In science, you only do work when a force actually moves something. Energy is simply the capacity to do work — and it never disappears, it just changes form!
Work
Force × distance moved in the direction of force. Unit: joule (J).
Energy
The ability to do work. Same unit as work — the joule (J).
Kinetic energy
Energy of a moving body. Depends on mass and speed.
Potential energy
Stored energy due to position or shape of a body.
1. What is work?
In everyday life we call any tiring activity “work” — reading a book, standing in a queue, pushing a wall that does not move. But in science the meaning is exact. Work is done only when two conditions are both satisfied: (a) a force must act on an object, and (b) the object must be displaced (move) in the direction of the force. If you push a heavy wall and it does not move, you may get tired, but the work done on the wall is zero, because there is no displacement. Similarly, if an object moves but no force acts on it (like a ball gliding on frictionless ice), no work is done by you.
2. Work done by a constant force
When a constant force F acts on an object and moves it through a displacement s in the direction of the force, the work done is the product of force and displacement: W = F × s. Work is a scalar quantity — it has only magnitude, no direction. Its SI unit is the joule (J). One joule is the work done when a force of 1 newton moves an object through 1 metre in the direction of the force, so 1 J = 1 N × 1 m = 1 N⋅m.
3. Positive, negative and zero work
Work can take three signs depending on the direction of the force relative to the displacement. Positive work is done when the force acts in the same direction as the displacement — for example, when you push a box forward and it slides forward, or when gravity pulls a falling stone downward. Negative work is done when the force acts opposite to the displacement — for example, friction acting on a sliding box, or gravity acting on a ball thrown upward. Zero work is done when the displacement is zero (pushing an unmoving wall) or when the force is perpendicular (at 90°) to the displacement, such as the work done by the Moon’s motion against Earth’s gravity, or a coolie carrying a load on his head while walking forward.
4. Energy
An object that is able to do work is said to possess energy. The object that does the work loses energy and the object on which work is done gains energy. Because energy is measured by how much work a body can do, it has the same unit as work, the joule. A larger unit is the kilojoule (kJ), where 1 kJ = 1000 J. Energy exists in many forms — mechanical (kinetic and potential), heat, chemical, electrical, light and nuclear energy. The Sun is the biggest natural source of energy for us; many forms ultimately trace back to it.
5. Kinetic energy
The energy possessed by a body because of its motion is called kinetic energy. A moving hammer drives a nail, flowing water turns a turbine, and a fast cricket ball can break a window — all because moving objects can do work. The kinetic energy of a body of mass m moving with velocity v is given by Ek = ½ m v². This means kinetic energy increases with mass, but it depends on the square of the speed — so if you double the speed, the kinetic energy becomes four times as large. This is exactly why fast-moving vehicles are so dangerous and need much longer distances to stop.
6. Potential energy
The energy possessed by a body because of its position or configuration (shape) is called potential energy. A stretched bow, a compressed spring, and water stored in a high dam all store potential energy that can later do work. When work is done to raise an object to a height, that work gets stored as gravitational potential energy. For a body of mass m raised to a height h above the ground, the gravitational potential energy is Ep = m g h, where g is the acceleration due to gravity (about 9.8 m/s², often taken as 10 m/s² for easy calculation). The potential energy depends only on the vertical height gained, not on the path taken to reach that height.
7. Law of conservation of energy
One of the most important laws in physics states that energy can neither be created nor destroyed; it can only be transformed from one form to another. The total energy before and after a transformation always remains constant. Consider a stone falling freely from a height. At the top it has maximum potential energy and zero kinetic energy. As it falls, potential energy steadily converts into kinetic energy, so it speeds up. Just before hitting the ground it has maximum kinetic energy and almost zero potential energy. At every point, the sum of kinetic and potential energy (the mechanical energy) stays the same. This continuous exchange is a beautiful example of conservation of energy.
8. Rate of doing work — power
Two students may do the same amount of work, but one may finish faster. The quantity that tells us how fast work is done is called power. Power is defined as the rate of doing work, or the rate of transfer of energy: P = W / t. The SI unit of power is the watt (W), where 1 watt = 1 joule per second (1 W = 1 J/s). A larger unit is the kilowatt (kW), equal to 1000 watts. Because power can vary from moment to moment, we often use average power = total work done ÷ total time taken.
