This MCQ module is based on: Simple Machines — Levers, Pulleys and Inclined Planes
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Simple Machines — Levers, Pulleys and Inclined Planes
🎓 Class 9
Science
CBSE
Theory
Ch 7 — Work, Energy, and Simple Machines
⏱ ~13 min
🌐 Language: [gtranslate]
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7.13 Why Do We Need Simple Machines?
Lifting a 100 kg crate straight up requires you to apply at least 1000 N — far beyond the capacity of an ordinary person. But push the same crate up a long ramp, or hoist it with a pulley system, and the job becomes manageable. The device that lets you trade a small force over a long distance for a large force over a small distance is called a simple machine.
A simple machine does not reduce the total work to be done — energy must still be supplied. It only changes the way effort is applied so the task feels easier. The six classical simple machines are: lever, pulley, inclined plane, wheel and axle, screw, and wedge.
7.14 Mechanical Advantage, Velocity Ratio and Efficiency
Three quantities are used to describe the performance of any simple machine.
Mechanical Advantage (MA)
Definition. The mechanical advantage of a machine is the ratio of the load lifted (output force) to the effort applied (input force):
\[ \text{MA} = \frac{\text{Load}}{\text{Effort}} \]
MA has no unit. MA > 1 → effort is multiplied. MA < 1 → speed/distance is multiplied instead.
Velocity Ratio (VR)
The velocity ratio is the ratio of the distance moved by the effort to the distance moved by the load in the same time:
\[ \text{VR} = \frac{\text{Distance moved by effort}}{\text{Distance moved by load}} \]
For an ideal (frictionless) machine, MA = VR.
Efficiency (η)
The efficiency of a machine is the percentage of input work that comes out as useful output:
\[ \eta = \frac{\text{Useful work output}}{\text{Total work input}} \times 100\% = \frac{\text{MA}}{\text{VR}} \times 100\% \]
A real machine always loses some energy to friction, so η < 100%.
7.15 The Lever
A lever is a rigid bar that turns about a fixed point called the fulcrum (F). There are three points of interest on a lever — the position of the load (L), the fulcrum (F), and the point where the effort (E) is applied. By the principle of moments (for an ideal lever):
\[ \text{Load} \times \text{Load arm} = \text{Effort} \times \text{Effort arm} \]
\[ \text{MA} = \frac{\text{Effort arm}}{\text{Load arm}} \]
Three classes of lever
⚖️ Three Classes of Lever — Click each to remember its MA L1 Remember
Every lever is one of three classes — the only difference is which point sits in the middle. Click each row to recall the order, the MA range, and a familiar example.
Click any of the three lever rows above to recall its order, MA, and an everyday example.
| Class | Order (along bar) | MA value | Examples |
|---|---|---|---|
| 1 | L – F – E | >1, <1, or =1 | Seesaw, crowbar, scissors, beam balance |
| 2 | F – L – E | always > 1 | Wheelbarrow, nutcracker, bottle opener |
| 3 | F – E – L | always < 1 | Tongs, broom, forearm, fishing rod |
Worked Example — Crowbar L3
A crowbar 100 cm long is used to lift a stone. The fulcrum is placed 20 cm from the stone. Find the MA.
Effort arm = 100 − 20 = 80 cm. Load arm = 20 cm.
MA = 80 / 20 = 4 — effort is multiplied 4 times.
7.16 The Pulley
A pulley is a wheel with a grooved rim that carries a rope. By changing the direction (and sometimes the magnitude) of the applied force, it makes lifting much more convenient.
A. Single fixed pulley
Mounted at a fixed point (e.g., the top of a flagpole). Pulling the rope downward lifts the load upward. MA = 1 (ideally) — it does not multiply force, only changes direction. Convenient because pulling down is easier than pulling up.
B. Single movable pulley
The pulley itself moves with the load; one end of the rope is tied to a support, the load hangs from the pulley axle, and the effort is applied at the free end. The load is shared by two rope segments → MA = 2 (ideally). VR = 2 (effort end moves twice as far as the load).
C. Block and tackle
A combination of fixed and movable pulleys arranged in two blocks. If \(n\) rope segments support the lower block, MA = n. Used for cranes and dock lifts. A 4-pulley system can let a single worker lift a 400 kg load with an effort of about 100 kg-weight (ignoring friction).
7.17 The Inclined Plane
An inclined plane is a flat sloping surface used to raise a load to a height by pushing it along the slope rather than lifting it vertically. Examples — a ramp into a temple, the slide in a playground, a sloping plank used to roll a barrel onto a truck.
Let \(L\) be the length of the slope and \(h\) the vertical height it rises. To lift a load of weight \(W\) directly, an upward force \(W\) is needed; on a frictionless ramp the effort needed is only \((W h / L)\). Therefore:
\[ \text{MA}_{\text{ideal}} = \frac{L}{h} \quad\text{and}\quad \text{VR} = \frac{L}{h} \]
The longer (and gentler) the slope, the smaller the effort required — but the larger the distance you must push.
Worked Example — Loading a barrel L3
A 120 kg barrel is rolled up a frictionless ramp 6 m long onto a truck 1.5 m high. (g = 10 m s⁻²) Find the effort needed and the MA.
Weight (load) = 120 × 10 = 1200 N. h = 1.5 m, L = 6 m.
MA = L/h = 6 / 1.5 = 4.
Effort = Load / MA = 1200 / 4 = 300 N.
