Mass and Momentum - Definition, Example, FAQs

Mass and Momentum - Definition, Example, FAQs

Edited By Vishal kumar | Updated on Nov 26, 2024 03:04 PM IST

Mass describes the amount of matter in an object that an object is made up of. It is a property of substance and because it is without direction it is known as a scalar quantity. On the other hand, momentum is calculated by using the product of mass and velocity. Both mass and momentum is a fundamental concepts in Physics. Let's clarify this concept in the given article.

Mass and Momentum - Definition, Example, FAQs
Mass and Momentum - Definition, Example, FAQs

What is Mass?

Mass is a fundamental property of matter that specifies the amount of matter contained in an object. It has magnitude but no direction, hence it is a scalar quantity.

According to Newton's second law of motion:

$$
F=m a
$$

where $m$ is the mass.

Unit of Mass

SI Unit of mass: Kilogram (kg)
Other units include grams ( g ), metric tons ( t ), and in atomic physics, atomic mass units (amu).

Difference Between Mass and Weight

Mass: A measure of the amount of matter in an object (in kg ) is Mass.
Weight: The force due to gravity acting on the mass is called as a Weight.


$W=\mathrm{m} \mathrm{g}$

where

  • $W$ is weight,
  • $m$ is mass, and
  • $g$ is the gravitational acceleration.

How are inertia and mass related?

Objects with more mass have more inertia than an object with a smaller mass.

This means that inertia is directly proportional to the mass. We need to apply more unbalanced force to move an object with more mass than an object with light mass.

For example – we can easily move a chair from its initial position than to move a sofa.

Mass and Velocity

The relationship between mass ( $m$ ) and velocity ( $\mathbf{v}$ ) is called linear momentum ( $\mathbf{p}$ ):

$$
\mathbf{p}=m \mathbf{v}
$$

  • Mass is scalar, and velocity is vector, so momentum (p) is a vector quantity with the same direction as velocity.
  • The SI unit of momentum is $\mathrm{kg} \cdot \mathrm{m} / \mathrm{s}$.
  • Momentum measures the difficulty of stopping an object and is crucial in analyzing collisions and motion.

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What is momentum?

Momentum is defined as the product of the mass and velocity of that object. Momentum is a measure of the time required through constant force to put an object at rest. Being a vector quantity it gives both the direction and magnitude.

The SI unit of momentum is kilogram meter per second ( $\mathrm{kg} \cdot \mathrm{m} / \mathrm{s}$ ).

Momentum Formula

$$
\mathbf{p}=m \mathbf{v}
$$

where:

  • $\mathbf{p}$ is the momentum (a vector quantity),
  • $m$ is the mass of the object (scalar),
  • $\mathbf{v}$ is the velocity of the object (vector).

Conservation of Momentum

Law of Conservation of Linear Momentum is a fundamental concept in Physics stating that the total momentum of an isolated system remains constant, provided no external forces act on the system. This law applies to all physical systems, including particles, objects, and even large-scale systems like galaxies.

Mathematical Statement of Conservation of Momentum:

$\mathbf{p}_{\text {initial }}=\mathbf{p}_{\text {final }}$

Proof of Momentum Conservation

From Newton's second law:

$$
\mathbf{F}=\frac{d \mathbf{p}}{d t}
$$

If the net external force $\mathbf{F}_{\text {net }}$ on the system is zero:

$$
\frac{d \mathbf{p}}{d t}=0
$$

This implies that $\mathbf{p}$, the momentum, is constant over time.

Applications of Conservation of Momentum

The concept of Conservation of Momentum is applied to :

  • Elastic Collision: Both momentum and kinetic energy are conserved.
  • Inelastic Collision: Momentum is conserved, but kinetic energy is not (some energy is converted to other forms like heat or deformation).
  • Rocket Propulsion: Rockets work based on momentum conservation. As exhaust gases are expelled backward, the rocket gains forward momentum.

Frequently Asked Questions (FAQs)

1. Difference between mass and velocity.

Mass is the fundamental property of all matter . It gives resistance to any force trying to change its properties like shape , direction , velocity or state . Its si unit is kg .

Velocity is the displacement of any body in given time . It is a derived physical quantity of the object . Its si unit is m/s .

2. What is the newton's first law of motion?

According to newton’s first law of motion, any body tends to be in its initial state whether it is of motion or rest.

3. What is newton's third law of motion?

“for every action there is equal and opposite reaction”. It is newton’s third law of motion.

For example during gunshot we experience a backlog of the hand due to the reaction in backward direction , made by the gun because of the bullet force in forward reaction .

4. State the law conservation of momentum?

Law of conservation of momentum states that if two or more bodies kept in an isolated system working on each other dad total momentum will remain conserved unless and until there is any unbalanced external force applied to that system .

5. What is impulse?

Impulse is the change in momentum it is the force experience for very short interval of time.

6. Define momentum of a body/ what is meant by momentum?

Momentum is the product of mass and velocity of a body.

7. What is difference between mass and inertia?

According to inertia and mass class 9, mass is the measure of quantity of an object without considering the volume while inertia is the tendency to remain in the state of rest or uniform motion of an object.

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