Environmental Physics
Chapter 2:
Energy Mechanics
Copyright © 2012 by DBS
Introduction
• “Physics” is derived from the Greek word “physike” meaning science
or knowledge of nature
Introduction
Science as a way of knowing…
Observation
Observation
Hypothesis
Hypothesis
Theory
Theory
Limitations of science…
Science can address how something happened but not why something happened
Forms of Energy and Conversions
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Kinetic energy – associated with an object’s motion
Potential energy – associated with an object’s position
KE and PE are also
classified as
mechanical energy
It is possible to categorize all the different forms of energy
as either kinetic or potential energy
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Chemical energy – energy stored in the bonds between atoms in molecules
Nuclear energy – energy of the nucleus released during fission or fusion
Thermal energy – associated with the motion of particles
Electric energy – associated with movement of electrical charge
Radiant energy – electromagnetic energy that travels in waves
Forms of Energy and Conversions
Forms of Energy and Conversions
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Energy conversion process –
transforms energy from primary source to end use
Figure 2.2: Illustration of conversions between different
forms of energy. Here, solar energy is converted into
electrical energy by a solar cell, which is used to run a
motor.
Forms of Energy and Conversions
Table 2-2, p. 37
Forms of Energy and Conversions
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Mechanical Energy
Kinetic energy – e.g. moving water, spinning flywheel, the wind
Figure 2.3: Two examples illustrating the conversion of kinetic energy (KE) of water
or air into the motion of a waterwheel or a blade, which can be used to grind grain or
generate electricity, respectively. (a) An undershot water wheel, (b) wind turbine.
Forms of Energy and Conversions
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Mechanical Energy
Potential energy – e.g. water at the top of a dam, a compressed spring
PE = ½ kx2
Figure 2.3: Examples of potential energy. (a) The gravitational potential
energy of the water in the reservoir behind the dam is equal to the weight of
the water times its height above the turbine, (b) The potential energy of the
compressed spring is proportional to the square of the displacement of the
spring from equilibrium X.
Motion
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In order to appreciate the subject of energy from a physics perspective we need to
understand motion
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Speed = distance / time
– Units are meters per second (m/s)
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Velocity provides additional information, direction of travel
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Acceleration is the change in velocity (m/s) with time (s)
– Units are meters per second per second (m/s2)
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An object accelerates (changes velocity) when a force is applied
– Applied forces may be long range (gravitational) or contact forces (push-pull)
Motion
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Newton’s second law of motion states that the acceleration of an object is directly
proportional to the net force acting on it, and inversely proportional to its mass
F = ma
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The unit of force is the Newton (N), N = kg.m/s2
e.g. A 6 kg meteor is moving through space. If a 3 N force is applied, what is the
acceleration?
a = F / m = 3 N / 6 kg = 0.5 m/s2
Use dimensional analysis to find the units of a.
Motion
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Frictional forces may act to oppose motion
When the net force is zero, there is no acceleration
Acceleration only occurs if the object is acted on by a net force
Figure 2.4: Friction enters into almost every situation in the real world. In
order to accelerate the object, the force of the person’s push must exceed
the force of friction.
Motion
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If a cart is pushed at constant velocity (acceleration is 0) the net force on the cart must be zero
Figure 2.5: Pushing a cart at a constant velocity means that the net force
on the cart (the person’s force minus the force of friction on the tires minus
the force of gravity down the hill) must be zero. The acceleration is zero.
Motion
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Newton’s second law states that the acceleration of an object depends on both the net force
acting on it and its own mass
Motion
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Example: emission of fly-ash particles from stacks
– Small particles may travel great distances depending on the wind speed
– Net vertical force is zero when downward force due to gravity equals upward
buoyant force
e.g. An average sized fly-ash particle has a constant settling velocity of 0.3 m/s.
If these particles are emitted from a 200 m high stack and there is a 15 km/h wind,
how far from the stack will the particle land?
Time = distance
vertical velocity
= 200 m
0.3 m/s
= 667 s = 0.19 hr
In this time it will cover a horizontal distance of d = v t = 15 km/h x 0.19 hr = 2.8 km
Motion
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Driving in the city with stop-and-go traffic, we burn more fuel than we do driving comparable
distances in the country
In the city we quite frequently have to accelerate from rest, which requires a net force acting on
the car
Gas mileages have improved over time not only due to more efficient engines but more
importantly due to the mass of the car
Exception to city/highway fuel efficiency:
The Toyota Prius hybrid gets 60 mpg city and 51 mpg highway.
