Specific Objectives
By the end of this topic, the learner should be able to:
- Define mass.
- State units of mass.
- Convert units of mass from one form to another.
- Define weight.
- State units of weight.
- Distinguish between mass and weight.
- Relate volume, mass, and density.
Content
- Mass and units of mass.
- Weight and units of weight.
- Density.
- Problem solving involving real-life experiences on mass, volume, density, and weight.
Introduction
Mass
The mass of an object is the quantity of matter it contains. Mass is a constant quantity regardless of the object’s location. Matter is anything that occupies space. The three states of matter are solid, liquid, and gas.
The SI unit of mass is the kilogram (kg). Other common units include the tonne, gram, and milligram.
The following table shows units of mass and their equivalents in kilograms.
Weight
The weight of an object on Earth is the force exerted on it by Earth’s gravity. The weight of an object varies depending on its location on Earth’s surface because the gravitational pull changes with distance from the Earth’s center. For example, an object weighs more at sea level than on top of a mountain due to stronger gravitational pull at lower altitudes.
Units of Weight
The SI unit of weight is the newton (N). The gravitational pull exerted by Earth, the sun, and the moon on an object is called the force of gravity due to these bodies respectively. The force of gravity due to Earth on an object of mass 1 kg is approximately 9.8 N. The strength of Earth’s gravitational pull (symbol ‘g’) on an object at the surface is about 9.8 N/kg.
Weight of an object = mass of the object × gravitational acceleration
Weight (N) = mass (kg) × g (N/kg)
Density
Density of a substance is defined as the mass per unit volume of the substance. For a body with mass (m) in kilograms and volume (v) in cubic meters (m³), the following relationships hold:
- Density (d) = mass (m) / volume (v)
- Mass (m) = density (d) × volume (v)
- Volume (v) = mass (m) / density (d)
Units of Density
The SI unit of density is kilograms per cubic meter (kg/m³). Another common unit is grams per cubic centimeter (g/cm³).
1 g/cm³ = 1,000 kg/m³
Example
Find the mass of an ice cube with side length 6 cm, given that the density of ice is 0.92 g/cm³.
Solution
Volume of cube = 6 × 6 × 6 = 216 cm³
Mass = density × volume
= 0.92 × 216
= 198.72 g
Example
Find the volume of cork with mass 48 g, given that the density of cork is 0.24 g/cm³.
Solution
Volume = mass / density
= 48 / 0.24
= 200 cm³
Example
The density of iron is 7.9 g/cm³. Convert this density to kg/m³.
Solution
1 g/cm³ = 1,000 kg/m³
7.9 g/cm³ = 7.9 × 1,000
= 7,900 kg/m³
Example
A rectangular slab of glass measures 8 cm by 2 cm by 14 cm and has a mass of 610 g. Calculate the density of the glass in kg/m³.
Solution
Volume of the slab = 8 × 2 × 14 = 224 cm³
Mass of the slab = 610 g
Density = mass / volume = 610 / 224 = 2.72 g/cm³
Convert to kg/m³: 2.72 × 1,000 = 2,720 kg/m³
End of Topic
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Past KCSE Questions on the Topic
1. A square brass plate is 2 mm thick and has a mass of 1.05 kg. The density of brass is 8.4 g/cm³. Calculate the length of the plate in centimeters. (3 marks)
2. A sphere has a surface area of 18 cm2. Find its density if the sphere has a mass of 100 g. (3 marks)
3. Nyahururu Municipal Council is to construct a floor of an open wholesale market whose area is 800 m2. The floor is to be covered with a slab of uniform thickness 200 mm. To make the slab, sand, cement, and ballast are mixed in the ratio 3:2:3 by mass. The mass of a dry slab of volume 1 m3 is 2000 kg. Calculate:
(a) (i) The volume of the slab (2 marks)
(ii) The mass of the dry slab (2 marks)
(iii) The mass of cement to be used (2 marks)
(b) If one bag of cement weighs 50 kg, find the number of bags to be purchased (1 mark)
(c) If a lorry carries 10 tonnes of ballast, calculate the number of lorries of ballast to be purchased (3 marks)
4. A sphere has a surface area of 18.0 cm2. Find its density if the sphere has a mass of 100 grammes. (3 marks)
- A piece of metal has a volume of 20 cm3 and a mass of 300 g. Calculate the density of the metal in kg/m3.
2.5 litres of water with density 1 g/cm3 is added to 8 litres of alcohol with density 0.8 g/cm3. Calculate the density of the mixture.
