Section 1 of 5Levers as Force Multipliers
A lever is a rigid bar that turns about a pivot, letting a small force balance or overcome a larger one.
Effort
- The effort is the force you apply to the lever, usually at a point far from the pivot.
Load
- The load is the force the lever has to overcome, such as the weight of a stone or a bottle top.
Principle
- Effort × distance of effort from pivot = load × distance of load from pivot when the lever is balanced.
Advantage
- If the effort acts further from the pivot than the load, a small effort can overcome a larger load.
Section 2 of 5Gears Transmit Rotation
Gears Transmit Rotation
Structure
- Gears are toothed wheels whose teeth mesh, so turning one wheel makes the next one turn.
Direction
- Two meshed gears turn in opposite directions, and an extra gear between them restores the original direction.
Speed
- A small gear driven by a large gear turns faster, and the number of turns is in the inverse ratio of the teeth.
Moment
- A larger gear gives a bigger turning effect because the force acts further from its axle, but it turns more slowly.
| Driving gear | Driven gear | Speed | Turning effect |
|---|---|---|---|
| Small | Large | Slower | Greater |
| Large | Small | Faster | Smaller |
Section 3 of 5Worked Reasoning with Teeth
The number of teeth passing the contact point must be the same on both gears.
1
Count the teeth on the driving gear and on the driven gear.
2
The driving gear turns a certain number of times, and each turn passes its full set of teeth through the contact point.
3
Multiply the turns by the number of teeth on the driving gear to find the total teeth that have passed.
4
Divide this total by the number of teeth on the driven gear to find how many turns it makes.
5
Check the answer: the gear with fewer teeth should turn more often than the gear with more teeth.
Section 4 of 5Worked Example
Question (a) A lever has the effort applied 0.60 m from the pivot with a force of 40 N.
- The load is 0.15 m from the pivot on the other side.
- What load force can be balanced?
- (b) A gear with 30 teeth is turned 10 times and drives a gear with 12 teeth.
- How many turns does the driven gear make?
- (a) Moment of effort = 40 × 0.60 = 24 Nm.
- (a) For balance, load × 0.15 = 24, so load = 24 ÷ 0.15 = 160 N.
- (b) Teeth passing the contact point = 30 × 10 = 300.
- (b) Turns of the small gear = 300 ÷ 12 = 25.
Answer (a) 160 N; (b) 25 turns
Section 5 of 5Exam Checklist & Tips
2.6.4 – Key Points for the Exam
- Lever A rigid bar that turns about a pivot to magnify a force or a movement.
- Effort The force applied to a machine such as a lever.
- Load The force that a machine has to overcome.
- Gear A toothed wheel that meshes with another to transmit rotation.
Common Mistakes
- Saying a lever gives out more energy than is put in;
- it increases the force at the cost of a larger movement of the effort.
- Forgetting that meshed gears turn in opposite directions.
- Dividing the number of teeth the wrong way round and finding that the larger gear turns faster.
- Measuring lever distances from the ends of the bar instead of from the pivot.