What is a force?

A force is a push or a pull acting on an object. It can make a stationary object move, stop a moving object, change its direction, or change its shape.

Effects of force

When unbalanced forces act on an object, they can cause:

• A change in the state of motion (starting or stopping movement)
• A change in speed or acceleration
• A change in shape or size (deformation)
• A change in direction of motion

Measuring force

The magnitude of a force is measured using a spring balance. It has a coiled spring, a hook, and a calibrated scale. When a force is applied, the spring stretches. The more the spring stretches, the greater the force.

The unit of force is the newton (N).

What is density?

Density is the mass of a substance per unit volume. It tells us how tightly packed the matter is in a substance.

Formula for density

$\rho = \frac{m}{V}$

Where:

• $\rho$ = density (kg/m³ or g/cm³)
• $m$ = mass (kg or g)
• $V$ = volume (m³ or cm³)

The SI unit of density is kg/m³. Common substances have different densities: aluminum (2.7 g/cm³), iron (7.8 g/cm³), gold (19.3 g/cm³), and water (1 g/cm³).

Relative density

Relative density (also called specific gravity) is the ratio of a substance's density to the density of water:

$R.D = \frac{\rho_{\text{substance}}}{\rho_{\text{water}}}$

Relative density has no unit because it is a ratio.

Worked example

A piece of copper has a mass of 83.2 g and a volume of 10.2 cm³. Find its density and relative density.

Step 1: Calculate density

$\rho = \frac{m}{V} = \frac{83.2\ \text{g}}{10.2\ \text{cm}^3} = 8.16\ \text{g/cm}^3$

Step 2: Calculate relative density

$R.D = \frac{8.16\ \text{g/cm}^3}{1\ \text{g/cm}^3} = 8.16$

What is pressure?

Pressure is the force exerted per unit area on a surface.

Formula for pressure

$P = \frac{F}{A}$

Where:

• $P$ = pressure (pascals, Pa or N/m²)
• $F$ = force (newtons, N)
• $A$ = area (m²)

The key idea is: the smaller the area, the greater the pressure for the same force.

Worked example

A wooden block weighing 30 N rests on a table. The dimensions of its base are 5 m × 4 m. What pressure does it exert on the table?

Calculate the area

$A = 5\ \text{m} \times 4\ \text{m} = 20\ \text{m}^2$

Calculate the pressure

$P = \frac{F}{A} = \frac{30\ \text{N}}{20\ \text{m}^2} = 1.5\ \text{N/m}^2$

What is work?

Work is done when a force causes an object to move in the direction of the force.

Formula for work

$W = F \times d$

Where:

• $W$ = work done (joules, J)
• $F$ = force (newtons, N)
• $d$ = distance moved in the direction of the force (metres, m)

Important: If the object does not move, no work is done even if a force is applied.

Worked example

A student lifts a school bag weighing 70 N onto a bench that is 1.5 m high. How much work is done?

Given: Force = 70 N, distance = 1.5 m

Calculate work

$W = F \times d = 70\ \text{N} \times 1.5\ \text{m} = 105\ \text{J}$

What is energy?

Energy is the ability to do work. It exists in different forms.

Gravitational potential energy

This is the energy stored in an object due to its position above the ground.

$E_p = m \times g \times h$

Where:

• $E_p$ = gravitational potential energy (joules, J)
• $m$ = mass (kg)
• $g$ = gravitational field strength (approximately 10 N/kg on Earth)
• $h$ = height (m)

Kinetic energy

This is the energy an object has due to its motion.

$E_k = \frac{1}{2} m v^2$

Where:

• $E_k$ = kinetic energy (joules, J)
• $m$ = mass (kg)
• $v$ = speed (m/s)

Worked example

A ball of mass 2 kg is lifted to a height of 5 m. Calculate its gravitational potential energy.

Given: m = 2 kg, g = 10 N/kg, h = 5 m

$E_p = mgh = 2\ \text{kg} \times 10\ \text{N/kg} \times 5\ \text{m} = 100\ \text{J}$

What is power?

Power is the rate at which work is done, or the rate at which energy is transferred.

Formula for power

$P = \frac{W}{t}$

Where:

• $P$ = power (watts, W)
• $W$ = work done (joules, J)
• $t$ = time (seconds, s)

The unit of power is the watt (W). One watt equals one joule per second.

Worked example

A student climbs a staircase in 10 seconds, doing 500 J of work. What is the student's power?

Given: W = 500 J, t = 10 s

$P = \frac{W}{t} = \frac{500\ \text{J}}{10\ \text{s}} = 50\ \text{W}$

In Tanzania, understanding density and pressure is essential in everyday activities. For example, when a fisherman in Lake Victoria checks whether his net will float or sink, he applies the concept of density — materials with density less than water (1 g/cm³) will float, while those with greater density will sink. Similarly, farmers in rural areas use knowledge of pressure when inflating tractor tyres to the correct pressure: too little pressure causes excessive wear, while too much pressure can lead to tyre bursts, affecting safety and cost.