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Work and energy: Class 9 Physics
Work and its unit, kinetic and potential energy, conservation of energy, power and its units, efficiency of machines, and the main sources of energy including fossil fuels and renewable sources.
Key points
In physics, work is done when a force moves a body. Work is the product of the force and the displacement in the direction of the force: W = Fd cosθ, where θ is the angle between the force and the displacement. Work is a scalar. Its SI unit is the joule (J). One joule is the work done when a force of 1 N moves a body through 1 m in its own direction.
Work can be positive, negative or zero:
- Positive work: force and displacement are in the same direction (θ = 0°), as when you push a trolley forward.
- Negative work: the force is opposite to the displacement (θ = 180°), as with friction on a sliding box or gravity on a ball moving upwards.
- Zero work: there is no displacement, or the force is at right angles to the displacement (θ = 90°). Carrying a bag along a level road does no work against gravity, and neither does holding a heavy weight without moving it.
Energy is the capacity to do work. It is a scalar and has the same unit as work, the joule. Larger units are the kilojoule (1 kJ = 1000 J) and the megajoule (1 MJ = 10⁶ J). Energy exists as mechanical (kinetic and potential), heat, light, sound, chemical, electrical, nuclear and other forms.
Kinetic energy is the energy a body has because of its motion. For a body of mass m moving with speed v, KE = ½mv². It grows with the square of speed, so doubling the speed makes it four times larger. This is why fast vehicles are more dangerous. The work done on a body equals the change in its kinetic energy.
Potential energy is the energy a body has because of its position or state. Gravitational potential energy is the energy stored in a body raised above the ground. For a mass m raised through a height h, PE = mgh. It is measured from a chosen reference level, usually the ground. Water stored in a dam, a stretched spring and a drawn bow are all examples of stored energy.
The work done against gravity in raising a body is stored as potential energy. If a body of mass m is lifted by a height h, the work done is mgh, so PE = mgh. When it is released, this energy changes back into kinetic energy.
The law of conservation of energy: energy can neither be created nor destroyed. It can only change from one form to another. The total energy of an isolated system stays constant. For a falling body without air resistance, the loss of PE equals the gain of KE, so mgh = ½mv² and v = √(2gh). A pendulum swings because its energy keeps changing between kinetic and potential energy.
Some energy conversions in daily life are:
- Electric fan: electrical energy to kinetic energy.
- Electric bulb: electrical energy to light and heat.
- Solar cell: light energy to electrical energy.
- Battery in a torch: chemical energy to electrical energy.
- Hydroelectric station: potential energy of water to kinetic to electrical energy.
Power is the rate of doing work: P = W/t. Its SI unit is the watt (W), which is 1 joule per second. A kilowatt is 1000 W. Another unit is the horsepower: 1 hp is about 746 W. Since W = Fd, power can also be written as P = Fv for a body moving with speed v. The unit of energy used by electricity companies is the kilowatt hour (kWh): 1 kWh = 3.6 × 10⁶ J.
Efficiency tells us how much of the input energy becomes useful output energy: efficiency = (useful energy output/total energy input) × 100%. No machine is 100% efficient, because some energy always changes to heat due to friction, sound and other losses. This lost energy is not destroyed. It is spread into the surroundings and is not useful.
Sources of energy are classed into two groups:
- Non-renewable: fossil fuels (coal, oil and natural gas) and nuclear fuel. They will run out and burning fuels adds carbon dioxide to the air.
- Renewable: solar, wind, hydro, geothermal, tidal and biomass energy. They are replaced by nature and cause less pollution.
Fossil fuels formed from dead plants and animals over millions of years. Pakistan uses coal, gas, oil, hydropower, wind and solar energy. Energy should be saved because supplies are limited, by switching off unused lights, using efficient appliances and using renewable sources where we can.
Study tip: List the given values in SI units first. Choose between W = Fd cosθ, KE, PE and P = W/t by looking at what is asked. For conservation of energy problems, write PE at the top and KE at the bottom as two lines and equate them. State the unit in every answer, since marks are often lost for a missing joule or watt.
Definitions and flashcards
Say the meaning first, then open the card to check.
Work
Force times displacement in the direction of the force, measured in joules.
Joule
The work done when 1 N moves a body 1 m in the direction of the force.
Energy
The capacity to do work.
Kinetic energy
Energy due to motion, ½mv².
Potential energy
Stored energy due to position or state, mgh for gravity.
Power
The rate of doing work, in watts.
Watt
A power of one joule per second.
Efficiency
The percentage of input energy that becomes useful output.
