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Mass and Momentum are related terms in physics, yet they both are much different from each other. They both represent different states of an object. Every object on this earth has some mass and every moving object possesses some momentum.
- Mass is the total volume of an object whereas momentum is the mass of a moving body.
- Mass and Momentum are the fundamental properties of matter.
- Momentum depends upon two variables mass and velocity.
- Mass is an intrinsic property of matter.
Read More: States of Matter
| Table of Content |
Key Terms: Mass, Inertial Mass, Acceleration, Momentum, Newton’s Second Law of Motion, Newton’s Third Law of Motion, Conservation of Momentum
What is Mass?
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Mass is defined as the total amount of matter in a physical body. It can also be defined as the measure of the resistance offered by an object to change in its velocity when a net force is applied to it. This is called inertial mass. Mass is the fundamental property of a matter.
- In the presence of an applied force, mass determines an object's acceleration.
- Mass is independent of the direction of an object, thus it is a scalar quantity.
- It is denoted by ‘m’.
- The SI unit of mass is the kilogram (kg).
Laws of Motion Video Lecture
The mass of an object can be calculated using the given formula:
| Mass = Density/Volume |
Mass of an object is always constant. It is not affected by external factors like gravitational force, location, etc. The mass of an object determines the acceleration produced by it when a certain amount of force is applied. This can be understood as when a net force F is applied on an object of mass m, the acceleration (a) produced by it is given by:
| a = F/m
|
or
| F = ma |
So, the greater the mass, the smaller the acceleration produced by an object or vice-versa.
Read More: Moment of Inertia
What is Density?
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Density of any material is determined by dividing its mass by its volume. The density of a substance indicates its denseness in a given area. It is a unique physical characteristic of a specific thing. The Greek scientist Archimedes discovered the density principle. Various substances have different densities. Hence, the same substance weighs differently for a different volume. Density is a qualitative term, it describes the heaviness of an object at constant volume.
The symbol ρ represents density or it can also be represented by the letter D.
Mathematically, density is represented as follows:
| Density = Mass/Volume |
or
| ρ = m/v |
The SI unit of Density = kilograms per cubic meter (kg/m3).
Read More:
| Relevant Concepts | ||
|---|---|---|
| Pressure and Density | ||
| Types of Forces | ||
Difference Between Mass and Weight
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Mass is not the same as weight. The weight of an object takes acceleration due to gravity (g) into account. It is the measure of the gravitational force exerted on an object of mass m. It is calculated using the formula,
| W = mg |
Where,
g → Acceleration due to gravity (9.8 m/s²)
The mass of an object is constant but its weight is not. It changes as the value of ‘g’ changes. Since weight has both magnitude and direction, thus it is a vector quantity. The direction of the weight is towards the center of gravity.
Weight takes into account acceleration due to gravity
The table below contains differences between mass and weight:
| Mass | Weight |
|---|---|
| Mass measures the total amount of matter present in a physical body. | Weight is the gravitational force acting on an object of mass m. |
| It is denoted by m. | It is denoted by W. |
| Its SI unit is the kilogram (kg). | Its SI unit is Newton (N). |
| It is a scalar quantity. | It is a vector quantity. |
Read More: Vector and Scalar Quantities
What is Momentum?
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Momentum is defined as the measure of the mass of a moving object. Whenever an object of mass m is moving with a velocity v, it carries some momentum. Therefore, momentum is the fundamental property of all moving objects.
Momentum has both magnitude and direction, thus it is a vector quantity. The SI unit of momentum is kgs-1. It is the product of the mass and velocity of an object and is given by the formula;
| Momentum = Mass velocity |
Or
| p = mv |
Newton’s Second Law of Motion describes the relationship between momentum and force acting on an object. It states that for a moving object, the rate of change of momentum is equal in magnitude and direction to the force applied to it. It can be written as;
F = ma
Also,
a = Δv/Δt
F = m. Δv/Δt
We know that, p = mv
So,
F = Δp/Δt
Read More: Oscillations
Law of Conservation of Momentum
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According to the law of conservation of momentum, the momentum of a system always remains constant. It does not change. It is based on the principle of Newton’s third law of motion which states that when object A exerts a force on object B, B also exerts a force on A which is equal in magnitude and opposite in direction to that of A. This law is used to derive the law of conservation of momentum.
The law of conservation of momentum states that in an isolated system, the momentum remains constant when two or more bodies act upon each other.
A collision between two objects and a change in momentum
The formula can be derived as follows:
Let there be a collision between two particles A and B having masses m1 and m2 respectively.
Initial velocity of A = u1
Initial velocity of B = u2
Final velocity of A = v1
Final velocity of B = v2
The time of contact between A and B is taken as t
So, after a collision between A and B, let the acceleration of A and B be a1 and a2
a1 = (v1 - u1) / t
a2 = (v2 - u1) / t
From Newton’s third law of motion, FBA = -FAB
FBA = m2 . a2 = m2 (v2 - u2)/ t
FAB = m1 . a1 = m1 (v1 - u1)/ t
Now, FBA = -FAB
m2 (v2 - u2) / t = - [ m1 (v1 - u1) / t ]
m2v2 - m2u2 = -m1v1 + m1u1
m2v2 + m1v1 = m1u1 + m2u2
Hence,
m1u1 + m2u2 = m1v1 + m2v2
The initial momentum before the collision of A and B is equal to the final momentum of A and B after the collision.
