Additional Physics Topic 6  Forces and Energy
Force, Energy, and Work
If we push or pull an object with a force through a certain distance in the direction of the force, we do a job of work. Energy enables us to do jobs of work. When work is done, energy is transferred. We can say:
Energy transferred = work done
Both energy and work are measured in joules (J). Many people call work energy, but the best way to think about it is that energy is the potential to do work.
Is there likely to be more work got out than energy transferred? 
We can relate work and force by the simple equation which you need to use in the exam:
work done (J) = force applied (N) × distance moved in direction of force (m)
In Physics code:
W = Fd
In Triangle form:
Note that the direction of the force and the direction of the movement have to be the same. If they are at right angles, zero work is done. To explain this, look at the picture of the crane:
The crane does work by lifting the load vertically. If the load is hanging and swings from side to side, work is not done.
Worked Example What is the work done by the crane lifting a box of mass 250 kg from the boat through a vertical distance of 4 metres? 
Answer First find the weight of the box (who said 250 kg?). Remember that weight is a force.
Weight = mg = 250 kg × 10 N/kg = 2500 N
Work done = Fd = 2500 N × 4 m = 10 000 J 
A common bear trap is to fail to convert a mass to a weight.
A box is dragged 5 m across a floor with a force of 20 N. How much work is done? How much energy is transferred? 
Gravitational Potential Energy
In the last worked example, we saw how the work done was the weight multiplied by the vertical distance. Work was done by the crane against the weight of the load. What has happened to the work done when the load is hanging there from the crane? It hasn't disappeared.
Why has the work done not disappeared? 
The work done has been converted to gravitational potential energy (GPE). The load has the ability to do a job of work. If the load falls, it can turn the crane's motor. The motor can act as a generator to make electricity. The formula for gravitational potential energy is:
Gravitational potential energy (J) = mass (kg) × acceleration due to gravity (m s^{2}) × vertical height (m)
In Physics code:
E_{p} = mgh
Let us go back to the crane example above:
Worked Example What is the gravitational potential energy gained by a box of mass 250 kg being lifted from the boat through a vertical distance of 4 metres? 
Answer Formula: E_{p} = mgh E_{p} = 250 × 10 × 4 m = 10 000 J 
You can see that the work done is the same as the gravitational potential energy gained.
Some electric trains can convert their potential energy into electrical energy as they run down a hill. A particular train is going to run down a bank where there is a vertical height change of 45 metres. The train has a mass of 1000 tonnes (1 × 10^{6} kg). (a) How much potential energy is there in the train? (b) The efficiency of the process is 65 %. How much energy is converted to electricity? (c) What has happened to the rest of the energy? 
Work Done and Friction
If you look at the example in Question 2, you will see that the work done is NOT against the weight of the box. The work done is in the direction of the force, horizontally. This work is done against the force of friction.
Friction arises because even the smoothest of surfaces are rough if you look at them under a microscope.
Friction can be reduced by lubricating the surfaces with oil. PTFE and ice have very low friction, so they are very slippery.
Rubber has a great deal of friction.
When work is done against friction, most of the energy is turned to heat. You can see this very clearly when a large plane lands on a runway:
Photo by Karel x, Wikimedia Commons
You can see the smoke coming from the tyres. The wheels are stationary just before touchdown, so they are dragged along the runway for several metres before they are turning at the landing speed. The tyres got very hot and smoke. Plane tyres are thicker than car tyres for this reason. Even so they have to be periodically replaced. You may wonder why the wheels are not spun to prevent this heating on landing. The reason for this is that there would be extra weight for each motor. Also if one motor failed, the aeroplane would be difficult to control on landing.
What other kind of energy other than heat do you get when you do work against friction? 
Power
When you are cycling at a constant speed, the drag force and friction are balanced by the force that you put into the pedals. You have to do work against those forces all the time. Therefore you have to put in a certain power.
Power is defined as:
the rate of doing work
or
the rate of using energy.
The rate of doing work means how many joules you use every second. The equation that describes this definition is:
power (W) = energy used (J) ÷ time taken (s)
In Physics code:
P = E/t
In triangle form:
The units for power are watts (W) or joules per second (J s^{1}).
1 W = 1 J s^{1}
Worked Example What is the work done by the crane lifting a box of mass 250 kg from the boat through a vertical distance of 4 metres in 5 seconds? 
Answer Weight = mg = 250 kg × 10 N/kg = 2500 N
Work done = Fd = 2500 N × 4 m = 10 000 J
Power = E/t = 10000 ÷ 5 = 2000 W 
Elastic Potential Energy
We saw in the previous topic how we can store up energy by deforming a solid material. This is called elastic potential energy. The little boy in the picture below is winding the propeller of his toy plane.
Energy is stored in the rubber band as elastic potential energy. When he releases the plane, the energy stored in the rubber band is released as kinetic energy in the propeller, which makes the plane fly.
Another example is the elastic energy stored in the wood of this archer's bow.
Clockwork motors in many toys use elastic potential energy.
Where is the elastic energy stored in a clockwork motor? 
Kinetic Energy
Movement energy is called kinetic energy (from the Greek "kinein"  to move). All moving objects have kinetic energy:
objects moving in a straight line;
objects going round in a circle;
objects vibrating.
All the devices above convert the elastic potential energy into kinetic energy.
The equation for kinetic energy needs to be learned for the exam:
kinetic energy (joule, J) = ½ × mass (kilogram, kg) × speed^{2} ((metre/second) ^{2}, m^{2}/s^{2})
In Physics Code:
E_{k} = 1/2 mv^{2}
Worked Example What is the kinetic energy of a runner, mass 70 kg, running at 8 m/s? 
Answer Formula first: E_{k} = 1/2 mv^{2}
E_{k} = 1/2 × 70 kg × (8 m/s)^{2} = 1/2 × 70 × 64 = 2240 J 
A model racing car has a mass of 0.1 kg and kinetic energy of 5 J. How fast is it travelling? 
Converting Gravitational Potential Energy into Kinetic Energy and back
In a swinging pendulum, kinetic energy is turned into potential energy, which is turned back into kinetic energy. The interchange goes on until the pendulum stops swinging. This is because some energy is transferred to work done against the small opposing forces of friction and air resistance.
Another common example is an object falling from a height.
If an object falls, the potential energy is turned into kinetic energy. Then we combine the equations for E_{p}_{ }and E_{k} (conservation of energy):
E_{p}_{ }= E_{k},
mgDh = ½ mv^{2}
mgDh
= ½ mv^{2} [masses cancel]
Þ v^{2} = 2gDh
(a) Calculate the speed of a 10 kg canon ball dropped from the tower in the picture as it is just about to hit the ground. The tower is 20 m tall. (b) State, without calculation, what the speed of the 2 kg watermelon is just as it is about to hit the ground. (c) Which data are irrelevant in this answer? Explain why. 
Summary
