ICSE Class 7 Physics Chapter 01 Mass Weight and Density

Mass, Weight and Density

The common objects around you are made of different materials, such as iron, cement, wood, plastic and glass. All these materials are collectively called matter. The entire world, with all the living beings and nonliving things, in fact, the whole universe, is made up of matter. In this chapter, we will study a few characteristics of anything made of matter.

Mass and Weight

Mass is a basic property of all material objects, or of all things made of matter. The mass of a body is the amount of matter in the body. To begin with, you must be clear about one thing. Mass is not always related to size. To take an example, a ball of candy floss made from a spoonful of sugar takes up much more space than the sugar. However, the two have the same mass because they contain the same amount of matter. Similarly, if you compress some loose cotton, it takes up less space, but its mass remains the same.

The weight of a body is its property of being heavy or light. It depends on the mass of the body. A body of greater mass appears heavier than a body with less mass. You know that the earth attracts all objects towards itself. This pull, called the force of gravity, depends on the mass of the object. And it is this force that we call the weight of an object. Thus, the weight of a body is the force with which it is attracted by gravity.

Comparing Mass and Weight

We can now compare the two quantities mass and weight.

Both mass and weight are physical quantities, with magnitudes that can be measured and expressed in terms of numbers and units. Although they are closely related to each other, the two are different physical quantities, and not two names for the same physical quantity.

The SI unit of mass is the kilogram (kg). Since weight is, by definition, a force, its SI unit is the newton (N).

The weight and mass of a body are related.

Weight = constant - mass

You will learn about this constant later. It is called the acceleration due to gravity and is written as 'g'. It may be different at different places. For example, it is different on the earth and on the moon. Thus, though the mass of a body remains constant, its weight may be different at different places.

Ordinarily, when we speak of weighing an object, we mean measuring its mass. Thus, when we say that an object weighs 1 kg, we mean that its mass is 1 kg. The weight of an object of mass 1 kg is 9.8 N, as you already know.

Measurement of Mass

The mass of a body can be measured using different methods. In the common beam balance, the unknown mass is compared directly with a known mass. The two masses are placed on pans suspended from the two ends of a horizontal beam. This beam is supported at the middle and becomes horizontal when the two masses are equal. Balances which work on this principle are the common tarazu used by vegetable and fruit sellers, the physical balance used in laboratories, the scales used by jewellers, and the scales used in grocery stores and sweet shops.

The Physical Balance

The physical balance, shown in Figure 1.2, is used for scientific work. It can measure masses up to 1 kg with an accuracy of 10 mg. Its principal parts are as follows.

A base board provided with levelling screws

A brass pillar fixed at the centre of the base board

A horizontal beam made of brass or aluminium, with a triangular piece, called the knife edge, fixed at its exact centre

A long pointer, which is attached to the beam and can move over a scale fixed at the base of the pillar

Two identical pans suspended from knife edges at the ends of the beam

A case made of wood and glass to cover the entire device

A weight box is provided along with the balance. It contains weights from 500 g to 10 mg, such that they can be combined to obtain any weight between 10 mg and 1 kg.

When the balance is not in use, the beam rests on supports fixed to the pillar. To make the balance ready for use, a knob or handle on the base board is rotated clockwise. The beam then moves up from its supports and can swing about the knife edge. When the pans are empty, the pointer should swing its supports and can swing equally to both sides of the scale at the bottom.

To weigh an object (or measure its mass), the pans are brought down and the object is placed on the left pan. Suitable weights are placed on the right pan and the pans are moved up. The weights are adjusted till the pointer swings equally. At this position, the total weight on the right pan is equal to the weight of the object.

The Spring Balance

If you fix one end of a spring and pull at its other end, its length increases. The increase in the length of the spring is proportional to the force you apply on it, as the following activity will show you.

Fix paper clips to the ends of a spring (use one from a pen). Hang locks of different sizes from the clip at the lower end, as shown in Figure 1.3(a). Heavier locks will stretch the spring more.

A spring balance works on the principle illustrated by this activity. A steel spring is placed inside a cover. It can be suspended from a ring fixed at its upper end. The object to be weighed is attached to a hook at its lower end. A small pointer attached to the spring can move over a scale marked on the cover. When the

spring is stretched by the weight of an object suspended from the hook, the pointer moves down along the scale. The reading on the scale shown by the pointer gives the mass of the object in kilograms.

Kitchen scales and the dial balance used for weighing luggage are also spring balances, but they use springs of different shapes.

Spring balances are convenient to use and portable, but are less accurate than beam balances. Electronic balances are more accurate than beam balances. They work on a different principle. Choose an object that weighs about 1 kg. Weigh it using a spring balance, kitchen scales, a grocer's balance and an electronic balance. Compare your readings and see what conclusions you can draw from them.

Density

Most people would say that iron is heavier than wood. Though this appears reasonable, it is not always true. For example, a small iron nail is lighter than a large log of wood. Thus, in order to compare the 'heaviness' or 'lightness' of two different materials, we need to compare the masses of objects of the same size or volume. We do this with the help of a quantity called density. The density of a material is equal to its mass per unit volume.

This can also be expressed as

\[\text{density} = \frac{\text{mass}}{\text{volume}}\]

The definition of density makes it easy to compare the heaviness or lightness of different materials. For example, we would express the common observation that iron is heavier than wood more accurately as "the density of iron is greater than that of wood". This would always be true and there would be no confusion related to volume.

Density is a physical quantity with a magnitude that can be measured. Its SI unit is kilograms per cubic metre, can be written in symbols as \(\text{kg/m}^3\). Another unit of density that is in common use is \(\text{g/cm}^3\). The relation between the two units is

\[1000 \text{ kg/m}^3 = 1 \text{ g/cm}^3\]

If you look at Table 1.1, it will be obvious that the density of water is 1 g/cm³, that of ice is 0.916 g/cm³, and so on.

Teacher's Note

Understanding mass and weight helps explain why astronauts feel lighter on the moon despite having the same mass, and why we use different scales for different purposes in daily life - a kitchen scale for cooking and a weighing machine for our body weight.

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