (36.0 kW ⋅ h)($0.120 per kW ⋅ h) = $4.32 per
month.
• The cost of using the computer in this example is neither
exorbitant nor negligible. It is clear that the cost is a
combination of power and time. When both are high, such
as for an air conditioner in the summer, the cost is high.
Conservation of Energy
As many objects move, energy changes from
kinetic to potential back to kinetic energy.
Mechanical energy is the total amount of
kinetic and potential energy in a system.
In any given situation, energy may change
from one form to another, but the total amount
of energy remains constant: energy is
conserved.
The law of conservation of energy states
that energy may change form but it cannot be
created or destroyed under ordinary conditions.
Conservation of Energy continued
Even as objects move, they eventually slow
down and stop. Where does the energy go?
Friction and air resistance are constantly
acting on moving objects.
These forces cause some mechanical
energy to be changed to thermal energy or
heat.
Mechanical energy can be changed to
thermal energy.
TME
• As already mentioned, the mechanical energy of an object
can be the result of its motion. The total amount of
mechanical energy is merely the sum of the potential
energy and the kinetic energy. This sum is simply referred
to as the total mechanical energy (abbreviated TME).
• TME = PE + KE
• As discussed earlier, there are two forms of potential
energy discussed in our course - gravitational potential
energy and elastic potential energy. Given this fact, the
above equation can be rewritten:
• TME = PEgrav + PEspring + KE
5-2 Temperature and Heat
Hot and cold are commons terms used to
describe the temperature of materials. Are hot
and cold definite? No, but, hot and cold are
relative terms, they compare the temperature of
two objects.
All objects are made of matter and these
particles of matter are in constant motion.
Since moving objects have KE, the faster they
move the more KE they have.
Temperature and Heat
Temperature is a “measurement” of the
average KE of the particles in a sample of
matter.
As the particles in matter move faster, their
average KE increases, therefore the
temperature increases.
As the particles in matter move more slowly,
their average KE decreases, and their
temperature decreases.
Thermal Energy
Thermal energy is the total energy of the particles
in a material, the total KE and PE in the material.
The KE is due to vibrations and movement of the
particles of material.
The PE is determined by forces that act within or
between the particles.
The more mass a material has at the same
temperature, the greater its thermal energy.
Different kinds of matter have different thermal
energies, due mainly to the ways the particles are
arranged.
Heat
Energy flows from warmer objects to cooler
objects. Heat is the “movement” of energy that
flows from higher temperature objects to lower
temp objects. (It never moves from cool to
warm.)
Heat is measured in Joules since it is a form
of energy and involves the transfer of energy.
5-3 Energy from the Oceans & Earth
Ocean waters - the temperature change
between the surface and deeper waters can
be up to 15°C. This causes the waters to
constantly move and churn. This movement
can be used to generate electricity.
5-3 Energy from the Oceans & Earth
Magma - is the molten rock that lies deep
beneath Earth’s surface. Wells could be
drilled to use this heat to generate electricity.
Both methods are very expensive, will take
many years to produce practical results, and
could also cause damage to the environment.
Read ch.
5-4 Measuring Thermal Energy
Different materials need different amounts of heat
to produce similar changes in their temperatures.
The materials have different specific heats.
Specific heat (Cp) is the amount of energy it
takes to raise the temperature of 1 kg of the
material 1 degree Kelvin.
5-4 Measuring Thermal Energy
Specific heat is measured in J/kg•K
(Joules per kilogram per degree Kelvin)
Specific heat depends on the chemical makeup
of the substances.
Objects with high specific heats can absorb a lot
of energy with little change in temperature.
Water and alcohol have high specific heats.
Objects with lower specific heats change
temperature more quickly as they absorb heat.
Using Specific Heat
Specific heat can be used to measure changes
in thermal energy using the formula:
Q = m x  T x Cp
T = Tfinal - Tinitial
change in thermal energy =
mass x change in temp x specific heat
When T is positive, temp increased,
when T is negative, temp decreased.
Even though different substances have
different specific heats, the mass and shapes of
the substances also help determine the thermal
energy characteristics - how the thermal energy
moves.
Solve Practice Problems:
Section Review