ScienceCBSE Class 9 · Work, Energy, and Simple Machines

Power and Simple Machines: Pulley, Inclined Plane and Lever (Class 9)

Updated 17 October 2026 · Fact-checked

Power is the rate of doing work, P = W ÷ t, measured in watts (1 W = 1 J s⁻¹; 1 hp = 746 W). A simple machine makes work easier by changing the size or direction of the force but cannot reduce the total work. Mechanical advantage MA = load ÷ effort: a fixed pulley has MA = 1, a smooth inclined plane has MA = L ÷ h, and a lever has MA = effort arm ÷ load arm, with the law effort × effort arm = load × load arm.

Understand Power, Pulleys, Inclined Planes and Levers

Power. Running up the stairs in one minute and walking up in five minutes need the same work, but running needs more power. Power is the rate of doing work: P = W ÷ t. The SI unit is the watt (W), 1 W = 1 J s⁻¹, named after James Watt. One horsepower (hp) = 746 W, still used for engines and pumps. More work in the same time, or the same work in less time, means more power. If a machine gives an object speed, the work done equals the gain in kinetic energy, so P = ½mv² ÷ t (ignoring losses).

Simple machines. A simple machine makes a task easier by changing the size or the direction of the force needed. It cannot reduce the total work: ignoring friction, work put in equals useful work out. The effort is the force we apply, and the load is the force to be overcome. Mechanical advantage (MA) = load ÷ effort; it has no unit.

Pulley. A grooved wheel guiding a rope. A fixed pulley (flagpole, well) changes only the direction of the force, so effort = load and MA = 1; pulling down is easier than lifting up. Movable pulleys and pulley systems (cranes, lifts) have MA greater than 1.

Inclined plane. Pushing a load of weight mg up a smooth ramp of length L to a height h: work in = work out, so effort × L = mg × h, and MA = mg ÷ effort = L ÷ h. Since L is greater than h, MA is greater than 1: a longer, gentler slope needs less force but over a longer distance. This is why hill roads wind round in gentle slopes.

Lever. A rigid bar that turns about a fixed point, the fulcrum. The effort arm is the distance of the effort from the fulcrum and the load arm is the distance of the load from it. Law of the lever: effort × effort arm = load × load arm, so MA = load ÷ effort = effort arm ÷ load arm. A longer effort arm needs less effort; the end with the small effort moves through a large distance and the load end through a small one. Class I levers have the fulcrum in the middle (seesaw, crowbar, scissors, pliers, beam balance; MA can be more than, equal to or less than 1). Class II have the load in the middle (bottle opener, wheelbarrow, lemon squeezer; MA always more than 1). Class III have the effort in the middle (tongs, tweezers, broom, fishing rod, forearm; MA always less than 1, gaining speed or convenience). Many machines combine several simple machines.

Power, Pulleys, Inclined Planes and Levers: formulas and key facts

Power: $P = W \div t ∣1 W = 1 J s^{- 1} ∣1 h p = 746 W$
Work from lifting: $W = m g h (g = 9.8 m s^{- 2})$
Mechanical advantage: $M A = l o a d \div e f f or t$
Fixed pulley and inclined plane: $F i x e d p u l l ey : M A = 1∣ s m oo t hin c l in e d pl an e : M A = L \div h$
Law of the lever: $E f f or t \times e f f or t a r m = l o a d \times l o a d a r m ∣ M A = e f f or t a r m \div l o a d a r m$
Work in and out: $I g n or in g f r i c t i o n : e f f or t \times d i s t an ce m o v e d b y e f f or t = l o a d \times d i s t an ce m o v e d b y l o a d$

How to solve Power, Pulleys, Inclined Planes and Levers questions

Use this method for power and machine numericals.

1Write the load, effort, arms or lengths with units; convert hp to W and minutes to seconds if needed.
2For power, find the work (F × s or mgh) and divide by the time in seconds.
3For a lever, equate effort × effort arm with load × load arm and solve for the unknown.
4For an inclined plane, use MA = L ÷ h and effort = load ÷ MA (smooth ramp).
5Check that work in = work out when friction is ignored: effort × distance = load × distance.
6Classify a lever by finding which of fulcrum, load and effort lies in the middle.

Power, Pulleys, Inclined Planes and Levers in real life

Each concept, met in an everyday situation. Read the situation, try the problem, then check the solution. The one-line hook is what to remember.

Power of a student climbing stairs

Suppose a 50 kg student climbs a flight of stairs 4 m high in 10 s, and another time takes 20 s for the same climb (g = 9.8 m s⁻²).

