Mass and Weight

Introduction

Measurement denotes the comparison of an unknown quantity with a known quantity. It is the measure of quantity. Length, mass, time, electric current, temperature, amount of substance, and luminous intensity are the seven fundamental quantities. There are many systems of units used such as the KGS system, CGS system, and International SI system. Different systems assign different units for basic elements.

If the quantity has only magnitude then it is called a scalar quantity. Example mass, distance, time, etc. If the quantity has both direction and magnitude then it is called a vector quantity. Examples are velocity, displacement, force, etc.

What is mass?

It is the property of a body that refers to the amount of matter that the body constitutes. It is the fundamental quantity. The resistance offered by the body to the motion or velocity of the body. Everything around us has mass. A chair, football, glass, and even air has mass. The mass of a body is measured as

$$\mathrm{mass\:=\:density\times\:volume}$$

The mass of the body is constant. The S.I. unit of mass is the kilogram.

According to Newton’s law of motion, the force applied on the body is given by,

$$\mathrm{Force\:=\:mass\:\times\:acceleration}$$

$$\mathrm{F\:=\:ma}$$

The force that acts on the body is the rate at which the momentum changes with time. Thus the force acting on the body also be written as

$$\mathrm{F\:=\frac{dp}{dt}}$$

P denotes the momentum of the body and it denotes as $\mathrm{P\:=\:mv}$

$$\mathrm{F\:=\frac{d(mv)}{dt}\:=\:m\:\frac{dv}{dt}}$$

$$\mathrm{F\:=\:ma}$$

What is weight?

Weight of the object is the force that exerts on the mass of the body by the acceleration due to gravity. It is also defined as the force that attracts the body to the earth. Due to the acceleration due to gravity the weight of the body changes with place. It is denoted as W and the S.I unit of weight is Newton. If the mass of the body is high the weight will be high. The weight of the object is measured by

$$\mathrm{Weight\:=\:mass\times\:acceleration\:due\:to\:gravity}$$

Scales to measure the mass and weight

There are many instruments used to measure the mass and weight of the object in many places. They are given below. They are common scale, manual scale, body scale, ohaus scale, Quartz micro scale, hanging scale, digital scale, hybrid scale and weighing bridge. The common scale and the manual scales are used to measure weight and mass of the object in places such as grocery shops and markets. Body scales are used to measure the weight of the body used in places such as hospitals, health centers and pharmacies.

Ohaus scales are used in laboratories and pharmaceuticals to measure small scale substances. Quartz micro scales are also used in laboratories with high accuracy. Hanging balance is used to measure the weight of the body by hanging it by the balance. Digital scales and hybrid scales are used to measure the weight of the object in a large scale. Weighing bridge is used to measure the weight of the vehicle passing on it.

Gravity

The force of attraction that attracts the body towards it is called gravity. Any object with mass has gravity. The body with higher mass has high gravity. This gravity is responsible for the rotation of earth around the sun. In 1687, Si Isaac Newton discovered gravity. Every particle in the universe attracts every other particle with a force. This force directly depends on the product of masses of the particles and it inversely depends on the square of distance between them.

$$\mathrm{F\:=\:G\:\frac{m_1m2}{r^2}}$$

Here G denotes the gravitational constant and carries the value as,

$$\mathrm{G\:=\:6.674\:\times\:10^{-11}m^{3}kg^{-1}s^{-2}}$$

Difference between mass and weight

Mass	Weight
Mass is the quantity of matter that it constitutes	weight is the quantity of force exerted on a mass of the body by the acceleration due to gravity
Mass is denoted as M	Weight is denoted as W
The mass of the body does not change. It is always constant	weight of the body changes with a gravitational force acting on it
The formula for mass is $\mathrm{mass\:=\:density\times\:volume}$	The formula for weight is $\mathrm{weight\:=\:mass\times\:acceleration\:due\:to\:gravity}$
The S.I unit of mass is kilogram(kg)	The S.I unit of weight is Newton(N)

Solved examples

Example 1: Ramesh has a book whose mass is 2.5kg. Then what is the weight of the book on the earth and moon?

Solution: Given

The mass of the book (m) = 2.5kg, acceleration due to gravity on the Earth is 9.8 𝑚/𝑠2and acceleration due to gravity on the moon is 1.625 𝑚/𝑠2

The weight of the book on the Earth is $\mathrm{weight\:=\:mass\times\:acceleration\:due\:to\:gravity}$

$$\mathrm{W\:=\:2.5\:\times\:9.8}$$

$$\mathrm{W\:=\:24.5\:kg}$$

The weight of the book on the moon is $$\mathrm{W\:=\:2.5\:\times\:1.625}$$

$$\mathrm{W\:=\:4.0625\:kg}$$

Thus the weight of the book on the Earth and Moon are 24.5 kg and 4.06 kg.

Example 2: A body accelerated to 10 𝑚/𝑠2 by the applied force of 15 Newton. then calculate the mass of the body.

Solution − Given

The force acting on the body F=15N and acceleration is 𝑎 = 10 𝑚/𝑠2

According to Newton’s law of motion $\mathrm{F\:=\:ma}$

$$\mathrm{m\:=\:\frac{F}{a}}$$

$$\mathrm{m\:=\:\frac{15}{10}}$$

$$\mathrm{m\:=\:1.5\:kg}$$

The mass of the body is 1.5 kg.

Conclusion

In this tutorial, the fact of mass and weight were discussed in detail. The scales to measure the mass and weight and gravity were also discussed. The difference between mass and weight and some solved examples were also discussed.

FAQs

1. Differentiate vector and scalar.

Scalar	Vector
Gives magnitude only	Gives both direction and magnitude
Used for only one-dimensional problem	It is used for multi-dimensional problem
It can be divided into another scalar	It cannot be divided into another vector quantity
Ex: distance, speed	Ex: displacement, velocity

2. What is momentum?

Momentum has both magnitude and direction so it is a vector quantity. It is measured from the product of velocity of the object and its mass.

$$\mathrm{F\:=\:ma}$$

3. How does the volume of the object affect the mass?

Volume and mass are two independent quantities. So they are an independent quantity. The mass of the object is constant for change in volume.

4. What are the differences between the mass and volume?

Mass	Volume
It is the quantity of matter in the body	It is the amount of space that is covered by the matter of the body
Mass of the body is constant	volume of the body can change
S.I unit of mass is kg	S.I unit of volume is cubic meter

5. What are the errors that occur during mass measurement?

Dust that occurs on the surface of the devices. Condensation water on the devices. The effect of magnetic field. The change in temperature causes the material to expand or contract which causes errors in the measurements. vibration of the material.