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Forces and Motion - Mechanisms like levers, pulleys, and gears

Grade 5Cambridge (IGCSE)

Review the key concepts, formulae, and examples before starting your quiz.

🔑Concepts

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A mechanism is a device that transmits or modifies force (FF) to make work easier.

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A lever consists of a rigid bar that rotates around a fixed point called a fulcrum or pivot. The three components are the Load (LL), Effort (EE), and Fulcrum (PP).

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Moments (turning effects) are calculated by multiplying the force by the perpendicular distance from the pivot (M=F×dM = F \times d).

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Pulleys consist of a wheel and a rope. A fixed pulley changes the direction of the force, while a movable pulley reduces the Effort (EE) required to lift a Load (LL).

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Gears are wheels with teeth that mesh together. They can change the speed, direction, or force of a motion. If a large gear drives a small gear, the small gear rotates faster but with less force.

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Mechanical Advantage (MAMA) is a measure of how much a machine multiplies the input force.

📐Formulae

Moment=Force(F)×Distance from Pivot(d)\text{Moment} = \text{Force} (F) \times \text{Distance from Pivot} (d)

Mechanical Advantage (MA)=Load (L)Effort (E)\text{Mechanical Advantage (MA)} = \frac{\text{Load (L)}}{\text{Effort (E)}}

Gear Ratio=Number of teeth on driven gearNumber of teeth on driver gear\text{Gear Ratio} = \frac{\text{Number of teeth on driven gear}}{\text{Number of teeth on driver gear}}

💡Examples

Problem 1:

A student uses a lever to lift a stone weighing 200 N200\ N. If the student applies an effort of 50 N50\ N, what is the Mechanical Advantage (MAMA) of the lever?

Solution:

MA=4MA = 4

Explanation:

Using the formula MA=LEMA = \frac{L}{E}, we substitute the values: MA=200 N50 N=4MA = \frac{200\ N}{50\ N} = 4. This means the lever multiplies the input force by 44 times.

Problem 2:

A driver gear with 1010 teeth is connected to a driven gear with 2020 teeth. If the driver gear makes 66 full rotations, how many rotations will the driven gear make?

Solution:

33 rotations

Explanation:

The gear ratio is 2010=2\frac{20}{10} = 2. This means the driver gear must turn 22 times for the driven gear to turn once. If the driver turns 66 times, the driven gear turns 6÷2=36 \div 2 = 3 times.

Problem 3:

Calculate the moment of a force where a 15 N15\ N force is applied at a distance of 2 m2\ m from the pivot.

Solution:

30 Nm30\ Nm

Explanation:

The moment is calculated using Force×Distance\text{Force} \times \text{Distance}. Thus, 15 N×2 m=30 Nm15\ N \times 2\ m = 30\ Nm (Newton-meters).