Find the work done and the power in each case.

Try it first, then show the solutionSolution

Work done against gravity = mgh = 50 × 9.8 × 4 = 1960 J in both cases.
Power in 10 s: P = 1960 ÷ 10 = 196 W.
Power in 20 s: P = 1960 ÷ 20 = 98 W, half as much, though the work is the same.

Answer: 1960 J in both; 196 W and 98 W.

Memory hook: Same work, less time, more power.

A wheelbarrow as a lever

Suppose a wheelbarrow carries sand weighing 600 N, with the load 0.4 m from the wheel axle (the fulcrum) and the handles 1.2 m from the axle.

Find the effort needed and the mechanical advantage, and name the class of lever.

Try it first, then show the solutionSolution

Effort × 1.2 = 600 × 0.4, so effort = 240 ÷ 1.2 = 200 N.
MA = load ÷ effort = 600 ÷ 200 = 3 (also effort arm ÷ load arm = 1.2 ÷ 0.4 = 3).
The load lies between the fulcrum and the effort, so it is a Class II lever.

Answer: 200 N; MA = 3; Class II lever.

Memory hook: Long handles save effort.

Tricks to remember Power, Pulleys, Inclined Planes and Levers

Short memory aids. Say each one aloud once, then use it on a question the same day.

FLE: Fulcrum, Load, Effort
Class I: F in the middle. Class II: L in the middle. Class III: E in the middle: 'F-L-E' is 1-2-3 by who is centre.
Use it when: Classifying levers.
Power is work per second
Divide the work by the time in seconds to get watts.
Use it when: Power numericals.
Longer slope, smaller push
MA = L ÷ h: a ramp twice as long halves the effort, but you push twice as far.
Use it when: Inclined-plane reasoning.
You cannot cheat work
A machine trades force for distance; it never gives more work out than put in.
Use it when: Explaining why machines help.

Power, Pulleys, Inclined Planes and Levers: solved examples

Ordered from board level to HOTS. Try each one before you open the solution.

Example 1: Power of a lifting motor · 3 marks · Short answerBoard level

(Take g = 9.8 m s⁻².) A motor lifts a 60 kg load through 5 m in 10 s.
(a) Find the work done. (1)
(b) Find the power in watts. (1)
(c) Express the power in hp, to two decimal places (1 hp = 746 W). (1)

Try it first, then show the solutionSolution

(a) W = mgh = 60 × 9.8 × 5 = 2940 J. (1)
(b) P = W ÷ t = 2940 ÷ 10 = 294 W. (1)
(c) 294 ÷ 746 = 0.39 hp. (1)

Answer: (a) 2940 J; (b) 294 W; (c) 0.39 hp.

Example 2: Mechanical advantage of a lever and a pulley · 3 marks · Short answerBoard level

(a) A lever has an effort arm of 1.2 m and a load arm of 0.3 m. Find its MA and the effort needed to lift an 80 N load. (2)
(b) What is the MA of a fixed pulley, and what is it used for? (1)

Try it first, then show the solutionSolution

(a) MA = effort arm ÷ load arm = 1.2 ÷ 0.3 = 4. Effort = load ÷ MA = 80 ÷ 4 = 20 N. (2)
(b) MA = 1; it only changes the direction of the force, so it is easier to pull down than to lift up (flagpole, well). (1)

Answer: (a) MA = 4, effort 20 N; (b) MA = 1, changes direction.

Example 3: Loading a drum up a ramp · 5 marks · Long answerHarder board level

A drum weighing 600 N is raised 1.5 m onto a platform using a 6 m long ramp.
(a) Find the MA of a smooth ramp and the effort needed. (2)
(b) Show that work in equals work out. (1)
(c) With friction the effort needed is 180 N. Find the work put in and the fraction of it that is useful work. (1)
(d) What effort is needed with a 12 m smooth ramp? (1)

Try it first, then show the solutionSolution

(a) MA = L ÷ h = 6 ÷ 1.5 = 4; effort = 600 ÷ 4 = 150 N. (2)
(b) Work in = 150 × 6 = 900 J; work out (useful) = 600 × 1.5 = 900 J. They are equal. (1)
(c) Work in = 180 × 6 = 1080 J; useful fraction = 900 ÷ 1080 = 0.83, about 83% (the rest goes to heat against friction). (1)
(d) MA = 12 ÷ 1.5 = 8; effort = 600 ÷ 8 = 75 N. (1)

Answer: (a) MA = 4, effort 150 N; (b) 900 J = 900 J; (c) 1080 J, about 83% useful; (d) 75 N.

