Download 12.1 Work Energy Power

Work Energy Power
Force
• Force is a push or pull. Force is measured in newtons (N)
Definition of Work
• Work is a force applied over a distance in the same
direction as the motion. W (work) = f (force) x d (distance)
W = f x d Work is measured in Nm. 1 Nm = 1 J (joule) The
units of work are joules (J). James Prescott Joule
determined the relationship between mechanical work and
energy forms.
Objects moving steadily in a straight line have
balanced forces on them.
The force needed to steadily lift an object.
• The force needed to steadily lift an object is equal to its
weight (but in the opposite direction).
The Work in lifting an object
• The work needed to lift an object is equal to the lifting force
times the distance the lifting force acts (W = f x d).
The work needed to horizontally move an object.
• If an object is moved through air, the force acting in the
direction of motion is essentially zero so the work done is also
zero (W = 0 x distance = 0).
Work to slide an object
• The work to slide an object is equal to the effort force
(equals friction) time the distance the object slides.
Work to go up a stairs
• A
Energy Definition
• Energy is the ability to do work. The amount of energy
present depends on the amount of work it can do. Energy
is measured in joules (J). The farther back a bow string is
pulled, the more potential energy (stored energy) it has.
Potential and Kinetic Energy
• Kinetic energy is the energy moving objects have because
of their motion (the work they can do because of their
motion).
• Potential energy is the energy stored in an object (the work
that can be done when the stored energy is released).
Gravity Potential Energy
• The gravitational potential energy an object has is equal to
the force times the distance that the object can exert its
force over (PE = mgh)
Potential Energy of a Skier
The potential energy that a skier has is mgh, the work that
gravity can do on the skier.
Kinetic Energy: The Energy of Motion
• The kinetic energy of an object (KE) = ½ mv2 . This formula
is derived as follows:
KE is work, W or KE = fd
but f = ma
So, KE = mad
but a = v2 2 – v1 2/2d from v2 2 = v12 + 2ad
So, KE = m(v2 2 – v1 2/2d)d which simplifies to
KE = m(v2 2 – v1 2/2) which simplifies to KE = ½m(v2 2 – v1 2)
If v1 = 0, then the KE of a moving object, KE = ½mv2 where v
is the v2 or speed of the object as compared to rest (V1 = 0)
Energy is Conserved but Changes Forms
Energy can change from one form to another. Eventually all
forms of energy change into heat which is lost to space. 4.18
J of any energy (work) will become 1 cal of heat (the amount
of heat that raises the temperature of 1 g of water 1 celsius
degree). Conservation of energy means that energy can not
be created or destroyed.
Conversion of Potential to Kinetic Energy
When an object is dropped, the potential energy the object
has at the top of its drop (mgh) is converted to kinetic energy
(energy of motion) as it falls. Neglecting air resistance, the
sum of the PE and KE throughout the fall remains constant.
Sample Problem
Determine the velocity of a 5.00 kg object which was dropped
from a height of 25.0 m, when this object is 5.00 m from the
Mass =
PE = 1225 J
ground. Neglect air resistance.
5.00 kg
KE = 0 J
25.0 m
PE = 245 J
KE = 980 J
5.00 m
The potential energy of the object (mgh) at the top of its drop
is 1225 J. At 5.00 m from the ground, the PEobject is 245 J
(mgh). The object has lost 1225 J - 245 J = 980 J of energy.
This potential energy lost has been converted into kinetic
energy. From KE = ½ mv2, v2 = 2KE/m, so that v = √(2KE/m).
V = √(2*980 kgm2/s2/5.00 kg) = 19.8 m/s
Sample Problem
Determine the PE, KE, ME (Mechanical Energy = sum of KE
and PE) and v, given the skateboarder’s initial v and mass.
At position 3, the boarder is at his maximum height.
Sample Problem Answers
At 1 the boarder has 0 J PE, 1920 J KE and ME = 1920J
At 2 the boarder has 588 J PE, 1332 J KE, 1920 J ME, v = 6.7
m/s (√(2KE/m).
At 3 (maximum height), the boarder has 1920 J PE, 0 J KE,
1920 J ME, v= 0 m/s, and height = 3.27 m
Energy Conversion and Conservation in a Pendulum
When a pendulum bob is brought from rest position (M) to
position E1, it is at a height h above its rest position which
gives it a potential energy of mgh. When released, the
pendulum bob converts all its potential energy at E1 into
kinetic energy at M and then back into potential energy at E2.
Energy Conversion and Conservation in a Pendulum
Energy just changes forms as a pendulum swings. If there
were no friction or wind resistance, a pendulum would swing
to exactly the same height on both sides.
Demonstrating Conservation of Energy
When a ball is given potential energy by lifting it to a side, it
transforms this potential energy into kinetic as it falls and
then passes this energy through the balls to the other side
where the kinetic energy moves the ball upward until it has
converted all kinetic into potential energy.
Requirement for Energy Conservation?
To conserve energy (PE = mgh) with balls 1&2, what must
happen?
