Mass Formula

The mass of an object relates to how much matter it contains. Consider three scales containing a bowling ball, a tennis ball, and a pebble. The bowling ball would undoubtedly have the highest weight rating on the scale among these three. Because a bowling ball is far heavier than a tennis ball or a marble, this is the case. The mass is the most important quantity measured by the scale. Let’s look at the concept of the Mass formula.

Mass

A body’s mass is its physical attribute. In addition, when a net force is applied, it is a measure of the resistance to acceleration. It’s a dimensional-less quantity that represents the amount of matter contained in a particle or item. The kg is the standard unit of mass according to the International System (SI).

The terms “mass” and “weight” aren’t synonymous. This is true even if the most common method for determining an object’s mass is to weigh it on a spring scale. A person on the moon, for example, would weigh significantly less than someone on Earth. However, whether on the moon or on Earth, such an individual’s mass would remain the same.

Mass Formula

Mass formula is given as,

m = F/a

Where,

• m = Mass,
• F = Force,
• a = Acceleration.

The mass formula is also written as follows,

m = ρ × v

Where,

• m = Mass,
• ρ = Density,
• v = Volume.

The weight mass formula is written as follows,

m = w/g

Where,

• m = Mass,
• w = Weight,
• g = Gravity.

Derivation

When the net force acting on an object equals the rate of change of its momentum, the object is said to be in equilibrium.

F_net = dp / dt

The derivative of momentum in relation to time is also the rate of change of momentum. Furthermore, manipulating the specific equation necessitates calculus.

F_net = d / dt (mv) 

∴ F_net = m × dv/dt + v × dm/dt

∴ F_net = ma + v × dm/dt

Both m and v are unquestionably changeable quantities in this situation. The derivative should be treated as if it were a product’s derivative. The dv/dt value denotes the rate at which the object’s velocity varies, which is undoubtedly the acceleration. dm/dt also shows the rate at which the object’s mass varies over time.

Sample Questions

Question 1: What is the SI unit of mass?

Answer:

SI unit of mass is kg.

Question 2: Write the formula of weight mass.

Answer:

The weight mass formula is written as follows,

m = w/g

Where,

• m = Mass,
• w = Weight,
• g = Gravity.

Question 3: Under a force of 7 Newton, an item accelerates at a constant 3 m/s². Calculate the object’s mass.

Solution:

Given: F = 7 N, a = 3 m/s²

Since,

m = F/a

∴ m = 7/3

∴ m = 2.3 kg

Question 4: If the density and volume of a body are 7 kg/m³ and 15 m³, calculate the mass of the body.

Solution:

Given: ρ = 7 kg/m³, v = 15 m³

Since,

m = ρ × v

∴ m = 7 × 15

∴ m = 105 kg

Question 5: Calculate the weight of an object that mass 30 kg on Earth and is placed on the moon.

Solution:

Given: m = 30 kg, g = 1.6 m/s²

Since,

m = w/g

∴ w = m × g

∴ w = 30 × 1.6

∴ w = 48 kg m/s²

Question 6: If a body weighs 56 kg m/s², calculate the mass.

Solution:

Given: w = 56 kg, g = 1.6 m/s²

Since,

m = w/g

∴ m = 56 / 1.6

∴ m = 35 kg

Question 7: If the mass and volume of a body are 33 kg and 6 m³, calculate the density of the body.

Answer:

Given: m = 33 kg, v = 6 m³

Since,

m = ρ × v

∴ ρ = m/v

∴ ρ = 33/6

∴ ρ = 5.5 kg/m³

Question 8: Assume that the force and acceleration are 40 N and 6 m/s². Then Calculate the mass of object.

Answer:

Given: F = 40 N, a = 6 m/s²

Since,

m = F/a

∴ m = 40/6

∴ m = 6.66 kg