The amount of matter contained in an object is measured by its mass, which is the most fundamental property of any object. With different approaches and solved problems, this post will discuss how to find mass without acceleration, i.e., without using Newton’s second law.

**The most popular method for determining mass is to apply Newton’s second law, which includes both force and acceleration. Aside from that, mass can be calculated using density and volume and specific heat as well as energy.**

Let’s take a look at each approach of finding mass one by one.

**⇒ Finding mass from the Density:**

The density of an object is its one-of-a-kind physical property. Density was discovered by Archimedes, a Greek scientist. The density of an object’s matter (mass of an object) shows how much space it occupies, i.e., its volume. Essentially, **it is a measurement of how tightly or loosely a substance or material is packed together. As a result, this **property is derived from mass and volume and can be expressed as:

Thus, mass can be simply determined if the density and volume of an object or material are known. Making mass the subject of an equation, it can be calculated as follows:

m = 𝜌V

**⇒ Finding mass from Specific Heat:**

**The amount of heat required to increase the temperature of one gram of a substance by one degree Celsius is referred to as its specific heat.** When this statement is converted into an equation, the specific heat equation is as follows:

Where c stands for specific heat, the letter Q denotes the amount of heat that has been provided, m denotes the mass of the substance, and T denotes the temperature change.

**The specific heat value of each substance or material is different. It is simple to find the mass of any substance if the value of specific heat is known, as well as the amount of heat delivered and the temperature change.** The mass in the form of specific heat can be calculated as follows:

**⇒ Finding mass from Kinetic energy:**

**When an object or particle is in motion, it has the type of energy known as kinetic energy. When a force is applied to an object, it is said to be work done on the object, which causes it to accelerate and gain kinetic energy.** As a result, if an object is moving, it possesses the property of kinetic energy. The kinetic energy of an object is determined by the object’s motion as well as its mass and given by:

Where k stands for kinetic energy and V stands for velocity of an object.

Thus, the mass of an object is given by:

The mass of an object is conserved according to the law of conservation of mass.** However, the absoluteness of mass is not always true**. **It means that the above equation is valid only when the object is traveling at a low to relatively high speed. However, when an object moves at an extremely high speed, such as the speed of light, its mass increases.** As a result, at that time, Albert Einstein’s principle of relativity must be applied, as follows:

E = mc^{2}

**According to the above equation, mass and energy are essentially the same physical entity and can be interchanged.**

In this scenario, the energy is referred to as relativistic kinetic energy, and the mass is referred to as relativistic mass.

The following equation can be used to determine the relativistic mass:

Where,

- The object’s rest mass is denoted by m
- its velocity is denoted by V
- and the speed of light is denoted by c.

So far, we’ve looked at how to find mass without acceleration using a variety of approaches. So, let’s have a look at some solved cases for each.

**Solved Examples of Finding Mass Without Acceleration:**

**Problem 1: On a lake, a boat with a length of 3 metres and a width of 2 metres is floating. When a man gets on a boat, the boat sinks by 1 cm. Then find the mass of man.**

**Solution:** Here we are given:

Length l = 3 m

Width b = 2 m

Height h = 1 cm = 0.01 m

Mass M = ?

The dimensions length, breadth, and height are given here. As a result, volume can be simply found.

V = lbh

∴ V = 3 X 2 X 0.01

∴ V = 0.06 m^{3}

Now, the density of water is 1000 kg/m^{3}.

Thus, mass of person is:

m = ρV

m = 1000 X 0.06

∴ m = 60 kg

Thus, the mass of a man sitting on a boat is 60 kg.

**Problem 2: Calculate the mass of a water sample that has been heated from a starting temperature of 25 ℃ to a final temperature of 100 ℃ after receiving 1200 J of heat energy.**

**Solution:** Here,

Q = 1200 J

T_{i} = 25 ℃

T_{f} = 100 ℃

∴ 𝛥T = T_{f} – T_{i} =100 ℃ -25 ℃ = 75 ℃

And the specific heat of water c = 4.184 J ℃^{-1} g^{-1}

Now, mass of water sample is given by:

∴ m = 3.8 g

Thus, the mass of the water sample, in this case, is 3.8 g.

**Problem 3: If the K.E. is 80 J and the velocity of the object is 7 m/s, determine the mass of the object.**

**Solution:** Here,

K = 80 J

v = 7 m/s

Thus, mass of an object is:

∴ m = 3.26 kg

Thus, an object with a velocity of 7 m/s and a kinetic energy of 80 J has a mass of 3.26 kg.

**Problem 4: With a velocity of 0.85 c, an object is moving through the air. An object’s mass is 11 kg when it is in motion. So, what is that object’s rest mass?**

**Solution:** Here,

Mass m = 11 kg,

Velocity v = 0.85 c,

Velocity of light c = 3 X 10^{8} m/s

Relativistic mass

∴ m_{0} = 5.8 kg

As a result, an object’s rest mass is 5.8 kg.