Lesson Notes By Weeks and Term v5 - Grade 10

Lesson Video

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Performance objectives

• Define the six simple machines.
• Explain and calculate Mechanical Advantage, Velocity Ratio, and Efficiency.
• Describe the relationship between force and distance in simple machines.
• Solve practical problems using these principles.
• Identify real-world applications in South Africa.

Lesson summary

This week, we delve into the fascinating world of simple mechanisms and mechanical advantage. Understanding how simple machines work is crucial because these principles are fundamental to many tools and machines we use daily, from bicycles and cars to levers and pulleys used in construction. In South Africa, especially in various industries like agriculture, construction, and manufacturing, simple machines play a significant role in improving efficiency and reducing physical effort. For instance, farmers use levers to lift heavy objects, construction workers rely on pulleys to raise materials, and mechanics utilize gears in vehicle transmissions.

Lesson notes

2.1 Simple Machines: Simple machines are basic mechanical devices that multiply force or change the direction of force to make work easier. They don't reduce the amount of work done, but they reduce the effort required to do it.

The six classic simple machines are: Lever: A rigid bar that pivots around a fixed point called a fulcrum. Levers are used to multiply force.

Examples: seesaw, crowbar, bottle opener.

Wheel and Axle: A wheel attached to a smaller axle that rotate together. A small force applied to the wheel can produce a larger force on the axle.

Examples: steering wheel, screwdriver, bicycle pedals.

Pulley: A grooved wheel with a rope or cable running along the groove. Pulleys can change the direction of force or multiply it.

Examples: lifting heavy objects on a construction site, raising a flag.

Inclined Plane: A sloping surface used to raise objects. It reduces the force needed to move an object vertically but increases the distance over which the force is applied.

Examples: ramp, stairs, a slide.

Wedge: A double inclined plane used to split or separate objects.

Examples: axe, knife, chisel.

Screw: An inclined plane wrapped around a cylinder. It converts rotational motion into linear motion.

Examples: screw, bolt, jar lid. 2.2 Mechanical Advantage (MA): Mechanical advantage is the ratio of the output force (load) to the input force (effort). It indicates how much a machine multiplies the force applied to it. MA = Load / Effort or MA = Output Force / Input Force A mechanical advantage greater than 1 means the machine multiplies the force, making it easier to lift or move a load. A mechanical advantage less than 1 means the machine requires more force than the load but can increase speed or distance. 2.3 Velocity Ratio (VR): Velocity ratio is the ratio of the distance moved by the effort to the distance moved by the load. It indicates how much further you have to move the input compared to the output. VR = Distance moved by effort / Distance moved by load 2.4 Efficiency: Efficiency is the ratio of the work output to the work input, usually expressed as a percentage. It represents how effectively the machine converts input energy into useful output energy. No machine is 100% efficient due to friction. Efficiency = (Work Output / Work Input) x 100% Since Work = Force x Distance, efficiency can also be expressed as: Efficiency = (Output Force x Output Distance) / (Input Force x Input Distance) x 100% Importantly: Efficiency can also be calculated as: Efficiency = (Mechanical Advantage / Velocity Ratio) x 100% 2.5 Levers: Levers are classified into three classes, depending on the relative positions of the fulcrum, load, and effort: Class 1 Lever: Fulcrum is between the load and the effort.

Example: See-saw. MA can be > 1,

1. Class 3 Lever: Effort is between the fulcrum and the load.

Example: Tweezers. MA is always <

1. Mechanical Advantage of a Lever: MA = Distance from Fulcrum to Effort (Effort Arm) / Distance from Fulcrum to Load (Load Arm) 2.6 Pulleys: Single Fixed Pulley: Changes the direction of force. MA = 1 (ideally). VR =

1. Single Movable Pulley: Multiplies the force. MA = 2 (ideally). VR =

2. Multiple Pulley System (Block and Tackle): Multiplies the force. The MA and VR are equal to the number of rope segments supporting the load.

Mechanical Advantage of Pulleys: For pulley systems, the ideal mechanical advantage is equal to the number of supporting ropes. 2.7 Inclined Plane: An inclined plane makes it easier to lift a heavy object by spreading the work over a longer distance.

Mechanical Advantage of an Inclined Plane: MA = Length of the Slope / Height of the Incline

Worked example

Example 1: Lever

A builder uses a 2-meter crowbar to lift a heavy rock. The fulcrum is placed 0.5 meters from the rock. If the rock weighs 800N, what force must the builder apply to lift the rock?

Solution:

Load (Output Force) = 800 N

Load Arm = 0.5 m

Effort Arm = 2 m - 0.5 m = 1.5 m

MA = Effort Arm / Load Arm = 1.5 m / 0.5 m = 3

Effort (Input Force) = Load / MA = 800 N / 3 = 266.67 N

The builder needs to apply a force of 266.67

N. Example 2: Pulley System