# Work, Energy and Power (A level)

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Work is done when a force moves the object in the direction of the force and is given by the product of the force and the distance moved in the direction.

• W = Fs , Where W= Work, F = Constant Force (N), S = Distance moved in the direction of the force (m)
• SI Unit for work is joules (J)
• One joule is defined as the work done when a force of 1N moves an object through a distance of 1m in the direction of the force

NO work is done when

• the object does not move
• the direction of the force and the direction in which the point of application moves are perpendicular to one another

Note:

This means that if you are carrying a stack of books and walking, you are NOT doing any work on the books! This is because the force exerted is not in the same direction as the motion!

Energy of a system is defined as its capacity to do work

• SI unit : joules (J)
• Scalar Quantity

Energy can be converted from one form to another. It can also be transferred from one body to another through work done and/or heat exchanges.

The Principle of conservation of energy states that energy cannot be created nor destroyed in any process.

• Total amount of energy of a closed system remains constant.
• E.g. A television converts electrical energy(electricity) into light, sound and thermal energies.

Kinetic Energy, $E_{k}$ is the energy a body possessed by virtue of its motion.

• $E_{k} = \frac{1}{2} m v^{2}$
• where m = Mass, v = Velocity

Gravitational Potential Energy is defined as the amount of work done in order to raise the body to the height h  from a reference level.

• G.P.E.= mgh, where m = mass, g = acceleration due to gravity, h = height

Power is defined as the rate of work done or energy converted with respect to time.

• $P = \frac{W}{t}$ OR $P = \frac{E}{t}$, where W = work, t = time, E = Energy
• SI Unit for power is watt (W), scalar quantity
• Another useful equation for power: P = Fv, where F = force, v = velocity (Simple derivation below)

Efficiency of a system is given by

• Efficiency = (Useful energy output/total energy input) X 100%

Simple derivation of P = Fv

$P = \frac{W}{t}$

$P = \frac{F \times d}{t}$

$P = Fv$, where $v = \frac{d}{t}$

### 7 thoughts on “Work, Energy and Power (A level)”

1. No work is done when object is not accurate for the definition. Object can be moving in constant velocity (net force=0) while work done is 0 as well.

2. this is nice conversation. i need more detailed derivation for this P=FV function.

regards

3. I dont get it. Why arent you doing any work when you are walking? I thought you are going against friction and air resistance?

• I slightly modified the sentence above:

From:

This means that if you are carrying a stack of books and walking, you are NOT doing any work! This is because the force exerted is not in the same direction as the motion!

To:

This means that if you are carrying a stack of books and walking, you are NOT doing any work on the books! This is because the force exerted is not in the same direction as the motion!

Will this be better?

Note: Usually, scenarios given are idealized. We take air resistance and friction to be negligible for the computation of work. Furthermore, the given scenario assumes that the books are staying at exactly same height throughout the walk. It is obvious that this cannot be true for a real life scenario.