Renewable energy
Energy from sources that nature replaces, such as solar and wind.
Formula sheet
| Name | Formula | What it means |
|---|---|---|
| Work | W = Fd cosθ | Force times displacement along the force |
| Kinetic energy | KE = ½mv² | Energy of a moving body |
| Potential energy | PE = mgh | Energy of a body raised through height h |
| Speed after falling | v = √(2gh) | From mgh = ½mv² |
| Power | P = W/t | Work done per unit time |
| Power and speed | P = Fv | Power from force and constant speed |
| Efficiency | (useful output/input) × 100% | Percentage of useful energy |
Short questions with model answers
These are the kind of questions asked for 2, 3 and 5 marks. Try each one before opening the answer.
Define one joule. (2 marks)
One joule is the work done when a force of 1 N moves a body through a distance of 1 m in the direction of the force.
Does a person holding a heavy bag at rest do any work? Explain. (2 marks)
No work is done in the physics sense. Work needs a displacement in the direction of the force. The bag does not move, so the displacement is zero, and W = Fd = 0. The person feels tired because the muscles use up chemical energy, but no work is done on the bag.
What happens to the kinetic energy of a car if its speed is doubled? (2 marks)
KE = ½mv². If v becomes 2v, KE becomes ½m(2v)² = 4 × ½mv². So the kinetic energy becomes four times larger.
Derive the formula for gravitational potential energy. (3 marks)
To lift a body of mass m at a steady speed, the lifting force must equal its weight, F = mg. If it is raised through a height h, the work done is W = F × h = mgh. This work is stored in the body as gravitational potential energy. Hence PE = mgh.
State the law of conservation of energy and show it for a freely falling body. (3 marks)
Energy cannot be created or destroyed. It only changes from one form to another. Take a body of mass m dropped from a height h. At the top, PE = mgh and KE = 0. When it has fallen a distance x, PE = mg(h − x) and its speed gives KE = mgx. The total is mgh again. Just before the ground, PE = 0 and KE = mgh = ½mv². So the total energy is the same at every point.
Compare renewable and non-renewable energy sources with examples. Why should we save energy? (5 marks)
Non-renewable sources such as coal, oil, natural gas and uranium took millions of years to form and will be used up. Burning fossil fuels adds carbon dioxide and other gases to the air. Renewable sources such as sunlight, wind, water, geothermal heat, tides and biomass are replaced by nature and cause little pollution. Their drawbacks are that some depend on weather and need a large initial cost. We should save energy because fuel supplies are limited, energy costs money and pollution harms health and the climate. We can save energy by using efficient appliances and switching off lights and fans that are not needed.
Numericals with worked steps
A boy pulls a box with a force of 50 N at an angle of 60° to the ground and moves it 4 m. Find the work done.
- F = 50 N, d = 4 m, θ = 60°, cos 60° = 0.5
- W = Fd cosθ = 50 × 4 × 0.5
- W = 100 J
Answer: 100 J
Find the kinetic energy of a car of mass 1000 kg moving at 20 m/s.
- KE = ½mv²
- = ½ × 1000 × 20²
- = ½ × 1000 × 400 = 200 000 J
Answer: 200 000 J (200 kJ)
A 5 kg stone is dropped from a height of 20 m. Take g = 10 m/s². Find its initial potential energy and its speed just before it hits the ground.
- PE = mgh = 5 × 10 × 20 = 1000 J
- All PE becomes KE: ½ × 5 × v² = 1000
- 2.5 v² = 1000, so v² = 400
- v = 20 m/s
- Check: v = √(2gh) = √(2 × 10 × 20) = √400 = 20 m/s
Answer: PE = 1000 J, speed = 20 m/s
A pump lifts 600 kg of water through 10 m in 60 s. Take g = 10 m/s². Find its power.
- Work = mgh = 600 × 10 × 10 = 60 000 J
- P = W/t = 60 000/60
- P = 1000 W
Answer: 1000 W (1 kW)
A machine takes in 500 J of energy and gives 350 J of useful work. Find its efficiency and the energy wasted.
- Efficiency = (350/500) × 100% = 70%
- Wasted energy = 500 − 350 = 150 J
Answer: Efficiency 70%, wasted energy 150 J
Common mistakes
- Using W = Fd even when the force is at an angle, instead of Fd cosθ.
- Saying work is done whenever a person feels tired or holds a load. Work needs displacement along the force.
- Forgetting to square the speed in ½mv².
- Writing the unit of power as joule instead of watt (joule per second).
- Saying energy is lost as heat. It is not destroyed, it changes to a less useful form.