PrepRung
Sign inSign up free

Class 9 Science Chapter 7: Work, Energy, and Simple Machines — Notes, Examples & Practice

In science, pushing a wall all day does no work at all — but lifting a bag does. This chapter defines work precisely, then measures how fast it is done (power), the energy that makes work possible (kinetic and potential), and the law that energy is never created or destroyed. Finally it explains how simple machines like levers, pulleys and ramps make tasks easier without giving free energy.

1Work in science

Work is done when a force makes an object move (be displaced) in the direction of the force. For a constant force FF along the displacement ss: W=F×sW = F \times s. The SI unit is the joule (J): 1 J is the work done when a 1 N force moves an object 1 m.

Two conditions must both hold: a force acts, and there is displacement with a component along the force. Pushing a wall (no displacement) or carrying a bag horizontally at constant height (the upward supporting force is perpendicular to the motion) does zero work on the object.

Work can be positive (force along the motion: lifting a load), negative (force opposite to the motion: friction on a sliding box, brakes on a car) or zero (force perpendicular to the motion: the pull of the string on a stone whirled in a circle).

Key points & definitions
  • W=FsW = F s (force along displacement), unit joule (J = N m).
  • Work against gravity in lifting: W=mghW = mgh.
  • Force ⊥ displacement ⇒ W=0W = 0.
Worked example 1

A porter lifts a 20 kg suitcase from the floor onto his head, 1.5 m high, and then walks 50 m on level ground. How much work does he do on the suitcase in each part? (g=10g = 10 m/s²)

  1. Lifting: W=mgh=20×10×1.5=300W = mgh = 20 \times 10 \times 1.5 = 300 J.
  2. Walking: his upward force is perpendicular to the horizontal displacement, so W=0W = 0 on the suitcase (ignoring small ups and downs).

Answer: 300 J, then 0 J.

Common mistakes
  • Saying someone holding a heavy load still does work on it — he gets tired (his muscles use energy), but no mechanical work is done on the load.
  • Using the distance walked instead of the height lifted.

2Power

Power is the rate of doing work (or of transferring energy): P=WtP = \dfrac{W}{t}. Its SI unit is the watt (W): 1 W = 1 J/s. Larger units: 1 kW = 1000 W.

Two people may do the same work — climbing the same stairs — but the one who climbs faster develops more power.

Electrical energy is billed in kilowatt-hours (kWh), the energy used by a 1 kW appliance in 1 hour: 1 kWh=1000×3600=3.6×1061 \text{ kWh} = 1000 \times 3600 = 3.6 \times 10^6 J. One kWh is the 'unit' on your electricity bill.

Key points & definitions
  • P=WtP = \dfrac{W}{t}, unit watt (W = J/s).
  • 1 kWh=3.6×106 J1 \text{ kWh} = 3.6 \times 10^6 \text{ J}
  • Energy =P×t= P \times t
Worked example 1

A 50 kg girl climbs 15 steps, each 20 cm high, in 10 s. Find her power. (g=10g = 10 m/s²)

  1. Height =15×0.2=3= 15 \times 0.2 = 3 m.
  2. W=50×10×3=1500W = 50 \times 10 \times 3 = 1500 J.
  3. P=150010=150P = \dfrac{1500}{10} = 150 W.

Answer: 150 W.

Worked example 2

A 1500 W geyser runs 2 hours a day. How many units does it use in 30 days?

  1. Per day: 1.5 kW×2 h=31.5 \text{ kW} \times 2 \text{ h} = 3 kWh.
  2. 30 days: 9090 kWh.

Answer: 90 units.

Common mistakes
  • Confusing kW (power) with kWh (energy).

3Kinetic and potential energy

Energy is the capacity to do work or to cause change. It is measured in joules, like work.

Kinetic energy is the energy of motion: KE=12mv2KE = \dfrac{1}{2}mv^2. It depends on the square of speed, so doubling the speed makes the kinetic energy four times as large — the reason speeding cars are so dangerous. It comes from the work done to speed the object up.

Potential energy is stored energy due to position or shape. Gravitational potential energy near Earth's surface is PE=mghPE = mgh, equal to the work done lifting the object through height hh. A stretched rubber band or a wound spring stores elastic potential energy.

Key points & definitions
  • KE=12mv2KE = \dfrac{1}{2}mv^2
  • PE=mghPE = mgh
  • Work done on a body = change in its kinetic energy.
Worked example 1

A 1000 kg car speeds up from 10 m/s to 20 m/s. Find the work done by the engine (ignoring friction).

