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š¬ A little push, a big lift
Balance a scale on a pencil and a light eraser can lift a heavy stapler. A lever lets a small force move a large load — if you give it the right arm.
What is a lever and how does it give a mechanical advantage?
- A lever is a rigid bar that can rotate about a fixed point. Its three parts are the fulcrum (the fixed pivot), the load (force to overcome), and the effort (force applied).
- The distance of the load from the fulcrum is the load arm ; the distance of the effort is the effort arm . Work transfers across the lever: $$F_1 \times d_1 = F_2 \times d_2$$ i.e. effort × effort arm = load × load arm.
- So $$\text{mechanical advantage} = \dfrac{\text{load}}{\text{effort}} = \dfrac{\text{effort arm}}{\text{load arm}}$$ A longer effort arm gives a larger force on the load — but the effort must move a larger distance, so total work is unchanged.
In this Activity, we will balance a scale on a pencil and use a light eraser to lift a heavier stapler, discovering how a lever works.
Steps
- Rest a 30 cm scale on a pencil placed closer to one end. Put a stapler on the short end (near the pencil).
- On the long end, place one eraser; if the stapler does not lift, add another. Notice a light eraser can lift the heavier stapler.
What you observe
- A much lighter object can lift a heavier one because the lighter effort acts on the longer arm — the scale acts as a lever about the pencil (the fulcrum).
In this Activity, we will hang a scale as a beam balance and use coins to discover the rule that balances effort and load about the fulcrum.
Steps
- Tie a string at the midpoint of a long scale (the fulcrum) and hang it so it swings freely. Fix paper cups as pans at both ends and level the beam.
- Put 1 coin in each pan (effort and load) — the beam stays level. Add coins to the load pan and slide it closer to the centre to balance; record its distance. Repeat for 4 and 8 coins.
| No. of coins in left pan, nā (Effort) | Distance of left pan from fulcrum, Lā (cm) | No. of coins in right pan, nā (Load) | Distance of right pan from fulcrum, Lā (cm) |
|---|---|---|---|
| 1 | 20 | 1 | 20 |
| 1 | 20 | 2 | 10 |
| 1 | 20 | 4 | 5 |
| 1 | 20 | 8 | 2.5 |
What you observe
- The beam balances when \(n_1 \times L_1 = n_2 \times L_2\), i.e. effort × effort arm = load × load arm . A longer effort arm needs a smaller effort.
Important Definitions
- Lever — a rigid bar that can rotate about a fixed point, used to lift heavy objects.
- Fulcrum — the fixed point about which a lever rotates.
- Load arm and effort arm — the distance of the load from the fulcrum, and the distance of the effort from the fulcrum.
ā Note
- A lever reduces the force required to perform a task, but not the total work done.
ā Example 7.13 — For a seesaw having four
On a seesaw (fulcrum C), AC = EC = 2 m and BC = DC = 1 m. Where should children of 15 kg and 30 kg sit to balance it?
Let the 15 kg child sit at A (2 m). For balance: \(15 \times 2 = 30 \times L \Rightarrow L = 1\ \text{m}\).
So the 30 kg child should sit at seat D (1 m from the fulcrum).
š¹ Ready to Go Beyond
- Levers come in three classes depending on the relative positions of fulcrum, load and effort:
| Class | Arrangement | Examples |
|---|---|---|
| Class I | Fulcrum in between effort and load | Tongs, scissors, crowbar, pliers, balance scale, seesaw |
| Class II | Load in between fulcrum and effort | Lemon squeezer, wheelbarrow, bottle opener |
| Class III | Effort in between fulcrum and load | Tongs, tweezers, broom, hammer, oar |
š¹ Ready to Go Beyond
- Many everyday machines are combinations of two or more simple machines.
- In all cases mechanical energy is conserved: the work we put in equals the useful work on the load (ignoring friction). Machines do not create energy — they only help us use it more effectively.
ā What If
- What if it were possible to build a perpetual motion machine — one that, once started, kept doing useful work forever with no fuel or electricity? (Real machines always lose energy to friction, so they slow down and stop.)
āøā¶ Pause and Ponder
- 9. Why do hill roads wind in gentle slopes? A gentler slope is a longer inclined plane (larger \(L/h\)), so vehicles need a smaller force to climb — safer and easier — though they travel a longer distance.
- 10. Why is an inclined ladder easier than a vertical one? The incline acts as an inclined plane, so the same height is reached with a smaller force over a longer path.
āøā¶ Pause and Ponder
- 11. Opening a can lid with a spoon: the spoon is a lever — a long effort arm gives a large force on the lid for a small effort.
- 12. Cutting a hard object near the scissors' fulcrum: close to the fulcrum the load arm is short, so the cutting force is larger for the same effort.
- 13. Why do real machines slow and stop? Friction (and air resistance) constantly converts mechanical energy into heat and sound, so a perpetual machine is impossible — energy is always lost, never created.
NCERT Question 9 — On a seesaw with sliding
A child and an adult (weight 2× the child) balance a seesaw. Draw the situation showing their distances from the fulcrum.
View the answer →
Concept Map
Work, Energy & Simple Machines
Work links force to energy; machines make tasks easier.
Work
Force × displacement in the direction of the force; can be positive or negative.
Zero work
No force, no displacement, or force perpendicular to displacement.
Energy
Capacity to do work; work done = change in energy (work-energy theorem).
Kinetic & potential
K = ½mv² (motion) and U = mgh (position); among many forms of energy.
Conservation
Total mechanical energy stays constant when no external force acts.
Power
The rate at which work is done, P = W/t, measured in watts.
Simple machines
Pulley, inclined plane and lever; mechanical advantage = load / effort.
š Bridging Science and Society
- In the Himalayan region, water flowing downhill converts its potential energy into kinetic energy. Traditionally this drove the gharat or panchakki — a watermill for grinding grain: water falls through a pipe, its kinetic energy turns a wheel, and the wheel turns the grinding stone.
- In modern times, the potential energy of water stored in dams is converted into kinetic energy to generate electricity.