Another Demonstration of Energy Conservation
• The bob is lifted to the height of the second horizontal
stripe. Its swing is interrupted midway by a protruding
peg. Note that the bob continues to rise to the level of the
second horizontal stripe.
The Energy of a Roller Coaster
A roller coaster continuously demonstrated conversion of
potential to kinetic to potential energy as it rises and falls.
Harnessing Water’s Potential Energy
A waterwheel converts water’s potential energy (mgh) into
kinetic energy in the moving wheel which can do work.
The Law of Conservation of Energy
Energy cannot be created or destroyed. It just changes
forms.
The Law of Conservation of Energy
Ultimately all energy on earth becomes heat which is radiated
out into space. The sun provides a constant input of
energy which provides the basis for motion on earth and
for life on earth.
Power
Power is defined as the rate of doing work. The power
formula is P = W/t or P = fd/t. Power equals work done
divided by the time it takes to do this work. If a device
does the same work as another device but does it quicker
(in less time), then it is more powerful.
1 m lift
300 N
Weight
If a conditioned person lifts a 300N weight 1 m in 2 seconds,
the work rate or power is 150J/s. If another person lifts 300
N 1m in 3 seconds, the work rate or power is 100 J/s.
The Power Unit: The Watt
The base power unit is called a watt. One watt is the power
when 1 J of work is done per 1 second. 1 W = 1J/s
The power formula can be rearranged to compute work or
time given power. For example, if a pump has a power of
4000.0 watts, how much time will it take to lift 5,000 L of
water a distance of 10.0 m from the bottom of a well, given
that 1 L of water has 1 kg of mass?
t = W/P = fd/P
t = (5,000 kg)(9.8 N/kg)(10 m)/4000 W = 122.5 s = 2.04 min.
Power as Energy per Time
Since energy is measured by the work it does, power can be
expressed as energy produced per time (for power
generated) or as energy consumed/used per time (for
power consumption) .
A 60 W stereo consumes 60 J/s of electrical energy.
A 100 W bulb consumes 100 J/s of electrical energy.
The Work of James Watt
James Watt improved the steam engine so that it could
replace animal power in England. To sell his steam engine
to prospective clients, Watt needed to show them how
many animals (usually horses) his new steam engine could
replace.
The English Power Unit: Horsepower
Watt measured how much work a horse could do per second and
called this 1 horsepower. He then measured the amount of work
his steam engines could do and rated his steam engines in
horsepower, indicating how many horses one of his engines
could replace. The metric power unit is named in honour of
James Watt. 1 H.P. = 746 W. (1 H.P. = 550 ftpd/s – English)
Thermal Energy
Thermal energy is the total kinetic energy of all the molecules
inside a substance (their colliding, spinning and vibrating)
and their potential energy as they move closer or farther
apart.
Temperature vs Thermal Energy
Temperature is a measure of the average energy per molecule.
Thermal energy is a measure of the total energy of all molecules.
V=1
V=4
V=5
V=2
Temperature or Vav =
(1+2+3+4+5)/5 = 3
Molecules at
various speeds
V =3
V=1
V=4
V=5
V=2
Molecules at
various
speeds
Thermal Energy or Vt
= 1+2+3+4+5 = 15
V =3
Thermal Energy and Temperature Measure Different
Things!
Temperature measures the average kinetic energy
(movement energy) of a substance’s particles.
Thermal Energy measures the total kinetic energy (sum)
of all the particles of a substance.
• A spoon of water at 100 • A bucket of water at 100
celsius
celsius. Equal temperatures!
But not equal thermal energy!
Heat
Heat is the thermal energy that gets passed from warmer to
cooler objects when they are in contact.
Summary
As the diagram to the
right shows, heat
moves from objects
with higher
temperatures to
objects with lower
temperatures. It can
move from an object
with less thermal
energy to an object
with higher thermal
energy provided that
the object with greater
thermal energy has a
lower temperature.
Measuring Heat by Calories
A calorie is the amount of heat required to raise the
temperature of 1 g of water by 1 celsius degree. For
example, the heat required to raise 1 g of water from 23 C
to 24 C would be 1 calorie.
Temp =
24o C
1 g water
1 calorie of
heat added
Temp =
23o C
1 g water
A Formula for Calculating Heat (For Water)
If 2 g of water were raised 3 celsius degrees in temperature,
the amount of heat required would be 6 calories. To
calculate heat (Q for quantity of heat),
Q = m(Δt)
where Q is heat, m is mass and Δt is the
temperature change
46
oC
1g
water
1 J heat/gCo
43 oC
46
oC
1g
water
1 J heat/gCo
1g
water
43 oC
1g
water
Food Calories (kilocalories or kcal)
A food calorie is actually a kilocalorie or Calorie (capital C)
which is 1,000 calories, the energy (heat) needed to raise 1
kg of water by 1 celsius degree.
Lean Ground Beef:
Snickers Bar:
Apple:
The Mechanical Equivalent of Heat
James Prescott Joule conducted experiments where he
measured how much heat a given quantity of work would
generate. He found that 4.18 J of work would raise 1 g of
water by 1 celsius degree.
