Peter's Physics Pages

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.

The unit of Power is the Watt, which is 1 Joule per second.

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.

Three gorges dam

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%generator 100%brake drum grav. 86%water turbine 85%hydroelectric electric 70-99.99%motors > 200W 80%pumped storage 40%gas laser 72%storage battery 100%heating coil radiant 25%solar cell 0.6%photo-synthesis 100%solar furnace chemical 30%muscle 91%dry cell battery 15%chemical laser 88%furnace of steam boiler thermal 47%steam turbine 7%thermo-couple 3%light bulb

Non-renewable Energy reserves (Estimated at time of writing)
 Gigatonscoal eq. 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."

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