  1. Initial KE=12×1000×100=50000KE = \dfrac{1}{2} \times 1000 \times 100 = 50000 J.
  2. Final KE=12×1000×400=200000KE = \dfrac{1}{2} \times 1000 \times 400 = 200000 J.
  3. Work =200000−50000=150000= 200000 - 50000 = 150000 J =150= 150 kJ.

Answer: 150 kJ — four times the original KE after doubling the speed.

Trick / memory aid

Double the speed → 4× KE. Double the height → 2× PE.

Common mistakes
  • Forgetting to square vv or the 12\dfrac{1}{2}.
  • Using hh as the length of a slope instead of the vertical height.

4Conservation of energy

Law of conservation of energy: energy can neither be created nor destroyed; it can only be transformed from one form to another or transferred between objects. The total energy of an isolated system stays constant.

A freely falling ball turns potential energy into kinetic energy: at every point PE+KEPE + KE is the same (if air resistance is ignored). At the top it is all PE; just before hitting the ground it is all KE.

In real situations some energy is dissipated — usually as heat and sound due to friction and air resistance. It is not lost from the universe, but it spreads out into a less useful form. Common transformations: a dam (PE → KE → electrical), a torch (chemical → electrical → light), a car engine (chemical → heat → kinetic).

Key points & definitions
  • Total energy is constant: PE+KE=constantPE + KE = \text{constant} (no friction).
  • Speed after falling height hh from rest: v=2ghv = \sqrt{2gh}.
  • Friction converts mechanical energy into heat.
Worked example 1

A 2 kg ball is dropped from 20 m. Find its PE and KE at the top, halfway, and just before landing. (g=10g = 10 m/s²)

  1. Top: PE=2×10×20=400PE = 2 \times 10 \times 20 = 400 J, KE=0KE = 0.
  2. Halfway (10 m): PE=200PE = 200 J, so KE=200KE = 200 J.
  3. Ground: PE=0PE = 0, KE=400KE = 400 J, so v=400=20v = \sqrt{400} = 20 m/s.

Answer: Total stays 400 J; landing speed 20 m/s.

Common mistakes
  • Saying energy is 'used up' — it is transformed, often into heat.

5Simple machines and mechanical advantage

A simple machine changes the size or direction of a force to make work easier. The force we apply is the effort; the force overcome is the load. Mechanical advantage MA=loadeffortMA = \dfrac{\text{load}}{\text{effort}}; MA > 1 means the machine multiplies force.

A lever turns about a fulcrum. It balances when load × load arm = effort × effort arm. Class I has the fulcrum in the middle (see-saw, scissors); Class II has the load in the middle (nutcracker, wheelbarrow) — always MA > 1; Class III has the effort in the middle (tongs, forearm) — MA < 1 but gives speed and range of motion.

A single fixed pulley only changes direction (MA = 1); a movable pulley gives MA = 2. An inclined plane lets a smaller force raise a load over a longer path: ideal MA = length ÷ height. A wheel and axle (steering wheel, screwdriver) multiplies force by the ratio of radii. In every case, a smaller effort moves through a larger distance — machines never give more work out than you put in.

Key points & definitions
  • MA=loadeffortMA = \dfrac{\text{load}}{\text{effort}} ; velocity ratio VR=distance moved by effortdistance moved by loadVR = \dfrac{\text{distance moved by effort}}{\text{distance moved by load}}
  • Lever: load × load arm = effort × effort arm
  • Inclined plane: ideal MA=lhMA = \dfrac{l}{h} · Movable pulley: ideal MA = 2
Worked example 1

A crowbar 1.2 m long has its fulcrum 0.2 m from the load end. What effort lifts a 600 N rock?

  1. Load arm =0.2= 0.2 m; effort arm =1.0= 1.0 m.
  2. 600×0.2=E×1.0⇒E=120600 \times 0.2 = E \times 1.0 \Rightarrow E = 120 N.
  3. MA =600120=5= \dfrac{600}{120} = 5.

Answer: 120 N (MA 5).

Trick / memory aid

Lever classes by what is in the middle: 1-2-3 = F-L-E (Fulcrum, Load, Effort).

Common mistakes
  • Thinking a machine reduces the work needed — it reduces the force, but the effort moves further.

6Efficiency

Efficiency compares useful work (or energy) out with work (or energy) put in: η=useful outputinput×100%\eta = \dfrac{\text{useful output}}{\text{input}} \times 100\%. For a machine, η=MAVR×100%\eta = \dfrac{MA}{VR} \times 100\%.

An ideal (frictionless) machine would be 100% efficient. Real machines are always less, because some input energy is wasted overcoming friction and lifting moving parts (like the pulley block itself), appearing as heat and sound.

