Machines, Levers, and Moments Practice Flashcards

Introduction to Machines

• A machine is defined as a device which converts energy from one form to another.

• The function of a machine allows a force to be applied at one specific point and used to overcome a force at another point.

Levers and Their Classifications

• A lever is a simple machine that utilizes a pivot (also known as a fulcrum) to transfer the work done by the effort to a load.

• There are three primary types of levers, categorized by the relative positions of the load, effort, and pivot:

1st Order Levers

• In a first-order lever, the pivot is located between the effort and the load.

• Structure: Effort → Pivot → Load

2nd Order Levers

• In a second-order lever, the load is located between the pivot and the effort.

• Structure: Pivot → Load → Effort

3rd Order Levers

• In a third-order lever, the effort is located between the pivot and the load.

• Structure: Pivot → Effort → Load

The Principle of Moments

• A lever operates based on the principle of moments. This means that the force applied to the lever creates a turning effect about the pivot.

• The magnitude of the turning effect depends on two factors:

  • The size of the force used.

  • How far away from the pivot the force was applied (the distance).

Moment Calculation

• The moment of a force is calculated as the product of the force and the perpendicular distance from the pivot:   $Moment = \text{force} \times \text{perpendicular distance from the pivot}$

• Mathematical Formula:   $M = F \times d$

• Units of Measurement: Moments are measured in Newton-metres ($Nm$).

• NOTE: The units of moments are NOT Joules ($J$), even though the components are similar to work.

Clockwise and Anticlockwise Moments

• Moments are directional. They can be classified as either clockwise or anticlockwise depending on the direction in which they attempt to turn the body around the pivot.

Increasing Turning Effects

• Using a spanner as an example (which produces a turning effect to remove a nut), the turning effect can be increased by:

  • a) Increasing the force ($F$) applied.

  • b) Increasing the length ($d$) of the spanner.

The Principle of Moments for Equilibrium

• When a body is in equilibrium (perfectly balanced), the sum of the anticlockwise moments is equal to the sum of the clockwise moments about the pivot.

• Formula for Equilibrium:   $\sum \text{Anticlockwise Moments} = \sum \text{Clockwise Moments}$

Worked Examples and Problems

Example 1: Balancing Two Forces

• Scenario: A pivot has a force of $20\,N$ acting at a distance of $2\,m$ in an anticlockwise direction. An effort force ($F$) acts at a distance of $5\,m$ in a clockwise direction.

• Calculation:   $\text{Anticlockwise moments} = \text{clockwise moments}$   $20\,N \times 2\,m = F \times 5\,m$   $40\,Nm = 5F$   $F = \frac{40}{5}$   $F = 8\,N$

Example 2: Multiple Forces on One Side

• Scenario: On the left side (anticlockwise), there is a force of $30\,N$ at $2\,m$ and another force of $20\,N$ at $1\,m$. On the right side (clockwise), an effort force ($F$) acts at $5\,m$.

• Calculation:   $\text{Anticlockwise moments} = \text{clockwise moments}$   $(30\,N \times 2\,m) + (20\,N \times 1\,m) = F \times 5\,m$   $60\,Nm + 20\,Nm = 5F$   $80\,Nm = 5F$   $F = \frac{80\,Nm}{5\,m}$   $F = 16\,N$

Example 3: The See-saw Problem

• Scenario: A boy weighing $600\,N$ sits at $6\,m$ from the pivot. A girl sits on the opposite side at a distance of $9\,m$ and balances the see-saw. How much does the girl weigh ($G$)?

• Calculation:   $\text{Anticlockwise moments} = \text{Clockwise moments}$   $600\,N \times 6\,m = G \times 9\,m$   $3600 = 9G$   $G = \frac{3600}{9}$   $G = 400\,N$

Practice Problem: The Complex Plank

• Problem: A boy of $80\,kg$ sits to the left of a plank $1\,m$ away from the pivot. A girl of mass $30\,kg$ sits $3\,m$ behind him (meaning she is $4\,m$ from the pivot). A man of $100\,kg$ sits on the right side of the pivot and balances the plank. How far from the pivot is the man sitting?

• Note on conversion: Mass must be treated as force (weight). In these problems, weight is proportional to mass (using $W = mg$, where $g \approx 10\,m/s^2$ or simplified by using mass if units remain consistent).

• Calculation Logic:

  • Left side (Anticlockwise): $(800\,N \times 1\,m) + (300\,N \times 4\,m) = 800 + 1200 = 2000\,Nm$

  • Right side (Clockwise): $1000\,N \times d = 1000d$

  • Setting them equal: $2000 = 1000d \Rightarrow d = 2\,m$

• Answer: The man is $2\,m$ from the pivot.