Chapter at a Glance: Simple Machines | Physics for JAMB PDF Download

Objective

The objective of these notes is to provide a clear understanding of simple machines, their types, and the concepts of mechanical advantage, velocity ratio, and efficiency. These notes will enable candidates to identify different types of simple machines and solve numerical problems related to them.

Definition of Simple Machines

• Simple machines are basic mechanical devices that help in performing work with minimal force.
• They provide mechanical advantage by multiplying or changing the direction of the input force.
• Simple machines are the building blocks of more complex machines and are widely used in everyday life.

Types of Machines

1. Lever

• A rigid bar that rotates around a fixed point called the fulcrum.
• Three classes of levers: First-class, Second-class, and Third-class.
• Formula: Mechanical Advantage (MA) = Length of effort arm / Length of load arm

2. Pulley

• Consists of a grooved wheel with a rope or chain running along it.
• Changes the direction of the applied force.
• Formula: Mechanical Advantage (MA) = Number of supporting ropes

3. Wheel and Axle

• Consists of a wheel connected to a smaller axle.
• Transfers force from one point to another with a larger force at the wheel.
• Formula: Mechanical Advantage (MA) = Radius of wheel / Radius of axle

3. Inclined Plane

• A sloping surface that reduces the effort required to move an object vertically.
• Formula: Mechanical Advantage (MA) = Length of slope / Height of slope

4. Wedge

• A triangular-shaped object used for splitting or cutting.
• Converts a smaller force into a larger force over a smaller distance.
• Formula: Mechanical Advantage (MA) = Length of slope / Width of wedge

5. Screw

• An inclined plane wrapped around a cylindrical post.
• Converts rotational motion into linear motion.
• Formula: Mechanical Advantage (MA) = Distance traveled by effort / Distance traveled by load

Mechanical Advantage, Velocity Ratio, and Efficiency of Machines

• Mechanical Advantage (MA): The ratio of the output force (load) to the input force (effort) of a machine.
  Formula: MA = Load / Effort
• Velocity Ratio (VR): The ratio of the distance moved by the effort to the distance moved by the load.
  Formula: VR = Distance moved by effort / Distance moved by load
• Efficiency: The ratio of the useful work output to the total work input, expressed as a percentage.
  Formula: Efficiency = (Useful work output / Total work input) × 100%

Explaining Formulas with Question & Answers (Numerical)

Q1: A lever has an effort arm of 5 meters and a load arm of 2 meters. Calculate the mechanical advantage.

Solution: MA = Length of effort arm / Length of load arm
= 5 meters / 2 meters
= 2.5

Q2: A pulley system has four supporting ropes. Calculate the mechanical advantage.

Solution: MA = Number of supporting ropes
= 4

Q3: A wheel has a radius of 20 centimeters, while the radius of the axle is 5 centimeters. Find the mechanical advantage.

Solution: MA = Radius of wheel / Radius of axle
= 20 cm / 5 cm
= 4

Q4: An inclined plane has a length of 8 meters and a height of 2 meters. Determine the mechanical advantage.

Solution: MA = Length of slope / Height of slope
= 8 meters / 2 meters
= 4

Q5: A wedge has a length of 10 centimeters and a width of 2 centimeters. Calculate the mechanical advantage.

Solution: MA = Length of slope / Width of wedge
= 10 cm / 2 cm
= 5

Q6: A screw requires an effort of 20 centimeters to move 5 centimeters. Determine the mechanical advantage.

Solution: MA = Distance traveled by effort / Distance traveled by load
= 20 cm / 5 cm
= 4

Q7: A machine has an output force (load) of 200 newtons and an input force (effort) of 100 newtons. Find the mechanical advantage.

Solution: MA = Load / Effort
= 200 N / 100 N
= 2

Q8: A machine has an effort distance of 10 meters and a load distance of 5 meters. Calculate the velocity ratio.

Solution: VR = Distance moved by effort / Distance moved by load
= 10 meters / 5 meters
= 2

Q9: If a machine has a useful work output of 500 joules and a total work input of 800 joules, what is its efficiency?

Solution: Efficiency = (Useful work output / Total work input) × 100%
= (500 J / 800 J) × 100%
= 62.5%