Oiling, using ball bearings and making parts lighter improve efficiency. A machine with efficiency over 100% would create energy — impossible.

Key points & definitions
  • η=outputinput×100%=MAVR×100%\eta = \dfrac{\text{output}}{\text{input}} \times 100\% = \dfrac{MA}{VR} \times 100\%
  • Real machines: η<100%\eta < 100\%.
Worked example 1

A 500 N load is pushed 2 m up a ramp to a height of 0.5 m using a 160 N force along the ramp. Find the efficiency.

  1. Useful work =500×0.5=250= 500 \times 0.5 = 250 J.
  2. Work put in =160×2=320= 160 \times 2 = 320 J.
  3. η=250320×100≈78%\eta = \dfrac{250}{320} \times 100 \approx 78\%.

Answer: About 78%.

Common mistakes
  • Swapping output and input and getting more than 100%.

Important questions

Try each question on paper first, then tap it to check the answer.

Basic Recall and direct use

Define one joule.Answer
The work done when a force of 1 N moves an object through 1 m in the direction of the force.
Find the kinetic energy of a 0.5 kg ball moving at 8 m/s.Answer
12×0.5×64=16\dfrac{1}{2} \times 0.5 \times 64 = 16 J.
Give one example each of Class I, II and III levers.Answer
Class I: see-saw or scissors. Class II: nutcracker or wheelbarrow. Class III: fire tongs or the human forearm.

Medium Two or three steps

A motor lifts 200 kg of water to a tank 15 m high in 1 minute. Find the power. (g=10g = 10 m/s²)Answer
W=200×10×15=30000W = 200 \times 10 \times 15 = 30000 J. P=3000060=500P = \dfrac{30000}{60} = 500 W.
Is work done when a satellite moves in a circular orbit around the Earth? Explain.Answer
No. Gravity acts towards the centre, perpendicular to the satellite's motion at every instant, so the work done by gravity is zero and its speed stays constant.
A stone of mass 1 kg is thrown up with 10 m/s. Using energy conservation, find the maximum height. (g=10g = 10 m/s²)Answer
12mv2=mgh⇒h=v22g=10020=5\dfrac{1}{2}mv^2 = mgh \Rightarrow h = \dfrac{v^2}{2g} = \dfrac{100}{20} = 5 m.

Advanced Reasoning and HOTS

A pulley system lifts a 900 N load by 1 m while the effort of 250 N moves 4 m. Find MA, VR and efficiency, and explain why efficiency is less than 100%.Answer
MA =900250=3.6= \dfrac{900}{250} = 3.6; VR =4= 4; η=3.64×100=90%\eta = \dfrac{3.6}{4} \times 100 = 90\%. Some input work is used against friction in the pulleys and to lift the movable pulley blocks.
Why is it easier to push a heavy trunk up a long gentle ramp than a short steep one to the same height? Does it take less work?Answer
A longer ramp needs a smaller force because the same work (mghmgh) is spread over a longer distance (F≈mghlF \approx \dfrac{mgh}{l}). The ideal work is the same; a real long ramp may even take slightly more total work because friction acts over a longer path.

Self-check quiz

Five quick questions. Tap an option to see if you are right.

No work is done on a body when the force is
If the speed of a body doubles, its kinetic energy becomes
1 kWh equals
A nutcracker is a lever of
Real machines have efficiency less than 100% because

FAQ

Why do we feel tired holding a heavy bag if no work is done?

No mechanical work is done on the bag, but your muscles constantly contract and relax to hold it up, using chemical energy that turns into heat.

Do simple machines save energy?

No. They let you use a smaller force or a more convenient direction, but the effort moves through a greater distance; the work you put in is at least the work you get out.

What is the difference between energy and power?

Energy is the capacity to do work (joules). Power is how quickly energy is transferred or work is done (joules per second = watts).

Book references

  • NCERT Exploration, Chapter 7: Work, Energy, and Simple MachinesRead the chapter and do every exercise set first.
  • Science for Class 9 (Physics, Chemistry, Biology) — Lakhmir Singh & Manjit Kaur (S. Chand)Extra numericals and short answers; chapter order follows the old syllabus, so match by topic.
  • S. Chand's Science for Class 9 — S. ChandUseful extra reading and practice; match by topic.
  • Exemplar Problems in Science, Class IX — NCERTConcept-testing MCQs and short answers (written for the old book).

These notes, examples and questions are written by PrepRung in our own words to help you study the NCERT Exploration book. NCERT and CBSE are not affiliated with PrepRung. Always study from your textbook too.