Mass, density and weight — KCSE Mathematics

Density is defined as the mass of an object per unit volume. The formula for density (ρ) is given by:

Density (ρ) = Mass (m) / Volume (V)

Where:

• Mass (m) is measured in kilograms (kg)
• Volume (V) is measured in cubic meters (m³)

To calculate density, rearrange the formula as needed:

• Mass = Density × Volume
• Volume = Mass / Density

Example Calculations:

1. If a block of wood has a mass of 300 kg and a volume of 0.75 m³, calculate its density:

   • Density = Mass / Volume = 300 kg / 0.75 m³ = 400 kg/m³

2. If you have a substance with a density of 2.5 kg/m³ and you know its volume is 2 m³, find its mass:

   • Mass = Density × Volume = 2.5 kg/m³ × 2 m³ = 5 kg

Understanding these calculations is essential for solving problems related to mass, density, and volume in physics and chemistry contexts.

In physics, mass and weight are related through the formula W = mg, where:

• W is the weight in newtons (N)
• m is the mass in kilograms (kg)
• g is the acceleration due to gravity (approximately 9.8 m/s² on Earth)

To relate mass and weight, remember:

• Weight is the force acting on an object due to gravity.
• Mass is a measure of the amount of matter in an object.

When solving problems, you can rearrange the formula to find mass or weight as needed. For example, if you know the mass of an object, you can calculate its weight by multiplying the mass by the acceleration due to gravity. Conversely, if you have the weight, you can find the mass by dividing the weight by the acceleration due to gravity.

Example Problem: Calculate the weight of a 10 kg object.

Solution:

• Using W = mg, where m = 10 kg and g = 9.8 m/s²:
• W = 10 kg × 9.8 m/s² = 98 N.

Thus, the weight of the object is 98 N.