Peter's Physics Pages
Peter's Index
Physics Home
Lecture 18
Course Index
Lecture 20
An Introductory Physics Course with Peter Eyland
Lecture 19 (Power and Energy Resources)
In this lecture the following are introduced:
Power as the rate of doing work
Engine power and speed
Drag
Efficiency
Types of Energy resources
Energy reserves
Definition of Power
Power is:
broadly, the rate at which energy is delivered, or
narrowly, the rate at which work is done.
Human power
The following table gives the typical power (in Watts) consumed by a man with 1.75m2 surface area, height 1.75m, and mass 76kg.
Info from: P.Webb in J.F.Parker & V.R.West (Eds) Bioastronautics Data Book.
Activity |
Power |
Sleeping |
83 |
Sitting at rest |
120 |
Standing relaxed |
125 |
Riding in a car |
140 |
Sitting in a lecture (awake) |
210 |
Walking slowly at 4.8km/h |
265 |
Cycling at 13-18km/h |
400 |
Playing Tennis |
440 |
Breaststroke swimming at 1.6km/h |
475 |
Skating at 15km/h |
545 |
climb stairs at 116 steps/min |
685 |
Cycling at 21km/h |
700 |
Playing Basketball |
800 |
Harvard Step test |
1120 |
Note: In the Harvard Step test you step up and down a 0.4m step 30 times/min. for 5 minutes.
Example
A man uses 300W when walking. A meat pie provides 0.5MJ of useful energy.
Find how far the man has to walk to use up the energy from the pie.
Engine power and speed
The output power from an engine is given by:
Example
An elevator has a weight of 5000N when empty and has no counterweight.
It is required to carry a maximum load of 20 passengers (700N each) from the ground floor to the 50th floor in 40s.
The distance between floors is 3.52m. Find the minimum constant power needed.
Drag
When you accelerate a car or boat from rest at full throttle, it will not increase speed without limit,
it will eventually settle at a constant speed.
This speed is the terminal speed for the object, and it depends on the available power from the engine and the aerodynamic drag.
The drag force at low speeds is proportional to the speed.
At higher speeds the drag is proportional to the square of the speed, then the 4th power etc.
For a car at typical speeds the drag force, D, is given by:
where
CD is the drag coefficient produced by the shape of the car.
A is the "front-on" cross-sectional area.
ρ is the density of the fluid.
v is the speed of the car.
For most cars CD lies between 0.2 and 0.5.
Including drag, the resultant force on a car is given by:
The acceleration initially causes the speed to increase from zero, but then the drag force
(which involves the square of the speed) reduces the resultant force and the acceleration decreases.
Equilibrium is achieved when the drag force is as large as the force the engine can provide.
At this point the acceleration goes to zero and a constant (terminal) speed is reached.
Terminal speeds for objects falling in air
Object |
Terminal speed (m.s-1) |
distance (m) for 95% v |
7.3kg shotput |
145 |
2500 |
skydiver |
60 |
430 |
baseball |
42 |
210 |
tennis ball |
31 |
115 |
basketball |
20 |
47 |
ping-pong ball |
9 |
10 |
raindrop (r=1.5mm) |
7 |
6 |
parachutist |
5 |
3 |
From: Peter J. Brancazio, Sport Science.
Efficiency
In every energy exchange there is some energy lost (usually in the form of heat).
Sometimes this is desirable, for example
the brakes on a car turn the kinetic energy of the car (linear motion) into heat in the brake pads or drums (random motion).
the waste heat when a battery converts chemical energy into electrical energy determines the maximum power that you can extract from it.
At other times, it is undesirable and just increases costs.
The efficiency of a machine measures the percentage of useful power out to the total power in.
Example
A 50kg woman climbs a mountain 3000m high. A Kilogram of fat supplies about 38 MJ.
The woman can convert fat into mechanical energy with 20% efficiency. Find
(a) the work done against gravity, in climbing the mountain, and
(b) the fat consumed by the mechanical energy against gravity.
Note that this is not the whole story.
Warm blooded animals expend considerable energy in just keeping their metabolism going.
Reptiles are much more energy efficient. Look up Basal Metabolic Rate, for further information.
Energy resources and the environment
Oil, gas and coal
Oil, gas and coal produce greenhouse gasses when burnt, which affects the heat absorbed by the atmosphere.
SO2 is also produced which leads to acid rain.