Motion
Energy Losses in a Car
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Overall fuel efficiency is a function of 2 factors:
– engine efficiency – how much chemical energy is converted into work moving the pistons
– mechanical efficiency – fraction of work delivered by the engine to move the vehicle
(including aerodynamic losses
Net force on a moving car is as follows:
Fnet = Fengine – Ffriction = ma
A car cruising on ground level at constant speed, Fnet = 0 (since acceleration =0)
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Frictional losses within the engine are larger
at low speed, whilst air drag increases at
higher speeds (see (a))
Motion
Energy Losses in a Car
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Around 2/3 of all the oil used in the US is for transport
Fuel efficiency of new cars rose until the 1980s and has since leveled off
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Total oil use for transportation has been increasing due to more cars on the road / miles travelled
In 1975 US Congress passed Corporate Average Fuel Economy (CAFÉ) standards for minimum
average fuel economy
Car minimum went from 13.8 mpg to 27.5 mpg in the 1980s - has not been changed since!
Trucks, vans, SUV minimum of 20.7 recently increased to 22.2 mpg
Overall fuel efficiency has declined since sales of the above vehicles have grown
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One of the reasons for the greater use of gasoline per person in the US than
other countries is the lower fuel prices.
Part (a), p. 44
Energy and Work
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Energy is defined as the “capacity to do work”
Work is defined as the product of a force times the distance through which that force acts
Work = force x distance
W=Fxd
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A consequence of doing work on an object is to give the object energy
e.g. A 1 kg book is lifted 1 m, how much work (W) is done?
W=Fxd
Where vertical force, F = m x a , and a = accn. due to gravity
F = m x g x d =10 N x 1 m = 10 Nm = 10 J
Table 2-4, p. 45
Energy and Work
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Work is one way of transferring energy to an object
e.g. If we push an object up a hill from rest, we are doing work to give it both kinetic energy,
gravitational potential energy and thermal energy (from friction)
W = Δ(KE + PE + TE)
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Another way of transferring energy to a system is by the addition of heat
Heat is the energy transferred as a result of a temperature difference between two objects
(Note: difference between heat and thermal energy: Heat is never contained within an object; an
object contains thermal energy)
W + Q = Δ(KE + PE + TE)
(Work or heat can also change the electrical or chemical energy of a system)
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First law of thermodynamics - The total energy of a system can be increased by doing work on
it or by adding heat
Examples of Work and Energy
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Gravitational potential energy (PEG) is energy as a result of the relative height of an object,
e.g. book example
PEG = weight x height = mgh
e.g. How much PE is possessed by 10,000 kg of water behind a dam if the distance the water will
fall before it hits the blades of a turbine is 20 m?
PEG = weight x height = mgh = 104 kg x 9.8 m/s2 x 20 m = 196 x 104 J = 1.96 MJ
Examples of Work and Energy
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Energy associated with motion is kinetic energy. An object at rest has no kinetic energy.
KE = ½ mv2
Where m = mass of object, v = velocity
e.g. What is the KE of 1 kg of air moving at 15 m/s?
KE = ½ mv2 = ½ x 1 kg x (15 m/s)2 = 112 J
(one of the problems with generating electricity with the wind is the low density (mass per volume)
of air. An equivalent volume of water with the same velocity will have about 1000 times as much
energy.)
Question
Show that the KE required to shoot 1 kg of CO2 into space is greater than the energy
gained in producing 1 kg CO2 from coal.
Data: 1 kg coal produces 3 kg CO2 and contains only 29 MJ energy, escape velocity = 11
km s-1
KE = ½ mv2
For 1 kg CO2:
Energy
= ½ x 1 kg x (11000 m/s)2
= 60.5 x 106 J or 60.5 MJ
Doesn’t take in to account < 100% efficient, friction, mass of pressurized canisters
Power
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Another basic concept of energy mechanics is “power”. Power Is the rate of doing work or the rate
at which energy is used, produced, or transformed
Power = work done
time taken
= energy used
time taken
= E / t or E = Pt
Where E = Energy (J), P = power (Watts, J s-1), and t = time (s)
1 watt = 1 joule
1 second
e.g. If it takes 2 seconds to raise an 8 kg block a vertical height of 1 m, what is the power output?
