Work and Energy
In physics, work is done only when a force moves an object, and energy is the capacity to do work. This Class 9 chapter defines work, the two main forms of mechanical energy (kinetic and potential), the law of conservation of energy, and power along with its commercial unit. The formulas are simple and the numericals are very scoring.
Learning objectives
- Define work and calculate it from force and displacement.
- Distinguish kinetic and potential energy.
- Apply the formulas for kinetic and potential energy.
- State the law of conservation of energy.
- Define power and the commercial unit of energy.
Key concepts
Work
Work is done when a force produces motion. When the force and displacement are along the same line, work W = F × s. The SI unit of work is the joule (J). No work is done if there is no displacement or if the force is perpendicular to the motion.
Kinetic and potential energy
Kinetic energy is the energy of a moving body, KE = ½mv². Potential energy is the energy due to position or height, PE = mgh. Energy, like work, is measured in joules.
Conservation of energy
Energy can neither be created nor destroyed; it only changes from one form to another, and the total energy stays the same. For a freely falling body, potential energy converts into kinetic energy while their sum stays constant.
Power
Power is the rate of doing work, P = W/t, measured in watts (W). One watt is one joule per second. The commercial unit of electrical energy is the kilowatt-hour (kWh): 1 kWh = 3.6 × 10⁶ J.
Important formulas
Work
W = F × s (joule)
Kinetic energy
KE = ½mv²
Potential energy
PE = mgh
Power
P = W ÷ t (watt); 1 kWh = 3.6 × 10⁶ J
Key definitions
- Work
- The product of force and the displacement in the direction of the force (W = Fs).
- Kinetic energy
- The energy possessed by a body due to its motion.
- Potential energy
- The energy possessed by a body due to its position or height.
- Power
- The rate of doing work or transferring energy (P = W/t).
Solved examples
Q1. A force of 10 N moves a body 5 m in its direction. Find the work done.
Solution: W = F × s = 10 × 5 = 50 J.
Q2. Find the kinetic energy of a 2 kg body moving at 4 m/s.
Solution: KE = ½mv² = ½ × 2 × 4² = ½ × 2 × 16 = 16 J.
Q3. A machine does 600 J of work in 30 s. Find its power.
Solution: P = W/t = 600/30 = 20 W.
Common mistakes to avoid
- Saying work is done even when there is no displacement.
- Forgetting to square the velocity in ½mv².
- Confusing power (rate of work) with energy (work done).
- Mixing up the joule (energy) with the watt (power).
Work and Energy — MCQ Quiz
12 questions with instant feedback. Use number keys 1–4 to answer.
The SI unit of work is the:
Practice questions
Short answer
When is no work said to be done by a force?
When there is no displacement, or when the force acts perpendicular to the displacement.
State the law of conservation of energy.
Energy can neither be created nor destroyed; it only changes form, and the total energy remains constant.
Define one watt.
One watt is the power when one joule of work is done in one second.
Long answer
Show that for a freely falling body, the total mechanical energy is conserved.
At the top, the body has maximum potential energy (mgh) and zero kinetic energy. As it falls, height decreases (PE falls) while speed increases (KE rises). At each point, the loss in PE equals the gain in KE, so the sum PE + KE stays constant. Just before hitting the ground, all the energy is kinetic and equals the original potential energy — total energy is conserved.
A boy of mass 40 kg climbs stairs of height 5 m in 10 s. Find the work done and his power. (g = 10 m/s².)
Work done against gravity = mgh = 40 × 10 × 5 = 2000 J. Power = W/t = 2000/10 = 200 W.
HOTS (Higher Order Thinking)
A coolie carries a heavy bag on his head and walks on a level platform. Is he doing work against gravity? Explain.
No work is done against gravity, because the displacement is horizontal while gravity acts vertically — the force of gravity is perpendicular to the motion, so the work done against it is zero.
If the speed of a moving body is doubled, how does its kinetic energy change?
Kinetic energy depends on v², so doubling the speed makes the kinetic energy four times (2²) larger.
Quick revision
Revision notes
- Work W = F × s (joule); no displacement ⇒ no work.
- KE = ½mv²; PE = mgh.
- Energy is conserved — only changes form.
- Power P = W/t (watt); 1 kWh = 3.6 × 10⁶ J.
Key takeaways
- Work needs a force AND a displacement along it.
- Square the velocity in kinetic energy.
- Power is how fast work is done, not how much.
Frequently asked questions
When is work done in physics?
When a force acts on a body and moves it in the direction of the force; W = F × s.
What is the difference between kinetic and potential energy?
Kinetic energy is due to motion (½mv²); potential energy is due to position or height (mgh).
What is the commercial unit of electrical energy?
The kilowatt-hour (kWh), where 1 kWh = 3.6 × 10⁶ joules.