Explain the principles of simple machines (lever, pulley, inclined plane, screw jack, wheel and axle, hydraulic press)

A pulley is a wheel with a groove that rotates freely on an axle. A rope passes through the groove to transmit force.

Single Fixed Pulley

The pulley is attached to a fixed support. It changes the direction of force (pulling downward lifts the load upward) but does not change the magnitude of force.

• M.A = 1
• V.R = 1

Single Movable Pulley

The pulley moves along with the load. One end of the rope is fixed, and effort is applied to the free end.

• M.A = 2
• V.R = 2

Block and Tackle System

This combines several fixed and movable pulleys. The mechanical advantage equals the number of rope sections supporting the load.

• $M.A = \frac{\text{Load}}{\text{Effort}}$
• $V.R = \text{Number of pulleys in the system}$

An inclined plane is a sloping surface used to raise a load vertically by applying force along the slope. It reduces the effort needed to lift a load by increasing the distance over which the force is applied.

• $M.A = \frac{\text{Load}}{\text{Effort}}$
• $V.R = \frac{\text{Length of plane}}{\text{Height of plane}}$

A screw jack consists of a threaded screw inside a cylinder. Turning the handle causes the screw to move up or down, lifting or lowering the load. The distance between adjacent threads is called the pitch.

• $V.R = \frac{\text{Circumference of handle}}{\text{Pitch}} = \frac{2\pi R}{p}$
• $M.A = \frac{\text{Load}}{\text{Effort}}$

where R is the handle radius and p is the pitch.

A wheel and axle consists of a large wheel attached to a smaller axle. When force is applied to the wheel, the axle rotates to move the load. It works on the same principle as a lever.

• $M.A = \frac{\text{Radius of wheel}}{\text{Radius of axle}} = \frac{R}{r}$
• $V.R = \frac{R}{r}$

A hydraulic press uses Pascal's principle, which states that pressure applied to a confined fluid is transmitted equally throughout the fluid. It consists of two pistons of different areas connected by a fluid.

• $\frac{F_1}{A_1} = \frac{F_2}{A_2}$
• $M.A = \frac{F_2}{F_1} = \frac{A_2}{A_1}$

A wheelbarrow is used to carry a load of 600 N. The distance from the wheel (fulcrum) to the load is 0.4 m, and the distance from the wheel to the handle where effort is applied is 1.2 m. The effort required to lift the load is 250 N.

Find: (a) Velocity ratio (b) Mechanical advantage (c) Efficiency

Solution:

(a) Velocity ratio: $V.R = \frac{1.2\,m}{0.4\,m} = 3$

(b) Mechanical advantage: $M.A = \frac{600\,N}{250\,N} = 2.4$

(c) Efficiency: $\text{Efficiency} = \frac{2.4}{3} \times 100\% = 80\%$

The wheelbarrow requires only 250 N effort to lift a 600 N load, making the work easier. The efficiency is 80%, meaning some energy is lost due to friction.

In Tanzania, simple machines are used everywhere in daily life. A farmer in Morogoro using a wheelbarrow to transport harvested maize from the field to the storage barn applies the principle of a second-class lever, where the wheel acts as the fulcrum and the effort applied at the handles multiplies the force to move heavy sacks. Understanding these principles helps people choose the most efficient tools for lifting and moving loads with minimum effort.