Thus 1 calorie heat energy = 4.18 J heat energy or ME.
The SI or Metric System Unit of Heat: J
Heat in the SI is measured in joules since it is a form of
energy like all other forms of energy that are also
measured in joules. The calorie unit is not a metric unit.
A Formula for Calculating Heat (For Water)
If 2 g of water were raised 3 celsius degrees in temperature,
the amount of heat required would be 24.72 joules. To
calculate heat (Q for quantity of heat),
Q = m(Δt)(c)
where Q is heat, m is mass, Δt is the
temperature change, and c is the specific heat capacity
46
oC
1g
water
4.12 Jheat/gCo
43 oC
46
oC
1g
water
4.12 Jheat/gCo
1g
water
43 oC
1g
water
The Heat Capacity of a Substance
Different substances have different heat cpacities. If 5 balls
of equal mass are allowed to sit in boiling water (100 oC) for
several minutes, these balls will have equal masses and
equal temperatures (100 oC). When placed in a wax pan
these balls melt different amounts of paraffin which shows
that they gained different amounts of heat even though
they had the same mass and initial temperature.
Different
metal
balls
Boiling
water
100 oC
Specific Heat Capacity (Specific Heat)
The specific heat capacity (c) or specific heat of a substance
is the amount of heat (J) to raise a given mass by a celsius
degree. The units of specific heat are J/kgCo or J/gCo or
cal/gCo . For any substance the heat gained, Q = mΔtc
QLead = mΔtc
= 2(3)(.130)
= .78 J
2 g lead at
25 oC
CPb = .130 J/gCo
2 g Lead
at 22 oC
QAl = mΔtc
= 2(3)(.900)
= 5.4 J
2 g Al at
25 oC
CAl = .900 J/gCo
2 g Al
at 22 oC
Explanation of Ball Expt.
Since each ball stores different
amounts of heat (different specific
heats), some balls release more
heat as they change the same
temp.
100 g balls at initial temperature
of 100 oC. Final temperature is 20
oC (room temperature). Change in
temperature = 80 Co .
Lead Ball
SpH =
.130 J/gCo
Paraffin
Wax
Heat stored
in Lead ball
Aluminum
Ball SpH =
.900 J/gCo
The Lead
ball lost
1,040 J of
heat.
Q=mΔtc
The Al ball
lost 7,200 J
of heat
(6.9X heat)
Q=mΔtc
Relative
amount of
heat stored
in Al ball
Relation of Specific Heat to Temperature Change
When given the same amount of heat, substances with low
specific heats will change their temperatures much more
than substances with high specific heats.
Final Temp =
60.43 oC
Final Temp. =
20 oC
Δt = Q/mc =
50.43 Co
C = 830 J/kgCo
4,186 J of heat
added to the equal
masses of sand and
water.
.1 kg of
sand at
10 oC
.1 kg of
water at
10 oC
Δt = Q/mc =
10 Co
C = 4,186 J/kgCo
Climate Implications Related to Specific Heat
Regions at the same latitude (Vancouver BC and Weyburn
Saskatchewan) differ in their yearly high and low
temperatures (Vancouver: -1 C to 20 C, Weyburn: -20 C to
27 C) because the ocean near Vancouver changes
temperature very little due to its high specific heat (From 6
C in winter to 12 C in Summer. At 10 m depth, the water is
a constant 9 C). The water cools the surrounding land in
summer and warms the surrounding land in winter.
Why are Beaches Always Warmer Than the Water?
Since sand has a low specific heat (830 J/kgC), it raises its
temperature more quickly than water whose high specific
heat (4,128 J/kgC) means it will absorb more heat before it
changes temperature.
4,128 J/kgC
830 J/kgC
Solar Heat Storage Systems
The high heat capacity of water makes it a suitable substance
to store energy in although its weight can be a negative
factor. Rock bed storage systems with lower heat
capacities use forced air to add and extract heat.
Energy Efficiency
Energy efficiency for a device or situation is defined as the
useful energy output per total energy input times 100%.
Efficiency = useful energy output x 100%
energy input
In an incandescent bulb if 100 J of electricity convert to 3 J of
light, its efficiency as a light producer is 2.5 % (97.5 %
efficient as a heat producer).
Comparing the Efficiency of Kinds of Lights
Incandescent
2.5 %
CFL (Compact Fluorescent
LED (Lightfluorescent lite) tube
emitting diode)
7.8%
10%
9%
Sample Problem
From 1,000 J of gasoline a car’s engine produces 750 J of
heat, the transmission and drive train produce 150 J of
heat and 100 J becomes kinetic energy of motion. What is
the car’s efficiency?
Efficiency = 100J/1000 J x 100% = 10%
Car Efficiencies
Gasoline Engine
Diesel Engine
10-25%
16-40%
Emissions
Emissions
Electric Engine
75%
No Emissions
Battery Replacement
Infrastructure Needed
Petroleum-Generated Electricity?
Cost – Rebate?
A
A