Lesson Notes By Weeks and Term v5 - Grade 7

Lesson Video

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Performance objectives

• Define levers, pulleys, and gears.
• Explain Mechanical Advantage (MA).
• Calculate MA for levers and pulley systems.
• Describe how gears change speed and force.
• Design a simple device using these mechanisms.

Lesson summary

Simple mechanisms are the fundamental building blocks of more complex machines. Understanding how they work and how they provide mechanical advantage is crucial for designing and building solutions to everyday problems. In South Africa, where access to advanced technology might be limited in some communities, a solid understanding of simple mechanisms allows us to create practical and affordable solutions for lifting, moving, and manipulating objects. From building a simple lever to lift a heavy rock in a garden to understanding how gears work in a bicycle, these concepts are directly applicable.

Lesson notes

Simple Mechanisms: These are basic mechanical devices that change the direction or magnitude of a force.

We will focus on three: Levers: A lever is a rigid bar that pivots around a fixed point called a fulcrum. Levers are used to multiply force. There are three classes of levers, defined by the relative positions of the load, effort, and fulcrum: Class 1 Lever: The fulcrum is between the load and the effort (e.g., a seesaw, crowbar).

Class 2 Lever: The load is between the fulcrum and the effort (e.g., a wheelbarrow, nutcracker).

Class 3 Lever: The effort is between the fulcrum and the load (e.g., tweezers, fishing rod).

Pulleys: A pulley is a wheel with a grooved rim around which a rope, cable, or belt passes. Pulleys are used to change the direction of a force or to multiply force.

Fixed Pulley: A fixed pulley only changes the direction of the force (e.g., a flag pole). The mechanical advantage is

1. Movable Pulley: A movable pulley is attached to the load. It multiplies the force.

Pulley System (Block and Tackle): A combination of fixed and movable pulleys creates a pulley system that can provide significant mechanical advantage. The mechanical advantage is approximately equal to the number of rope segments supporting the load.

Gears: Gears are toothed wheels that mesh together to transmit rotary motion. Gears can change the speed, torque, and direction of the motion. When a smaller gear drives a larger gear, the speed decreases but the torque (rotational force) increases. When a larger gear drives a smaller gear, the speed increases but the torque decreases.

Mechanical Advantage (MA): Mechanical advantage is the ratio of the output force (the force exerted on the load) to the input force (the force applied to the system). It tells us how much easier a machine makes the work. MA = Output Force / Input Force A mechanical advantage greater than 1 means the machine multiplies the force, making the work easier. A mechanical advantage less than 1 means the machine increases the distance or speed but requires more force.

Lever Calculations: The mechanical advantage of a lever can be calculated as: MA = Distance from Fulcrum to Effort / Distance from Fulcrum to Load Pulley Calculations: The mechanical advantage of a pulley system (block and tackle) can be calculated as: MA = Number of rope segments supporting the load Gear Calculations: The gear ratio and relationship between gear sizes and speeds are important concepts. Gear Ratio = Number of teeth on driven gear / Number of teeth on driving gear Speed of driving gear / Speed of driven gear = Number of teeth on driven gear / Number of teeth on driving gear

Worked example

Lever Example (Class 1): A farmer uses a crowbar (class 1 lever) to lift a rock. The rock is 0.5 meters from the fulcrum, and the farmer applies force 2 meters from the fulcrum. If the rock weighs 500 N, how much force does the farmer need to apply? What is the mechanical advantage?

Solution:*

MA = Distance from Fulcrum to Effort / Distance from Fulcrum to Load = 2 m / 0.5 m = 4

MA = Output Force / Input Force => Input Force = Output Force / MA = 500 N / 4 = 125 N

The farmer needs to apply 125 N of force. The mechanical advantage is

4.

Pulley

Example: A construction worker uses a pulley system with 4 rope segments supporting the load to lift a bag of cement weighing 200 N. What is the mechanical advantage of the pulley system, and how much force must the worker apply to lift the cement?

Solution:*

MA = Number of rope segments supporting the load = 4

MA = Output Force / Input Force => Input Force = Output Force / MA = 200 N / 4 = 50 N

The mechanical advantage is 4, and the worker needs to apply 50 N of force.

Gear

Example: A bicycle has two gears. The driving gear (attached to the pedals) has 48 teeth, and the driven gear (attached to the rear wheel) has 12 teeth. If the cyclist pedals at 60 revolutions per minute (RPM), how fast does the rear wheel spin? What is the gear ratio?

Solution:*

Gear Ratio = Number of teeth on driven gear / Number of teeth on driving gear = 12 / 48 = 1/4 = 0.25

Speed of driving gear / Speed of driven gear = Number of teeth on driven gear / Number of teeth on driving gear

60 RPM / Speed of driven gear = 12 / 48

Speed of driven gear = (60 RPM 48) / 12 = 240 RPM

The gear ratio is 0.25, and the rear wheel spins at 240 RPM. This increases the speed significantly!

Guided Practice (With Solutions)

A person uses a lever to move a heavy log. The log is positioned 1 meter away from the fulcrum. If the person applies a force 3 meters away from the fulcrum, what is the mechanical advantage of the lever?