9. Commercial unit of energy
The joule is a very small unit for measuring the large amounts of energy used in homes and industries. So electrical energy is sold in a bigger unit called the kilowatt-hour (kW h), commonly called “one unit” on the electricity bill. One kilowatt-hour is the energy used by a 1000 W appliance running for one hour. In joules, 1 kW h = 1000 W × 3600 s = 3.6 × 106 J = 3,600,000 J. So a single “unit” of electricity is 3.6 million joules of energy.
- Work: W = F × s (unit: joule, J)
- Kinetic energy: Ek = ½ m v²
- Potential energy: Ep = m g h
- Power: P = W / t (unit: watt, W)
- 1 J = 1 N⋅m | 1 W = 1 J/s | 1 kW = 1000 W
- 1 kW h = 3.6 × 106 J (one “unit” of electricity)
- g ≈ 9.8 m/s² (often taken as 10 m/s²)
A force of 15 N is applied on a box and it moves a distance of 4 m in the direction of the force. Calculate the work done. Then, if this box has mass 5 kg and is lifted to a height of 2 m, find its potential energy (take g = 10 m/s²).
- For work: use W = F × s, with F = 15 N and s = 4 m.
- W = 15 × 4 = 60 J.
- For potential energy: use Ep = m g h, with m = 5 kg, g = 10 m/s², h = 2 m.
- Ep = 5 × 10 × 2 = 100 J.
A car of mass 1000 kg is moving with a velocity of 10 m/s. (a) Find its kinetic energy. (b) If the speed is doubled to 20 m/s, what is the new kinetic energy, and how many times larger is it?
- Use Ek = ½ m v², with m = 1000 kg and v = 10 m/s.
- Ek = ½ × 1000 × (10)² = ½ × 1000 × 100 = 50,000 J = 50 kJ.
- Now v = 20 m/s: Ek = ½ × 1000 × (20)² = ½ × 1000 × 400 = 200,000 J = 200 kJ.
- Compare: 200 kJ ÷ 50 kJ = 4. Doubling speed makes kinetic energy 4 times larger (because of v²).
Remember “FoR Work, Move” — Force and Real movement together. No movement = no work, even if you sweat! For energy: Kinetic = Keeps moving (½mv²), Potential = Placed up high (mgh).
Do not forget to square the velocity in kinetic energy — many students write ½mv instead of ½mv². Also, always write the correct unit (J or W) with your final answer, and remember that work done against gravity when carrying a load horizontally is zero, because force (downward) is perpendicular to motion (forward).
Q1. When is work said to be done? State the conditions and the formula with its unit.
Answer: Work is said to be done when a force acts on an object and the object is displaced in the direction of the force. Two conditions must be satisfied: (i) a force must be applied, and (ii) there must be displacement of the object. The work done equals the product of force and displacement: W = F × s. Its SI unit is the joule (J), where 1 J = 1 N × 1 m. If either the force or the displacement is zero, the work done is zero.
Q2. Define kinetic energy and potential energy. Give one example of each and write their formulae.
Answer: Kinetic energy is the energy possessed by a body due to its motion; example — a moving cricket ball or flowing water. Its formula is Ek = ½ m v². Potential energy is the energy possessed by a body due to its position or shape (configuration); example — water stored in a dam or a stretched bow. Its gravitational form is Ep = m g h. Both are measured in joules (J).
Q3. State the law of conservation of energy and explain it using a freely falling body.
Answer: The law states that energy can neither be created nor destroyed; it can only change from one form to another, and the total energy always remains constant. For a freely falling body: at the top it has maximum potential energy and zero kinetic energy. As it falls, potential energy converts into kinetic energy, so its speed increases. Just before hitting the ground, kinetic energy is maximum and potential energy is nearly zero. At every point the sum of kinetic and potential energy stays constant, proving energy is conserved.
Q4. Define power and its unit. A machine does 6000 J of work in 30 seconds. Calculate its power.
Answer: Power is the rate of doing work or the rate of transfer of energy, given by P = W / t. Its SI unit is the watt (W), where 1 W = 1 J/s. For the given machine: W = 6000 J and t = 30 s, so P = 6000 ÷ 30 = 200 W. The machine has a power of 200 watts.
- ✅ Work is done only when force causes displacement: W = F × s (joule).
- ✅ Energy is the capacity to do work; measured in joules too.
- ✅ Kinetic energy Ek = ½mv² (motion); Potential energy Ep = mgh (position).
- ✅ Power = work ÷ time, measured in watts; 1 kW h = 3.6 × 106 J.
- ✅ Energy is always conserved — it only changes form.
Book a free demo class