6.1 Levers, Moments & Equilibrium

Introduction to Levers

One of the most fundamental simple machines you will encounter on the Defence Aptitude Assessment (DAA) is the lever. A lever is a rigid bar or beam that rests and pivots on a fixed point called a fulcrum (or pivot). Levers are used to apply a force to a load, and they can provide a mechanical advantage, allowing you to lift heavy objects with significantly less effort than would otherwise be required.

To fully grasp how levers work, you must first understand the three core components of any lever system:

1. The Fulcrum (Pivot): The fixed point around which the lever rotates.
2. The Effort (Force): The input force applied to the lever in order to move the load.
3. The Load (Resistance): The output force or the object that is being moved or lifted.

The relationship between these three components determines the "class" of the lever and how it functions in real-world mechanical systems.

The Three Classes of Levers

Levers are categorized into three distinct classes based on the relative positioning of the fulcrum, the effort, and the load. Memorizing these configurations is essential for the exam.

Class 1 Levers

In a Class 1 lever, the fulcrum is located in the middle, between the effort and the load. This is the most intuitive type of lever. When you push down on one end, the other end goes up.

• Mechanical Advantage: A Class 1 lever can have a mechanical advantage greater than, less than, or equal to 1, depending on exactly where the fulcrum is placed.
• Common Examples: A seesaw, a crowbar, scissors, and a pair of pliers. In a pair of scissors, the screw in the middle is the fulcrum, your fingers apply the effort at the handles, and the material being cut represents the load.

Class 2 Levers

In a Class 2 lever, the load is located in the middle, between the fulcrum and the effort. In this setup, the effort and the load move in the same direction.

• Mechanical Advantage: Because the effort is always farther from the fulcrum than the load, a Class 2 lever always provides a mechanical advantage greater than 1. This means it multiplies your force, allowing you to lift heavy loads with less effort.
• Common Examples: A wheelbarrow, a nutcracker, and a bottle opener. In a wheelbarrow, the wheel acts as the fulcrum, the load is in the bucket in the middle, and you apply the effort by lifting the handles at the opposite end.

Class 3 Levers

In a Class 3 lever, the effort is located in the middle, between the fulcrum and the load.

• Mechanical Advantage: In this configuration, the effort is closer to the fulcrum than the load. As a result, the mechanical advantage is always less than 1. While this means you must apply more force than the weight of the load, the trade-off is that the load moves a greater distance and at a higher speed than the effort.
• Common Examples: Tweezers, a fishing rod, a baseball bat, and the human jaw. When using tweezers, the fulcrum is at the connected end, you squeeze in the middle (effort), and pick up the object at the tips (load).

Moments and Torque

In mechanical comprehension, a "moment" (also known as torque) is the turning effect produced by a force acting at a distance from a pivot point. Understanding moments is critical because levers do not operate on linear force alone; they operate on rotational force.

The formula for calculating a moment is straightforward:

Moment = Force × Perpendicular Distance from Pivot

Where:

• Force (F) is measured in Newtons (N) or pounds (lbs).
• Distance (d) is measured in meters (m) or feet (ft).
• Moment is therefore measured in Newton-meters (Nm) or pound-feet (lb-ft).

Crucial Concept: The distance must be the perpendicular distance from the line of action of the force to the pivot. If you push at an angle, only the perpendicular component of your force contributes to the moment.

Calculating Moments: A Basic Example

Imagine you are using a wrench to loosen a tight bolt (the pivot). If you apply a force of 50 Newtons at a distance of 0.4 meters from the bolt, the moment is:

• Moment = 50 N × 0.4 m = 20 Nm. If you move your hand further down the wrench to a distance of 0.8 meters, the same 50 N force generates a moment of 40 Nm. This demonstrates why a longer wrench makes it easier to loosen a tight bolt—you increase the distance, thereby increasing the torque without needing to push harder.

The Principle of Equilibrium

The Principle of Moments states that for a system to be perfectly balanced (in static equilibrium) and not rotating, the total turning effect in one direction must exactly equal the total turning effect in the opposite direction.

Mathematically, this is expressed as: Sum of Clockwise Moments = Sum of Anticlockwise Moments

If the clockwise moments are greater, the system will rotate clockwise. If the anticlockwise moments are greater, it will rotate anticlockwise.

Equilibrium Worked Example

Consider a seesaw that is 4 meters long, with the fulcrum perfectly in the center (so each side is 2 meters long).

• Person A weighs 600 N and sits on the left side, 2 meters from the fulcrum.
• Person B wants to sit on the right side to balance the seesaw. Person B weighs 800 N. Where must Person B sit?

1. Calculate the anticlockwise moment (Person A): Moment = 600 N × 2 m = 1200 Nm.
2. Set up the equilibrium equation: Anticlockwise Moments = Clockwise Moments 1200 Nm = Person B Force × Person B Distance 1200 Nm = 800 N × Distance
3. Solve for Distance: Distance = 1200 Nm / 800 N = 1.5 meters. Person B must sit 1.5 meters from the fulcrum on the right side to balance the seesaw.

Mechanical Advantage in Levers

Mechanical Advantage (MA) is a ratio that quantifies how much a machine multiplies force. For a lever, it can be calculated in two ways:

1. MA = Load Force / Effort Force
2. MA = Distance of Effort from Fulcrum / Distance of Load from Fulcrum

If the effort is applied twice as far from the fulcrum as the load, the mechanical advantage is 2. This means you only need half as much effort force to lift the load, but you will have to move your end of the lever twice as far to lift the load the desired distance. This perfectly illustrates the conservation of energy: work input equals work output (Work = Force × Distance). What you gain in force, you pay for in distance.