Nuclear power
Nuclear power plants cost a lot of energy to build, maintain and then de-construct and dispose of the wastes.
It's not clear if it is a net energy producer or consumer.
controlling a nuclear power station
Solar power
Solar radiation can be used to create hot water e.g. for swimming pools and showers. It uses the available heat from the Sun.
Solar radiation can also be converted to electricity by "photovoltaic cells".
The Photovoltaics centre at UNSW is a world leader in research about converting solar energy to electrical energy.
Hydroelectric power
This contributes to about 3% of the world's electrical power production.
However the mass of water contained behind dams may contribute to earthquakes and environmental problems
for the downstream rivers, eg the Snowy river in Australia.
Wind power
From that site:
"Modern wind turbines usually have three bladed rotors of around 50 metres in diameter, supported on tubular steel towers
around 50 metres high.
When the wind blows, the blades turn at a constant speed of approximately 30 revolutions per minute, driving a gearbox and then a generator
which feeds its electrical output to the local electricity grid for delivery to consumers.
A well sited modern wind farm of about twenty turbines, has an average output sufficient to meet the electricity needs
of about 15,000 homes."
The major complaints about wind power generation are the unsightly turbines, the noise of the turbines and their danger to birds and bats.
Wave power
"The Pelamis device is a semi-submerged, articulated structure composed of cylindrical sections linked by hinged joints.
The wave induced motion of these joints is resisted by hydraulic rams which pump high pressure oil through hydraulic motors via
smoothing accumulators.
The hydraulic motors drive electrical generators to produce electricity.
Power from all the joints is fed down a single umbilical cable to a junction on the sea bed."
Tidal Power
Tidal Electric
"Tidal mills were invented in the early 1900's.
They didn't have two-way turbines then, so they could only use one tidal direction.
Tidal power stations are already being used in Canada, France, Russia and China.
The station that generates the most electricity (at the time of writing) is on the Rance River, in France.
It generates 320 megawatts of electricity.
A possible site for a tidal power station is at the Bay of Fundy, between New Brunswick and Nova Scotia.
The tidal head difference there is 50 feet."
Tidal Electric's concept.
Geothermal Power
Geothermal energy is produced from heat that is brought from the Earth's interior to ground level by thermal conduction, and by molten magma penetrating into the earth's crust. Ground water is heated in underground reservoirs to form naturally occurring hot water and steam. For electricity generation, hot water, at temperatures ranging from about 1500C to more than 3500C, is brought under pressure from the underground reservoirs to the surface by pipes. The water is "flash heated" into steam by releasing the pressure. The steam is separated from the water and fed to a turbine, which turns an electric generator. Electrical production from geothermal energy around the world is equivalent to that from 6 nuclear plants (6000MW).
Energy conversion efficiencies
Conversion from the vertical to the horizontal with example
from ↓ / to → |
mech. |
grav. |
electric |
radiant |
chem. |
thermal |
mech. |
99% |
100% |
||||
grav. |
86% |
85% |
||||
electric |
70-99.99% |
80% |
40% |
72% |
100% |
|
radiant |
25% |
0.6% |
100% |
|||
chemical |
30% |
91% |
15% |
88% |
||
thermal |
47% |
7% |
3% |
Non-renewable Energy reserves (Estimated at time of writing)
Gigatons |
Reserves |
Usage/yr |
Years |
Oil |
211 |
4.8 |
44 |
Gas |
199 |
2.8 |
71 |
Coal |
1032 |
3.3 |
313 |
U235 |
54 |
0.9 |
60 |
Renewable Energy
A comprehensive resources are:
Centre for Renewable Energy Systems Technology
and Renewable Energy Policy Project
Summarising:
Power is the rate at which energy is delivered, or the rate at which work is done. The unit is the Watt. |
|
The output power from an engine is given by: |
|
The drag force on a car at typical speeds: |
|
The efficiency of a machine measures the percentage of useful power out to the total power in. |
Energy resources are: Oil, gas and coal. Nuclear, Solar, Hydroelectric, Wind, Wave, Tidal, Geothermal.
"The greatest challenge facing humanity in the next twenty years is to preserve our fundamental life support systems
in the face of increasingly inequitable and unsustainable production and consumption patterns."
Peter's Index
Physics Home
Lecture 18
top of page
Lecture 20
Copyright Peter & BJ Eyland. 2007 -2015 All Rights Reserved. Website designed and maintained by Eyland.com.au ABN79179540930. Last updated 17 January 2015 |