Example 4: A pump and its power in horsepower · 5 marks · Long answerHarder board level

(Take g = 9.8 m s⁻².) A pump raises 500 kg of water every minute through 12 m.
(a) Find the work done each minute. (1)
(b) Find the power in watts. (1)
(c) Express it in hp (1 hp = 746 W). (1)
(d) How long does it take to fill a tank holding 6000 kg of water? (1)
(e) Find the work done in filling the tank. (1)

Try it first, then show the solutionSolution

(a) W = mgh = 500 × 9.8 × 12 = 58 800 J. (1)
(b) P = 58 800 ÷ 60 = 980 W. (1)
(c) 980 ÷ 746 = 1.31 hp. (1)
(d) 6000 ÷ 500 = 12 minutes. (1)
(e) W = 12 × 58 800 = 705 600 J; check: 6000 × 9.8 × 12 = 705 600 J. (1)

Answer: (a) 58 800 J; (b) 980 W; (c) 1.31 hp; (d) 12 minutes; (e) 705 600 J.

Example 5: Three levers in daily life · 4 marks · Case-basedHOTS / competency

(a) A uniform bar balances on a fulcrum. Five identical coins are placed 12 cm to the left of the fulcrum. At what distance to the right must three identical coins be placed to balance them? (1)
(b) Which class of lever is this beam balance? (1)
(c) A pair of tongs has its fulcrum at one end, the effort 0.1 m from it and the load 0.2 m from it. Find the MA and the effort for a 1 N load. (1)
(d) Why is a Class III lever still useful although its MA is below 1? (1)

Try it first, then show the solutionSolution

(a) Balance: 3 × d = 5 × 12, so d = 60 ÷ 3 = 20 cm. (1)
(b) Class I, because the fulcrum is between the two weights. (1)
(c) The effort is in the middle, a Class III lever. MA = effort arm ÷ load arm = 0.1 ÷ 0.2 = 0.5. Effort = load ÷ MA = 1 ÷ 0.5 = 2 N. (1)
(d) It trades force for speed and convenience: the load end moves a larger distance and faster than the effort end, as with tweezers or a fishing rod. (1)

Answer: (a) 20 cm; (b) Class I; (c) MA = 0.5, effort 2 N; (d) gains speed and convenience.

Where students lose marks in Power, Pulleys, Inclined Planes and Levers

The slips examiners see most often, and what to write instead.

Mistake: Using minutes in the power formula.
The unit of power requires seconds.
Wrong working
P = 58 800 J ÷ 1 min = 58 800 W
Right working
P = 58 800 ÷ 60 s = 980 W
Do this: Convert time to seconds first.
Usually costs: 2 marks.
Mistake: Putting effort and load the wrong way round in MA.
The ratio is inverted.
Wrong working
MA = effort ÷ load = 20 ÷ 80 = 0.25
Right working
MA = load ÷ effort = 80 ÷ 20 = 4
Do this: MA = load ÷ effort.
Usually costs: 1 to 2 marks.
Mistake: Claiming a machine increases the work done.
A big force gain is mistaken for a work gain.
Wrong working
A lever gives more work output than input.
Right working
Ignoring friction, work out equals work in; a smaller force acts over a larger distance.
Do this: Force × distance stays the same.
Usually costs: 1 mark.
Mistake: Mixing arms: using the lengths from the end of the bar instead of the fulcrum.
Arms are measured from the fulcrum.
Wrong working
Effort arm = full length of the bar.
Right working
Arm = distance from the fulcrum to the point of action.
Do this: Mark the fulcrum first.
Usually costs: 2 marks.
Mistake: Writing the MA of a fixed pulley as more than 1.
Pulleys are assumed to reduce effort.
Wrong working
MA of a fixed pulley is 2.
Right working
A fixed pulley has MA = 1; it only changes direction.
Do this: Only movable pulley systems have MA greater than 1.
Usually costs: 1 mark.

Exam tips

State the formula (P = W ÷ t, MA = load ÷ effort, effort × arm = load × arm) before substituting.
Draw the lever with the fulcrum, load and effort marked with arrows and arms labelled.
In an inclined-plane answer, write MA = L ÷ h and check that work in = work out.
Convert hp to W and minutes to seconds before using them.
Give the class of lever by naming what lies in the middle.

Practice questions on Power, Pulleys, Inclined Planes and Levers

Write each answer on paper first. Open the hint only if you are stuck, and the answer only when you have finished.

