Topic 5 - Work, Energy, and Power
| Key Words Work, distance moved in direction of force, Energy, Power, Conservation, Specific Heat |
Work is defined as:
The
product of force and the distance moved in the direction of the force.
Work = Force × distance moved in the direction of the force.
Units
are newton metres (Nm) or joules
(J).
Work
is actually a scalar quantity
despite being the product of a vector quantity.
Normally
we consider the line of action of the force and the line of displacement to
be at zero degrees to each other. The
cosine of zero is 1. However if
we have the line of action of the force and the displacement at an angle, we have to use the cosine
function to take this into account.
When
work is done, there must be movement. This
can result in acceleration, a rise in temperature, or deformation in shape.
| Why is Work a Scalar? | Click HERE |
It is wrong to say that Work = Force
× displacement. If we push the box in the animation back to where it
started, the displacement is 0, but the distance in the direction of the force
is 10 metres.
| Question 1 | A car owner is trying to bump-start his car, but he cannot get it to move. Sweat is pouring off him. Explain why he has done no work. | ANSWER |
| Question 2 | A horse is pulling a barge along a canal as shown in the diagram.
It pulls the barge with a force of 1000 N a distance of 75 m.
The angle the rope is at 15o to the direction of travel. The situation is shown in the diagram:
(a) Can you explain why the answer is NOT 75000 J? (b) What is the work done by the horse?
|
ANSWER |
Energy
Energy and work are very closely related.
Energy is the ability to do work. When work is done, energy is transferred.
Energy comes in many forms.
Some kinds of energy can be stored, while others cannot.
Energy is always conserved.
| A box is pushed 5 m across a room with a force of 30 N. What is the work done and how much energy is used? |
Power
Power is the rate at which energy is used.
Power = energy transferred (J) = work done (J)
time taken (s) time taken (s)
Units of power are watts (W).
1 watt = 1 joule
per second.
Also kilowatt (kW). 1kW = 1000 W.
megawatt (MW). 1 MW = 1 × 106 W.
|
It takes 20 seconds to push the box in Question 3 across the room. What is the power? |
We can also relate power, force and speed:
Work done = force x distance moved. W = Fs
Power = energy ÷ time. P = W/t
Speed = distance ÷ time: v = s/t
So we can write:
P = W/t = Fs/t
Therefore:
P = Fv
Power (W) = force (N) × speed (m/s)
|
(a) What force must the locomotive produce? Explain your answer. (b) What power does it develop? |
Conservation of Energy
The Law of Conservation of Energy States:
Energy is neither created nor destroyed; it is converted from one form to another.
The above nonsense (including spelling mistake) is reproduced from a student's answer in a test!
At GCSE you would have done some energy chains, for example in a nuclear power station.
Nuclear energy is converted into heat.
Heat boils water to steam
Heat in the steam is converted into kinetic energy in the turbines
Which is converted into electrical energy in the generator.
Potential Energy
This term is often used in the
context of gravitational potential energy.
If we lift an object of mass m
against gravity, we are doing a job of work.
Work done = PE = weight × distance moved against gravity.
Notice the term Dh ("delta h"). This means "change in height". So if we lifted an object from 200 m above sea level to 300 m above sea level, the change in height is 100 m, which we would use in the equation.
Watch out for the bear trap of
using weight in kilograms.
| What is the potential energy of a 12 kg mass raised from the ground to a to a height of 25 m? |
Kinetic Energy
Kinetic energy is the ability to do work through motion. If the motion is in a straight line, we call the kinetic energy translational. This is the only kinetic energy we will consider.
| Calculate the kinetic energy of a 4 kg shot-put thrown by an athlete at a speed of 15 m/s. |
If an object falls, the potential energy is turned into kinetic energy. Then we combine the equations for Ep and Ek, (conservation of energy):
Ep = Ek,
mgDh = ½ mv2
mgDh = ½ mv2
Ž v2 = 2gDh
| A coin is dropped from the viewing platform of an observation tower 80 m high. How fast will it travel just before it hits the ground? Why don't you need to know the mass? |
Heat Flow
Heat is the transfer of energy, a flow of energy from a hot body to a cooler body. It must not be confused with internal energy, caused by the vibrations of atoms or molecules within a body. Temperature is a representation of internal energy, not heat flow. The more internal energy there is, the higher the temperature.
| Professor Turner warned his first year university class, “…it is internal energy. If I catch any of you calling it ‘heat’, I will personally come out and thump you.” Can you explain the difference so that one of the professor’s students will not get into trouble with the professor? |
We can increase the internal energy by:
Transferring heat into the body
Doing a job of
work on the body.
Heat
capacity
Heat capacity is the quantity of heat required to raise the temperature of a unit mass through a unit temperature rise. It is given the physics code c. The formula associated with this is:
Heat flow (J) = mass (kg) × specific heat capacity (J kg-1 K-1) × temperature change (K)
DQ
is the flow of heat energy.
Dq
is the temperature
change. It doesn’t matter
whether temperatures are in Kelvin or degrees Celsius.
Since the steps are the same, the difference will be the same.
Units for are joules per kilogram per kelvin (J kg-1 K-1). It is important that the masses are in kilograms. Sometimes you might come across c in units of J g-1 K-1, but it is important that it is converted. A material with a heat capacity of 1 J g-1 K-1 will have a capacity of 1000 J kg-1 K-1 in SI units.
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Here are the results of an experiment:
(a) Which piece of data is irrelevant? (b) What is the specific heat capacity of the material? |
In
the exam:
Watch out for conversions. Make sure that your mass in the equation is in kilograms.
It does not matter whether the temperature is in Celsius or Kelvin.
The steps are the same, and it’s the difference that matters.
Missing
these conversions is a very common bear trap
Latent
Heat
The
specific latent heat is the energy to change the state of a unit
mass of liquid without a temperature change.
There is a value for specific latent heat during:
fusion,
or melting
vaporisation,
or boiling.
Whichever
of these latent heats we are using, the calculation is the same.
The code for latent heat is l.
The
units are Joules per kilogram (J kg-1).
For
water, the specific latent heat of fusion, lm
= 334 000 J/kg. The specific latent
heat of vaporisation is rather higher, lv
= 2.3 x 106 J/kg
| Question 12 |
(Harder) Calculate how much energy is needed to melt, bring to the boil, and boil away 0.5 kg water. How long would this take a 2 kW kettle? |
ANSWER |
| Now try Topic 5 Test | Home | Module 2 | Physics AS |