Read Also:
| Related Topics | ||
|---|---|---|
Difference between Mass and Momentum
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Mass and Momentum are the basic and principal units of motion. The differences between mass and momentum are tabulated below:
| Mass | Momentum |
|---|---|
| Mass is the amount of matter an object contains when it is at rest. | Momentum is the quantity a body gains due to its motion. |
| Inertia at rest possessed by the body is due to its mass only. | Inertia at motion possessed by the body is due to its motion only. |
| It is independent of other quantities of its measurement. | Momentum depends upon a velocity and mass of an object. |
| The mass of an object is constant throughout the universe. | Momentum changes with the change in velocity of an object. |
| It is a scalar quantity | It is a vector quantity. |
| SI Unit of mass is the kilogram (kg) | SI unit of momentum is kilogram- meter/second (kg-m/s). |
Read More: Rectilinear motion
Things to Remember
- Mass is a measure of the resistance offered by an object to change in its velocity when a net force is applied. Its SI unit is kg.
- The inertial mass of an object determines the acceleration produced by it when a net force is applied to it.
- Mass and weight are different from each other. Weight is calculated taking into consideration the value of acceleration due to gravity (g).
- Momentum is defined as the mass contained by an object when it is in motion. It is denoted by p.
- Density changes with changes in the velocity of an object.
- The law of conservation of momentum states that an isolated system's initial and final momentum always remains equal when two or more bodies act upon each other.
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Previous Years’ Questions
- The resultant of these forces is three times the first force… [KEAM]
- The tension in the string P is… [KEAM]
- If the resultant force is equal to 40√3, the magnitude… [KEAM]
- lf a force of 6 N is applied on the heavier mass… [KEAM]
- A truck is stationary and has a bob suspended by a light string… [NEET – 2019]
- An object flying in air with velocity … [NEET – 2019]
- Which one of the following statements is incorrect … [NEET – 2018]
- A man weighing 60 kg is in a lift moving down with an acceleration… [KCET – 2018]
- The speed of the bullet after it emerges out horizontally from the block … [NEET – 2016]
- A car is negotiating a curved road of radius R… [NEET – 2016]
Sample Questions
Ques. Calculate the momentum of a toy car of mass 200g moving with a speed of 5m/s. (2 Marks)
Ans. Here, the mass of the car (m) = 200g = 0.2 kg
Speed (v) = 5 m/s
Momentum (p) = m v
→ 0.2 5 = 1 kg m/s
Ques. A body of mass 25 kg has a momentum of 125 kg m/s. Calculate the velocity of the body. (3 Marks)
Ans. Mass (m) = 25 kg
Momentum (p) = 125 kg m/s
p = mv
v = p/m
v = 125 / 25
v = 5 m/s
Ques. Calculate the change in momentum of a body weighing 5 kg when its velocity decreases from 20 m/s to 0.20 m/s. (3 Marks)
Ans. Mass of the body (m) = 5 kg
v1 = 20 m/s
Momentum (p1) = 20 5 = 100 kg m/s
v2 = 0.2 m/s
Momentum (p2) = 5 0.2 = 1 kg m/s
Change in momentum = p2 - p1 = 1 - 100 = -99 kg m/s
Ques. A man throws a ball weighing 500g vertically upwards with a speed of 10 m/s.
What will be its initial momentum?
What would be its momentum at the highest point of its flight? (5 Marks)
Ans. Mass of ball (m) = 500g = 0.5 kg
Initial velocity = 10 m/s
- Initial momentum = mv = 0.5 10 = 5 kg m/s
- Velocity at the highest point = 0 m/s
Momentum at the highest point = 0.5 0
Momentum at the highest point = 0 kg m/s
Ques. A constant retarding force of 50 N is applied to a body of mass 20 kg moving initially with a speed of 15 ms-1. How long does the body take to stop? (3 Marks) [NCERT]
Ans. Here m = 20 kg
F = -50 N (minus sign represents retarding force)
F = ma
a = F / m = - 50 / 20 = - 2.5 ms-2
Using equation,
v = u + at
u = 15 ms-1 , v = 0
0 = 15 + (-2.5) t
t = 6 s
Ques. A rocket with a lift-off mass of 20,000 kg is blasted upwards with an initial acceleration of 5 ms-2. Calculate the initial thrust (force) of the blast. (5 Marks) [NCERT]
Ans. Mass (m) = 20,000 kg = 2 104 kg
Initial acceleration = 5 ms-2
The thrust should be such that it overcomes the force of gravity besides giving it an upward acceleration of 5 ms-2.
Thus, the force should produce a net acceleration of 9.8 + 5.0 = 14.8 ms-2.
Thrust = force = ma
F = 2 104 14.8 = 2.96 105 N
Ques. A 12,000 kg railroad car is traveling at 2 m/s when it strikes another 10,000 kg railroad car that is at rest. If the car locks together, what is the final speed of the two railroad cars? (3 Marks)
Ans. According to law of conservation of mass,
p1 = p2
m1v1 = m2v2
12000 2 = 22000 v2
24000 = 22000 v2
v2 = 1.1 m/s
Ques. Why does a cricket player move his hand backward while catching the ball? (2 Marks)
Ans. The momentum of a fast-moving cricket ball is very large. To stop or catch the ball, its momentum has to be reduced to zero. When a player moves his hands backward on catching the ball, the time taken to decrease the momentum to zero is increased. Due to an increase in the time taken to stop the ball, the rate of change of momentum of the ball is decreased and thus the force exerted on the hands of the player reduces.
Ques. Why is a mass sometimes called the coefficient of linear inertia? (1 Mark)
Ans. It is easier to pull a lighter body than a heavier body. Therefore, the more mass more the inertia. Hence it is sometimes termed the coefficient of linear inertia.
Ques. Describe density. (2 Marks)
Ans. Any material's density can be calculated by dividing its mass by volume. A substance's density is a measure of how dense it is in a specific space. Different materials have varying densities. As a result, the density of the same substance varies depending on the volume. Density is a qualitative term that refers to an object's weight at a certain volume. The symbol ρ represents density or it can also be represented by the letter D.
Density = Mass/Volume
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