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Mass is the amount of matter that makes up an object. It is a representation of the total atoms or particles that a body contains. That being said, big or small, are made up of matter and have mass. For example, a table, a chair, your bed, a football, a glass, and even air has mass. All the objects are light or heavy because of their mass. In Physics, mass is the most basic property of matter and is a fundamental quantity. Mass can be easily measured using any ordinary balance such as, beam balance, lever balance, pan balance, etc. The mass is measured in Kilograms, grams, pounds, etc.
| Table of Content |
Key Terms: Mass, Weight, Energy, Matter, Fundamental Quantity, Acceleration, Momentum, Density
What is Mass?
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Mass is the quantity that tells us about how much matter is present in a body. It is a quantitative measure of inertia. Mass is one of the fundamental quantities in Physics and is a quantitative property of an object against the acceleration, i.e., it is a measure of the resistance to acceleration when a net force is applied.
The mass of a body is constant and doesn’t change at any time. Only in certain extreme cases the mass may be impacted when a huge amount of energy is given or taken from a body. For example, in a nuclear reaction, a tiny amount of matter is converted into a huge amount of energy, this reduces the mass of the substance.
The S.I. unit of mass is kg(Kilogram) but various other units can be used as well to calculate mass, like grams, lbs, pounds, etc.
Also Read: Fundamental and Derived Units of Measurement
Mass Formula
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Mass can be calculated through several formulas. Some of the most important relations are listed below:
When force, mass and acceleration are given:
| F = ma or m = F/a |
where,
F = Force; m = mass; a = acceleration
When density, mass, and volume are given:
| \(\rho\) = m/V or m = \(\rho\)V |
where,
\(\rho\) = density; m = mass; V = volume
When Kinetic energy, mass, and velocity are given:
| K = ½ mv2 or m = 2K/v2 |
where,
K = kinetic energy; m = mass; v = velocity
When Potential energy, mass, the acceleration due to gravity and height are given:
| P = mgh or m = P/gh |
where,
P = potential energy; m = mass; g = gravitational acceleration; h = height
Using Einstein’s mass-energy relation:
| m = E / c2 |
where,
E = energy, m = mass, c = speed of light
When mass, velocity and momentum are given:
| p = mv or m = p/v |
where,
p = momentum; m = mass; v = velocity
Also Read:
| Topic Related Concepts | ||
|---|---|---|
| Types of Energy | Difference between Mass and Volume | Weightlessness |
| Gravity | Types of Forces | Gravitational Force Formula |
Difference between Weight and Mass
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It is common to hear mass and weight used interchangeably. However, mass and weight are two very different terms and it is crucial to understand the difference between them. The difference between mass and weight is shown in the table given below.
| Criteria | Mass | Weight |
|---|---|---|
| Definition | Mass is the amount of matter that makes up an object. It is the amount of matter present in a body. | Weight is defined as the amount of force acting on the mass of an object because of acceleration due to gravity. |
| Symbol | Mass is represented by: M | Weight is represented by: W |
| Formula | Formula of weight = m = \(\rho\)V where, \(\rho\) = density and V = volume | Formula of weight: Weight = mass × acceleration due to gravity = m x g |
| Unit of Measurement | S.I. unit of mass is Kilogram. | S.I. unit of weight is Newton. |
| Quantity Type | Mass is a fundamental quantity. It has only magnitude, thus, is a scalar quantity. | Weight is a derived quanity. It has both magnitude and direction, hence is a vector quantity. |
Also Read: Gravitationsl Potential Energy
Things to Remember
- Mass is the quantity that tells us about how much matter is present in a body.
- The mass of a body is constant and doesn’t change at any time.
- Mass is calculated by the formula: F = ma or m = F/a
- Weight is the amount of force acting on the mass of an object because of acceleration due to gravity.
- Relation between energy and mass is given by: m = E / c2
Sample Questions
Ques: Determine the mass of a body if the K.E is 70 J and velocity is 8m/s. (2 Marks)
Ans: Given:
K.E = 70 J; v = 8 m/s
the mass is expressed by:
m = 2 K.E / v2
m = (2 × 70)/ 82
m = 14o/64
m= 2.18 kg
Ques: Calculate the mass of a body if the density and volume of a body are 2 Kg/m3 and 5 m3. (2 Marks)
Ans: Given, density = 2 kg/m3
and volume = 5 m3
hence, mass = 2 x 5
m = 10 Kg
Ques: Calculate the mass if the weight of a body is 80 N.(2 Marks)
Ans: Given, weight of the body = 80 N
The mass of the body is expressed by:
m = w / g
m = 80 / 9.8
m = 8.163 kg
Ques: Why does mass remain the same but weight changes on different planets? (3 Marks)
Ans: The mass of an object is the measure of its contents but weight is the force due to gravity. And, the force due to gravity changes on different planets.
We know, that on earth g = 9.8 m/s2 and on moon its, g = 1.6 m/s2
Hence, the weight differs on moon but mass doesn’t.
Ques: An object accelerated at a constant 5 m/s2 under a force of 5 Newton. Calculate the mass of the object involved. (2 Marks)
Ans: Acceleration(a) of the object = 5 m/s2
Force on the object = 5 Newton
Therefore, F = ma
5 = 5 × m
m = 5/5 = 1
Hence, the mass of the object is 1 kg.
Ques: What is the relation between mass and weight? (2 Marks)
Ans: Weight(W) is the mass(M) of a body multiplied by the acceleration due to gravity(g).
W = M x g
Ques: What is relationship between kinetic energy and mass? (3 Marks)
Ans: The relation between kinetic energy and mass is given by the formula:
K = ½ mv2 or m = 2K/v2
Ques: Calculate the weight of an object on the moon which weighs 50kg on earth. (2 Marks)
Ans: We know that:
weight = mass x gravitational acceleration
thus, w = m x g
w = 50 kg x 1.6 m/s2
w = 80 Kg m/s2
Ques: Define weightlessnes. (3 Marks)
Ans: Weightlessness is the phenomenon involving absolute or near-complete absence of the sensation of weight. It is a condition of free-fall in which the gravity is cancelled by the inertial force arising from orbital flight or other gravity-negating situations.
Ques: Is mass a scalar quantity? (2 Marks)
Ans: Since, mass only has magnitude and no direction, it is a scalar quantity.
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