P = W = mgh = 8 kg x 9.8 m/s2 x 1 m
t
t
2s
= 39.2 Watts
You can determine your own power rating by measuring the time it
takes you to climb a flight of stairs,
Power = work done / time taken = mgh / t
p. 50
Mechanical Work – Forces and Energy
Energy – Power and Units
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Power is a measure of energy per unit time
E = Pt
Where E = Energy (J), P = power (Watts, J s-1), and t = time (s)
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Electricity is measured in kilowatt hours, kWh
1 kWh = 1 kW x 1 h
= 1000 J s-1 x 3600 s
= 3600000 J
= 3.6 MJ
kWh is a unit of energy
kW is a unit of power
Question
Given below are the electrical requirements for five household appliances. Determine
the number of kWh of electrical energy consumed if all these appliances are running
simultaneously for 2 hours in a house
Color TV: 145 W
Washing machine: 512 W
Furnace: 500 W
Clock: 2 W
Humidifier: 177 W
E = Pt
= (0.145 kW + 0.512 kW + 0.500 kW + 0.002 kW + 0.177 kW) x 2 h
= (1.336 kW) x 2 h = 2.67 kWh
Question
A typical computer on the internet consumes 100 watts of electrical power.
If you use your computer for 24 hrs a day, how much energy do you use in kW?
If energy costs 10 cents per kilowatt-hour, how much does it cost?
E = Pt
= 100 W x 24 h = 2400 Wh = 2.4 kWh
Cost = (10 cents / KWh) x 2.4 kWh = 24 cents
Energy Use in India
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Economic reforms (privatization) has doubled GDP to 6 % per year
Commercial/industrial energy use increasing at 5 % per year (highest of any country)
Yet still per capita use is 1/8th world average
Main energy resources: biomass (wood, dung) and coal
Population growth rate of 1.8 %
Access to clean water and air pose serious concerns
About 70 % of electricity coal derived
Street scene, New Delhi, India.
Power
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Average power expended per person in the US is about 12 kW
Annual consumption of energy = 98 x 1015 Btu/yr = 103 x 1018 J/yr
(1 Btu = 1055 J)
Average per capita energy consumption is:
103 x 1018 J/yr
281,000,000 people
= 3.67 x 1011 J/person/yr
Since 1 year = 316 x 107 seconds, the average per capita power expenditure in the US is:
3.67 x 1011 J/person/yr = 11.6 x 103 watts/person = 12 kW/person
3.16 x 107 sec/yr
(1 Watt = 1 J / s)
(Includes a share of cooling shopping malls, making steel and aluminum, lighting offices etc.)
Higher standards of living is
matched by higher per capita
energy consumption
Switz. =
6 kW/person
India =
0.5 kW/person
Figure 2.6: Comparison of 2003 energy use per capita versus GDP per
capita for various countries. 1 GJ = 109 J. 320 GJ/yr = 10 kW.
Fig. 2-6, p. 53
Summary
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Work is defined as the product of an applied force times the distance through which that force
acts.
Doing work gives an object (and/or the environment) energy.
Energy can be found in different forms (mechanical, thermal, electrical, radiant, chemical,
nuclear).
Energy is the capacity to do work.
Mechanical energy is the sum of an object’s kinetic energy and potential energy.
The study of energy includes its transformations from one form to another.
Coursework
Questions
12. Distinguish between work done in completing a task and the power expended.
13. Categorize the following units as those of work or power: joules, watts, kilowatt-hours, ft-lb, calories, kW, ft-lb/min
Problems
16. Suppose you apply a force of 40 N to a box of mass 2 kg. The force of friction opposing the motion of the box is 15
N. What is the acceleration of the box?
18. Calculate the daily per capita U.S. energy consumption in joules, kWh, and gallons of oil. (Appx B + F, 2010 value)
31. A small stream flowing at a rate of 8 liters per second has a vertical drop of 1.5 m. What is the maximum power
you can obtain from this stream? (1 liter of water has a mass of 1 kg).
p. 60
Figure 2.9: A freely falling object. (a) Positions of a ball at equally spaced time
intervals after it was dropped from a tabletop.)
Fig. 2-9a, p. 66
Figure 2.11: Foam rubber slows your landing. The small
deceleration of the pole-vaulter while landing on the foam rubber
makes the force he experiences also small, since F = ma.
Figure 2.10: Because of their inertia, the dishes should stay on the table
after the tablecloth is quickly pulled out.
Fig. 2-10, p. 67
Figure 2.12: Skater A experiences a force equal in
magnitude but opposite in direction to the force
she exerts on skater B.
Figure 2.13: The reaction force of the
exiting gases on the rocket accelerates it.
Fig. 2-12, p. 70
Figure 2.14: Several types of simple machines. (a) lever, (b)
wheelbarrow, (c) inclined plane (pyramid construction), (d) wheel and
axle, (e) pulley system
Fig. 2-14, p. 72