...and why do mills need weirs?
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| Image © OSI/Tailte Éireann |
Definitions
In physics, energy and work have very specific meanings:
- Energy is the ability to do work
- Work is done when a force moves a body through a distance
So for instance the head of a hammer has energy due to motion called kinetic energy.
The hammer loses its momentum and kinetic energy when it hits the head
of a nail, and this creates a force on impact as the hammer rapidly
decelerates. That force can be the equivalent of a tonne weight or more,
and is capable of driving the nail into a block of timber. The kinetic
energy of the hammer can do work, and the work done occurs as the force
on the nail moves it through a distance (i.e. into the wood) against the
force of friction.
Types of Energy
An
ongoing "theme" with energy is that it frequently changes from one form
to another, but work is strictly only done when that energy creates a
mechanical force that moves something through a distance. More about
this later.
Kinetic energy
This
is due to the motion of an object. A vehicle moving on a road has
kinetic energy. The energy is proportional to the mass of the vehicle
(measured in kilos in the SI system) and also the square of the velocity
(velocity is just speed in a certain direction. Technically it's a vector quantity, unlike mass and speed which are scalar
quantities and have no direction). So if speed doubles, kinetic energy
quadruples. If speed increases ten times, kinetic energy becomes one
hundred times what it was originally. This is why high speed vehicle
crashes are so destructive and why even a small meteorite travelling at
several tens of thousands of kilometres per hour can vaporise on impact
and release huge amounts of heat energy (even though the meteorite is
only made of rock and not combustible material)
For an object of mass m moving at a velocity v, the energy of the body is:
E = ½ mv²
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| © Eugene Brennan |
Potential Energy
An
object has energy due to its position in a force field. The field could
be magnetic, electric or gravitational. If you lift a brick, you're
giving that brick potential energy as you do work on the brick (in the
physics sense, i.e. you're exerting a force to lift the brick through a
distance, against the force of gravity). When you hold the brick
stationary, it now has potential energy and you're no longer doing work
on it. If you drop it, that potential energy is converted into kinetic
energy as the block gains momentum and increases in velocity. If the
block makes contact with the ground, it can do work. Think pile drivers
on construction sites, forcing pilings down into the ground. The mill we
had in the centre of Kilcullen, like any mill, had a weir. The function
of a weir is to act like a dam, causing water to back up and rise in
level so that it gains potential energy (like the lifting a brick
example). Often weirs were built some distance upriver to benefit from
the gradient along the river, and a mill race then connected the weir to
the mill. As water exited from the weir, the height of the water and
resulting potential energy gave it added kinetic energy to drive a mill
wheel. The pumped storage power station at Turlough Hill uses the same
principle: Pump water up hundreds of metres onto the top of a hill when
electricity is plentiful and then release it when there's an electricity
demand. The potential energy is then converted into electrical energy
as it flows downwards to spin the turbines and alternators. A wound
clock spring is another example of potential energy, the energy in this
case is stored in the tension of the spring. This energy is released and
does work when it turns the hands of a clock.
For an object of mass m at a height h, the equation for energy is:
E = mgh
Where g is the acceleration due to gravity = 9.81 m/s²
Electrical energy
Electricity
does work when it powers motors or electromagnets for lifting steel in
scrapyards. Electricity flowing through the stationary coils of a motor
creates a force on the armature/rotor (the bit that turns). Again work
is being done because of the forces and motion involved.
Chemical energy
Energy
can be stored in chemical form and then released later to do work.
Charged batteries are an example. As a battery discharges, chemical
energy is converted to electrical energy in the form of a flowing
current. The current can then power electric motors in power tools or
vehicles. Work is done when a drill bit is turned or a motor causes a
vehicle to move. Explosives are another form of chemical energy. Some of
the chemical energy is released as unwanted heat energy.
Heat energy
Heat
is another form of useful energy, due to the motion of atoms (moving,
twisting and shaking). In an internal combustion petrol engine or
external combustion steam engine, heat creates pressure that forces
pistons down cylinders (the pressure creating a force on a piston and
the piston doing work as it moves)
Electromagnetic energy
This
is energy transmitted in the form of electromagnetic radiation. All our
energy on Earth ultimately originates and originated from the Sun. This
is in the form of light, heat and other parts of the EM spectrum,
reaching Earth from space, but also as fossil fuel, created by
biochemical processes in the distant past that used solar energy to
power them. Electrical energy is generated from solar radiation landing
on solar panels, but the Sun also drives the rain cycle, evaporating
water from the land and ocean and giving it potential energy as it rises
into the atmosphere. That water then becomes clouds, rain and
eventually rivers that turn the turbines in hydroelectric power plants.
Our fossil fuels such as oil, coal and gas, originally started of as
plants or marine animals. Plants used solar energy for photosynthesis
which turned CO2 into cellulose and lignin, the chief constituents of
wood and coal. Marine organisms at the bottom of the food chain ate
tiny plants that again owed their existence to solar energy, these
animals ultimately becoming oil.
Units of Energy and Work
Energy
is measured in various types of units. On your electricity bill energy
is measured in "units" or kWh (kilowatt hours), however in the SI
system, both energy and work done are measured in joules.
Definition:
One joule of work is done when one newton displaces a body one metre in
the direction of the force. In general if W is work done, F is the
force and s is the distance
W = Fs
Energy Being Converted From One Form to Another
In
its position raised above the ground, our brick in the example above
has potential energy. As it falls, it loses that potential energy and
gains kinetic energy due to motion. As it hits the ground, it makes
sound energy and heat. Work is also done when the ground is compressed
and dented on impact.
Another
example is charging a phone. Electrical energy is converted to chemical
energy in the battery. That energy is released later as electrical
energy when it powers the phone and produces sound energy from the
speaker and electromagnetic energy in the form of light coming from the
screen.
A
third example is solar panels. These convert light (a form
electromagnetic energy, just like heat, X-rays or UV) into electrical
energy.
Brakes
on vehicles are a good example of nearly all the kinetic energy of the
vehicle being converted into heat in the brake pads and disks as the
vehicle slows down. Brake discs on racing cars can get red hot, so light
energy can also be produced.
More information on forces, newtons and weight here, that makes the questions below easier to understand.
Questions and Answers
Question 1
What is the energy of a one kilo mass moving at 1.8 m/s (metre per second, equivalent to fast walking speed )
Answer
The equation for kinetic energy is energy = ½mv²
where m is the mass and v is the velocity
Energy = ½mv² = ½(1)(1.8)² = 1.62 joules
Question 2
A
mass of 10 kg is lifted one metre above the ground. How much work is
done lifting the weight and how much potential energy does it gain?
Answer
If
the lifting force upwards is greater than the weight force acting
downwards, work is done giving the mass potential energy. However there
is a net upwards force (lifting force - weight) and hence the weight
also gains kinetic energy (Newtons second law, the force accelerates the
weight). So imagine the upwards force just balances the weight, but is
infinitesimally greater. The weight moves upwards infinitely slowly. In
this scenario, the upwards force equals the downwards force.
So let the mass be m, the height be h and the upwards force be F. The acceleration due to gravity is g.
The weight acting downwards is W =mg
The force F acting upwards balances the weight W acting downwards.
The work equation is work done = force x distance = Fs
s = h = 1 m
m = 10 kg
g = 9.81 m/s²
So work done = Fs =Fh
But force lifting weight upwards = weight acting downwards
So substituting for F gives
Work done = Fh = Wh = mgh
Plugging in the values gives:
Work done = mgh = 10 x 9.81 x 1 = 98.1 joules
So the equation for work done moving a mass m to a height h is mgh
This is also the potential energy gained by the mass.