Mass and Momentum

What is Mass?

We can define mass as the inherent property of matter. It is the measure of the inertia of a body, mass tells us how much matter there is in a body, we can measure the mass of a body on earth by measuring the force of gravity acting on it, the SI unit of mass is kilogram (kg).

Remember mass is not the same as weight, even though we measure the mass of a body by measuring its weight, a body with the same mass weighs differently on the moon than it weighs here on earth, mass is one property of matter that doesn’t change easily.

Mass

A bowling ball has more mass than football because it has more matter in it, hence, it weighs more too, and most of the physical quantities of matter are derived from mass, and mass plays a very important role in Physics. Momentum, inertia and other properties of matter are all because of mass.

Mass is a form of energy; it is energy at rest. In 1905 Albert Einstein formulated the theory of special relativity;

E = \( mc^2 \)

which states that energy is mass times the speed of light, as speed of light is approximately \(3\times 10^{8}m/s\), the energy inside 1 kilogram of matter would be a whopping 90000000000 joules of energy. That’s a lot of energy inside just 1 kilogram of matter, this energy can be tapped by recent advancements in nuclear technology and by means of nuclear fission, and a small amount of matter is converted into clean energy.

Acceleration of a body is \(\propto \frac{1}{Mass}\)

Therefore, for a given force: a \(\propto \frac{1}{Mass}\)

What is Momentum?

Momentum is defined as the quantity of motion of the body. It is measured by \(mass\times velocity\), as momentum depends upon velocity, and it depends on the direction of the motion of the body as well. Momentum is a vector quantity since velocity is vector while mass is scalar.

Momentum = Mass X Velocity

p = mv

Unit of momentum is given as:

SI unit kg.m.s-1

Imagine two friends Sam and Max running in the playground; Sam weighs 30 kilograms and Max weighs 40 kilograms, both of them are running at the same speed in the same direction.

  • (a) Who has more momentum, and why?
  • (b) Who will get hurt more if they hit a wall?

The answer to both the above questions would be Max, because he has more momentum, as the velocity of Sam and Max is same, their momentum will depend upon their mass, therefore Max will have more momentum than Sam.

The law of conservation of momentum states that the total momentum of a closed system does not change, which means that if two bodies collide with each other, their total momentum after the collision will be equal to their momentum before the collision.

Let’s get some terms clear:

What is Weight?

Weight is defined as the force exerted by an object due to acceleration due to gravity. Weight is the product of mass times acceleration due to gravity on the Earth.

The unit of weight is:

CGS unit dyne
SI unit N

One dyne is defined as 10-5 N.

Difference between mass and weight:
Mass is defined as the quantity of matter accommodated in an object. It is one of the properties of matter and remains unchanged. Whereas weight is related to gravity. An example of this difference between mass and weight is that person will have same mass on the Earth and on the moon, but the weight is dependent on the gravity of the Earth and the moon.

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What is Density?

For any material density is measured in terms of its mass per unit volume. Density is one of the properties of materials which is used to explain how closely matter are stuffed in any material. Greek scientist Archimedes was the first person to explain the concept of density. In his principle which is popularly known as Archimedes principle he explained how to determine density by calculating buoyant force and mass.

The formula of density is given as:

\(Density=\frac{Mass}{Volume}\)

The unit of density is given as:

CGS system \(\frac{g}{m^{3}}\)
SI unit \(\frac{kg}{m^{3}}\)

The dimensional formula of density is given as:

Dimensional formula M1L-3T0

What is Inertia?

The concept of inertia was first introduced by Sir Issac Newton. He explained inertia in his first law of motion which states that:
When an object is at rest or in motion, it tends to continue to remain in rest or in motion until an external force acts on it.
It can be said that inertia is the quantity of matter which is responsible for an object to either remain in rest or to continue in motion. To overcome inertia, an external force must be applied. The applied force will either stop the object or will slow down the motion. Inertia is the resistance offered by matter to acceleration, technically mass is the measure of inertia.

There are three types of inertia:

  • The inertia of rest: Body tends to remain in rest until an external force is applied.
    Example: People travelling in bus tend to fall back when the bus starts as the inertia is moved by external force.
  • The inertia of motion: Body continues to remain in motion unless force acts on it to stop the motion.
    Example: People tend to fall forward when brake is applied in the moving bus.
  • The inertia of direction: When a body is in motion, it has the tendency to change its direction and to continue to move in that direction unless force acts on it.
    Example: People sitting at the corners of the bus experience outward pull when the bus moves around the curved roads.

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