Mass Formula

Mass is a quantity that gives an idea about how much matter is present in an object. It is a quantitative measure of inertia.  And acceleration is inversely proportional to inertia.

The relation between force and mass is given by:

                 F = ma or m = F/a

The relation between density, mass, and volume is given by:

                 𝛒 = m/V or m = 𝛒V

The relation between Kinetic energy, mass, and velocity is given by:

                 K = ½ mv2 or m = 2K/v2

The relation between Potential energy, mass, the acceleration due to gravity and height is given by:

                 P = mgh or m = P/gh

The well known Einstein’s mass-energy relation that provides mass-energy formula is,

                   m = E / c2

Where, E = energy, m = mass, c = speed of light

The relation between mass(m), velocity(v) and momentum(p) is given by:

                    p = mv or m = p/v

Difference between mass and weight

Weight is the force due to gravity on a mass. So, mass remains constant but weight changes according to  the change in the gravitational field.

                W = mg or m = W/g

Solved Examples 

1. Calculate the mass of a body if the density and volume of a body are 2 Kg/m³ and 5 m³.

Ans:

Here mass = density x volume

                  = 2 x 5

                  = 10 Kg

2. If an object is moving with a velocity of 5 m/s and has a kinetic energy of 100J, Find the mass.

Solution: We know that KE = ½ mv2

100 = ½ x m x 5 x 5

100 = 25 m/2

m = 100x2/25 = 200/25 = 8 kg

Why does mass remain the same but weight changes on different planets?

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

Let’s understand this by an example:

Example:

1. Calculate the weight of an object on the moon which weighs 50kg on earth.

Ans:

Here weight = mass x gravitational acceleration

                  = m x g

    = 50 kg x 1.6 m/s²

                 = 80 Kg m/s²

So, as we can clearly see from this example, if your friend’s weight is 50kg on this planet, they will be 80kgs on the moon! 

Now, Calculate your weight on the moon.

Did you know?

• Even as most objects on Earth or in the earth’s gravitational field experience the gravitational pull and therefore attain the attribute of “weight”; there are some special circumstances that can give a sensation of “weightlessness”.

• Weightlessness is the phenomenon involving absolute or near-complete absence of the sensation of weight. This is also termed zero-G, although the more appropriate term will be "zero G-force". It occurs when there are no contact forces acting upon an object, including the human body.

• Weight, as we understand, is a measure of the force on an object at rest when under the influence of a  gravitational field (for example, for objects on the surface of the Earth). This "weight-sensation" can arise due to contact with supporting floors, seats, beds, scales, etc. 

• A sensation of weight can also be experienced when the gravitational field is zero; for such cases, the object is under the effect of contact forces, which are acting upon it. These forces help overcome a body's inertia (condition of rest) by some mechanical and non-gravitational influence- such as centrifugal force in a centrifuge, an orbiting space station, or within an accelerating vehicle.

• It is during these circumstances (when gravitational force experienced is zero) that a body is said to be in "free fall". Near a black hole, tidal effects due to a non-uniform gravitational field are found to be very strong. While in the case of the Earth, the effects are only minuscule, especially on objects of relatively small dimensions (such as the human body or a spacecraft). In such instances, the weightlessness of the objects is almost always guarded. This phenomenon is referred to as microgravity and it is found to exist in all orbiting spacecraft.

This is all about mass weight, their meanings, and differences along with the explanation of their formulas. Focus on how the formulas are derived and used to calculate the answers to the solved questions to clear your conceptual understanding of this topic.