Q1 · 2 marks · Very short answerBoard level
Two students of equal mass climb the same flight of stairs, one in 8 s and the other in 12 s. Which has the greater power and what is the ratio of their powers? Define power in one line.
Hint
Same work, different time.
Answer
Power is the rate of doing work. The student who takes 8 s has the greater power (1 mark). For the same work, power is inversely proportional to time: ratio = 12 ÷ 8 = 1.5, i.e. 3 : 2 (1 mark).
Q2 · 3 marks · Short answerHarder board level
An engine has a rating of 3 hp (1 hp = 746 W). Find (a) its power in watts and (b) the work it can do in 10 minutes, and (c) the time it takes to do 447 600 J of work.
Hint
Convert minutes to seconds.
Answer
(a) P = 3 × 746 = 2238 W (1 mark). (b) W = P × t = 2238 × 600 = 1 342 800 J (1 mark). (c) t = 447 600 ÷ 2238 = 200 s (1 mark).
Q3 · 2 marks · Assertion-reasonBoard level
Assertion (A): A fixed pulley has a mechanical advantage of 1 but is still useful. Reason (R): It changes the direction of the force, so we can pull downward to lift a load. Choose: (a) A and R both true, R explains A; (b) A and R both true, R does not explain A; (c) A true, R false; (d) A false, R true.
Hint
Effort equals load for a fixed pulley.
Answer
(a). A fixed pulley has effort equal to load (MA = 1) but lets us pull down, which is easier than lifting up, so it is useful because it changes the direction of the force.
Q4 · 3 marks · Short answerHarder board level
A crowbar has its fulcrum between the effort and the load, with an effort arm of 1.5 m and a load arm of 0.25 m. It lifts a load of 900 N. (a) Find the MA and the effort. (b) Name the class of lever. (c) If the effort end moves 0.6 m, how far does the load move?
Hint
Work in equals work out.
Answer
(a) MA = 1.5 ÷ 0.25 = 6; effort = 900 ÷ 6 = 150 N (1 mark). (b) Class I (fulcrum in the middle) (1 mark). (c) Load distance = effort distance ÷ MA = 0.6 ÷ 6 = 0.1 m; check 150 × 0.6 = 90 J = 900 × 0.1 (1 mark).
Q5 · 4 marks · Case-basedHOTS / competency
A truck of weight 5000 N must climb a hill 100 m high. Road A is 1 km long and Road B is 2 km long, both smooth in this model. (a) Find the MA and the force along the road for each. (b) Show that the work done is the same on both roads. (c) The truck travels at 10 m s⁻¹ on each road; find the power on each. (d) Why do hill roads wind in gentle slopes?
Hint
MA = L ÷ h with L and h in the same unit.
Answer
(a) Road A: MA = 1000 ÷ 100 = 10, force = 5000 ÷ 10 = 500 N; Road B: MA = 2000 ÷ 100 = 20, force = 250 N (1 mark). (b) Road A: 500 × 1000 = 500 000 J; Road B: 250 × 2000 = 500 000 J; both equal mgh = 5000 × 100 = 500 000 J (1 mark). (c) Time on A = 1000 ÷ 10 = 100 s, so P = 500 000 ÷ 100 = 5000 W; time on B = 200 s, so P = 2500 W (1 mark). (d) A gentler, longer slope needs less force and less power, although the work is the same (1 mark).

Test your recall

Answer in your head or on paper first, then open the card. Pulling an answer out of memory makes it stick far better than re-reading.

1.What is the SI unit of power?Show answer
The watt (W), equal to 1 J s⁻¹.
2.What is 1 horsepower in watts?Show answer
746 W.
3.What is the MA of a fixed pulley?Show answer
1.
4.State the law of the lever.Show answer
Effort × effort arm = load × load arm.
5.Which class of lever has MA always less than 1?Show answer
Class III.
6.What does MA equal for a smooth inclined plane?Show answer
L ÷ h, the length of the ramp divided by its height.

Power, Pulleys, Inclined Planes and Levers: frequently asked questions

Can a machine give out more work than we put in?

No. Ignoring friction, work out equals work in. A machine only changes the size or direction of the force.

Why is a longer ramp easier to climb?

The same work is spread over a longer distance, so the force needed is smaller.

What is the difference between power and energy?

Energy is the capacity to do work, measured in joules. Power is how fast work is done, in watts (joules per second).

Why do we use a lever with a long handle?

A longer effort arm gives a larger mechanical advantage, so less effort is needed.

Where is the fulcrum in a wheelbarrow?

At the wheel axle; the load lies between the wheel and the handles, which makes it a Class II lever.