Work and Energy
CBSE Class 9 · Science · Notes, formulas and practice questions
This chapter gives the scientific meaning of work and explores kinetic and potential energy, the work-energy relation, the law of conservation of energy, power and the commercial unit of energy. It explains how energy transforms while its total amount remains unchanged.
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Work in science has a restricted meaning. It is done only when a force causes a displacement. Both magnitude and direction matter, so when a force F acts at an angle θ to the displacement s, work is F s cosθ. The unit of work is the joule. If displacement is zero, or the force is perpendicular to displacement, no work is done.
Energy is the capacity to do work. An object in motion has kinetic energy; for mass m and speed v, kinetic energy is ½mv². An object raised to a height has gravitational potential energy, calculated as mgh. The work done by a force on an object is equal to the change in its kinetic energy, which is called the work-energy relation. This relation connects force, displacement and speed.
Energy can change from one form to another. In a falling stone, gravitational potential energy transforms into kinetic energy. The law of conservation of energy states that the total energy of an isolated system always remains constant, even though energy keeps changing form. Every transformation obeys this law, so no energy is ever destroyed or created.
Power is the rate of doing work, expressed as power equals work divided by time. Its SI unit is the watt; one watt is one joule per second. In industry and homes, energy is measured in kilowatt-hours, called the commercial unit of energy. One kilowatt-hour is the work done by a power of one kilowatt in one hour, equal to 3.6 × 10⁶ J.
Key terms
- Work
- In science, work is done when a constant force acts on an object and the object is displaced while the force has a component along the displacement. If F is the force, s is the displacement and θ is the angle between them, work W = F s cosθ. Work is a scalar, and its SI unit is the joule.
- Joule
- The joule is the SI unit of work and energy. One joule of work is done when a force of one newton moves an object through a distance of one metre in the direction of the force.
- Kinetic energy
- Energy possessed by an object because of its motion. For an object of mass m moving with speed v, kinetic energy = ½mv². It depends only on speed and mass, and it is always positive for a moving body.
- Work-energy relation
- The work done on an object by the net force equals the change in its kinetic energy. If the object speeds up from initial speed u to final speed v, the work done is ½mv² − ½mu².
- Gravitational potential energy
- Stored energy that a body has because of its height in the Earth's gravitational field. Raising a mass m by height h increases its potential energy by mgh, where g is the acceleration due to gravity.
- Law of conservation of energy
- States that in an isolated system, energy cannot be created or destroyed; it can only be converted from one form to another. The total energy before and after any transformation remains unchanged.
- Power
- The rate at which work is done, given by work done divided by the time taken. Average power is the total work done divided by the total time. Its SI unit is the watt.
- Kilowatt-hour
- A commercial unit of energy equal to the energy used when a power of one kilowatt acts for one hour. 1 kWh = 3.6 × 10⁶ J. This is the unit in which electrical energy is billed.
- Negative and zero work
- Work done by a force is negative when the force opposes the displacement (θ lies between 90° and 180°), and zero when θ = 90° or when there is no displacement. For example, gravity does no work on a suitcase carried horizontally.
Formula sheet
| What | Formula | Notes |
|---|---|---|
| Work done by a constant force | W = Fs cosθ | F is the applied force, s is the magnitude of displacement and θ is the angle between the force and the displacement. When the force acts along the displacement, θ = 0° and W = Fs. |
| Kinetic energy | KE = ½mv² | m is the mass of the object and v is its speed. This gives the energy stored in the object due to its translational motion. |
| Gravitational potential energy | PE = mgh | m is the mass, g is the acceleration due to gravity (about 9.8 m/s² on Earth) and h is the height above a chosen reference level. Only the change in h matters. |
| Work-energy relation | W = ½mv² − ½mu² | u is the initial speed, v is the final speed and m is the mass. The work done on the object by the force is equal to the change in its kinetic energy. |
| Power | P = W/t | W is the work done and t is the time taken. If the force and displacement are not constant, this gives average power over the interval. |
| Power for constant force and speed | P = Fv | F is the constant force acting in the direction of motion and v is the speed of the object. It follows from substituting W = Fs into P = W/t, since s/t = v. |
| Commercial energy unit relation | 1 kWh = 3.6 × 10⁶ J | kWh is kilowatt-hour. 1 kWh means energy consumed by a 1 kW device running for 1 hour, and this equals 1000 W × 3600 s = 3.6 × 10⁶ J. |
Practice questions with answers
1. A force of 20 N acts on a block at an angle of 60° to the direction of its displacement. If the block is displaced by 5 m, how much work is done by the force?
Work = F s cosθ = 20 N × 5 m × cos60°. cos60° = 0.5, so work = 20 × 5 × 0.5 = 50 J. Thus the work done is 50 J.
2. Calculate the kinetic energy of a car of mass 1000 kg moving with a speed of 20 m/s.
KE = ½mv² = ½ × 1000 kg × (20 m/s)² = 500 × 400 = 2 × 10⁵ J. The car's kinetic energy is 2 × 10⁵ J.
3. A stone of mass 5 kg is lifted to a height of 2 m. Taking g = 10 m/s², what is the gravitational potential energy gained?
PE gained = mgh = 5 kg × 10 m/s² × 2 m = 100 J. The stone gains 100 J of potential energy.
4. A person pushes a concrete wall strongly but the wall does not move. Is any work done by the person? Give the reason.
No. In physics, work requires displacement in the direction of the applied force. Since the wall does not move, the displacement is zero; therefore work done = F × 0 = 0 J, however much force is applied.
5. A boy lifts a load of mass 20 kg to a height of 1.5 m in 2 seconds. What is the work done and the average power developed? Take g = 10 m/s².
Work done against gravity = mgh = 20 × 10 × 1.5 = 300 J. Average power = work/time = 300 J / 2 s = 150 W.
6. State the law of conservation of energy and illustrate it with one example.
Energy can neither be created nor destroyed; it can only be converted from one form into another, and the total energy of the system stays constant. For example, when a ball is dropped, its gravitational potential energy gradually changes into kinetic energy, so the total energy remains the same.
7. An electric bulb of power 60 W is used for 5 hours. Find the energy consumed in kilowatt-hours and in joules.
Energy = power × time = 60 W × 5 h = 300 Wh = 0.3 kWh. In joules, 0.3 kWh = 0.3 × 3.6 × 10⁶ J = 1.08 × 10⁶ J.
8. Define one watt of power.
One watt is the power when one joule of work is done in one second; in symbols, 1 W = 1 J/s.
9. A body of mass 1 kg is dropped from a height of 20 m. Using the law of conservation of energy, find its speed just before it reaches the ground. Take g = 10 m/s².
At the top all energy is potential: mgh = 1 × 10 × 20 = 200 J. Just before the ground, this has become kinetic energy: ½mv² = 200 J. So ½ × 1 × v² = 200, giving v² = 400 and v = 20 m/s.
10. What is the commercial unit of energy? Convert 1 kWh to joules.
The commercial unit is the kilowatt-hour. Since 1 kW = 1000 W and 1 h = 3600 s, 1 kWh = 1000 W × 3600 s = 3.6 × 10⁶ J.
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