7.18 Wheel and Axle
A wheel and axle consists of a large wheel firmly attached to a smaller cylindrical axle, both turning on the same shaft. The effort is applied along the rim of the wheel; the load is raised by a rope wound on the axle. As the wheel turns once, both the effort cord (radius R) and the load cord (radius r) move through one complete turn.
\[ \text{MA} = \frac{R}{r} \]
Examples — the steering wheel of a car, screwdriver handle, doorknob, common village water-well winch, bicycle pedal-and-crank.
7.19 The Screw
A screw is essentially a long inclined plane wrapped around a cylinder. Each full turn of the screw advances it by a small distance equal to the pitch (the gap between two consecutive threads). If the handle radius is R and the pitch is p, then for one full turn:
\[ \text{Effort moves } 2\pi R,\quad \text{Load moves } p \]
\[ \text{VR} = \frac{2\pi R}{p} \]
Because p is very small compared with 2πR, screws give very large MA (with significant friction loss). Examples — a wood-screw, a bolt, the screw-jack used to lift cars while changing tyres.
7.20 The Wedge
A wedge is a portable inclined plane (or two inclined planes back to back). When driven point-first into a material, a downward effort is converted into a sideways force that splits the material apart. Examples — axe, knife, chisel, the cutting edge of a plough. MA = length of slope / thickness at base.
7.21 Activity — Measuring MA of an Inclined Plane
Activity 7.3 — Build Your Own RampL3 Apply
Predict first: If you make the ramp twice as long while keeping the same height, will the effort halve, double, or stay the same?
- Take a smooth wooden plank (about 80 cm long) and a small toy cart loaded with a known weight, say 500 g.
- Raise one end of the plank to a height of 20 cm so the plank length L = 80 cm and h = 20 cm.
- Use a spring balance to pull the cart up the slope at constant speed and read the effort.
- Repeat by raising the end to h = 10 cm and again to h = 40 cm. Tabulate Load, Effort, MA = Load/Effort, and L/h.
Sample observation: With Load = 5 N (500 g × 10), at h = 20 cm Effort ≈ 1.4 N → MA ≈ 3.6, while L/h = 4. The slight shortfall is due to friction. As h decreases (gentler slope), Effort decreases; as h increases (steeper slope), Effort increases.
Conclusion: MA increases with L/h. A real machine's MA is a little less than the ideal L/h because some work is wasted against friction.
Conclusion: MA increases with L/h. A real machine's MA is a little less than the ideal L/h because some work is wasted against friction.
7.22 Worked Example on Efficiency
Example — Pulley efficiency L4
In a single movable pulley, an effort of 60 N is applied to lift a load of 100 N. The effort moves 2 m and the load rises 1 m. Find MA, VR and efficiency.
MA = Load / Effort = 100 / 60 ≈ 1.67.
VR = distance moved by effort / distance moved by load = 2 / 1 = 2.
η = (MA / VR) × 100% = (1.67 / 2) × 100% ≈ 83.3%.
The remaining 16.7% is lost to friction in the pulley axle and the rope.
Quick Recap
| Machine | Ideal MA | Use |
|---|---|---|
| Lever (Class 1, 2) | Effort arm / Load arm | Multiply force / change direction |
| Fixed pulley | 1 | Change direction only |
| Movable pulley | 2 | Halve the effort |
| Block and tackle | n (rope segments) | Lift heavy industrial loads |
| Inclined plane | L / h | Raise load over distance |
| Wheel and axle | R / r | Multiply turning force |
| Screw | 2πR / p | Hold parts together; jack |
| Wedge | L / thickness | Split / cut material |
Competency-Based Questions
A worker uses a 3 m wooden plank as a ramp to roll a 60 kg drum onto a platform 1 m high. With a single movable pulley, his colleague lifts the same drum directly. (g = 10 m s⁻²; ignore friction.)
Q1. What is the MA of the inclined plane used by the worker? L3
(c) MA = L/h = 3 / 1 = 3.
Q2. How much effort does the colleague need with the movable pulley (ideal)? L3
Load = 60 × 10 = 600 N. With movable pulley MA = 2 → Effort = Load/MA = 600/2 = 300 N.
Q3. A pair of scissors and a wheelbarrow — match each to the correct lever class. L2
Scissors = Class 1 (fulcrum between blades and handles). Wheelbarrow = Class 2 (load between wheel-fulcrum and the lifter's hands).
Q4. The efficiency of a real machine is always less than 100%. Why? L2
Some of the input work is unavoidably converted into heat (and a little sound) due to friction in joints, bearings, ropes and surfaces. Therefore useful output < input.
Q5. A screw-jack has handle of length 35 cm and pitch 5 mm. Find its ideal mechanical advantage. (Take π = 22/7) L4
VR = 2πR/p = (2 × 22/7 × 35) / 0.5 = (220) / 0.5 = 440. For an ideal machine, MA = VR = 440 — a tiny effort can lift a car.
Assertion–Reason Questions
Options: (A) Both A and R are true and R is the correct explanation of A. (B) Both true but R is not the correct explanation. (C) A true, R false. (D) A false, R true.
A: A single fixed pulley does not multiply the effort.
R: A single fixed pulley only changes the direction of the applied force; the load and effort are equal in an ideal case.
(A) Both true; R explains A. MA of an ideal fixed pulley = 1.
A: A long, gently sloping ramp requires less effort than a short, steep one to raise the same load.
R: The MA of an inclined plane is the ratio of its slope length to its vertical height.
(A) Both true; R explains A. Larger L/h ⇒ larger MA ⇒ smaller effort.
A: A real machine can have efficiency greater than 100%.
R: Friction always converts some input energy into heat.
(D) Assertion is false — efficiency > 100% would violate energy conservation. Reason is true.
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