22. Levers and Gears

1. Levers

Levers are devices that transmit the turning effect of a force. They allow us to exert a large output force using a relatively small input force.

Key Principles of Levers:

• Force Multipliers: Because the input force is applied further from the pivot than the output force, a smaller input force can create a large enough moment to lift a heavy load.

• Direction of Force:

  • If the input and output forces are on opposite sides of the pivot (e.g., scissors), they act in opposite directions (one up, one down).

  • If they are on the same side of the pivot (e.g., a wheelbarrow), they act in the same direction.

• Mechanical Advantage Example: To lift a 1,960 N rock (200 kg) located 0.4 m from a pivot, you need an anti-clockwise moment of 784 Nm. If you can only exert 400 N of force, you must apply it at least 1.96 m away from the pivot ($784 / 400 = 1.96$ m) to successfully lift it.

2. Gears

Gears are circular toothed wheels used to transmit and multiply turning effects from one part of a machine to another (e.g., from a car engine to the wheels).

How Gears Work:

• Transmission: When one gear (the "driver") rotates, its teeth interlock with a second gear, causing it to rotate as well.

• Direction: Interlocking gears always rotate in opposite directions (e.g., if Gear A turns anti-clockwise, Gear B turns clockwise).

• Turning Effect (Moment) Multiplication:

  • If a larger gear is driven by a smaller gear, the turning effect is magnified.

  • If the radius of the larger gear is twice that of the smaller gear, the turning effect (moment) produced by the larger gear is also twice as large.

• Rotation Speed: * A smaller gear must rotate more times to turn a larger gear once.

  • If the larger gear has twice the radius, the smaller gear must rotate twice for every one rotation of the larger gear.

  • This ensures that the total "work done" remains the same.

3. Summary Table