# Relativistic Kinetic Energy Calculator

You can simply examine an object's kinetic energy by using the Relativistic Kinetic Energy Calculator. The Relativistic Kinetic Energy helps to identify the energy of the body in both rest and motion within short period of time.

### What is Kinetic Energy?

Kinetic energy is defined as the energy generated by an object's motion. A automobile travelling down the highway, for example, has a certain amount of energy; if it meets up with another vehicle, the result will be far more devastating than if it were travelling at 5 mph. The kinetic energy of objects moving at low speeds can be calculated using the following formula:

**KE = 0.5mv ^{2}**

- Where, KE stands for kinetic energy in Joules
- m for the object's mass
- v for its speed

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### Relativistic Kinetic Energy Formula

The kinetic energy must be calculated using Einstein's famous E = mc^{2} equation. This equation describes the total (both potential and kinetic) energy of the body. To find the relativistic kinetic energy, subtract the total energy from the potential energy (calculated before using the potential energy formula):

**KE = E - PE**

In this situation, the potential energy is equal to the rest mass energy:

PE = m_{0}c^{2}

KE = mc^{2} - m_{0}c^{2}

- where, c denotes the speed of light, which is a constant of 299,792,458 m/s
- m
_{0}is the object's rest mass

The rest mass, m_{0} is not the same as the regular mass, m. m_{0} is the mass of an item while it is at rest, that is, when it is not moving. The real mass of an object rises as it moves according to the following formula:

m = m_{0} /(√(1 - v^{2} /c^{2}))

You can derive the relativistic kinetic energy equation by combining all of these equations:

**KE = m _{0}c^{2} * [√(1 - v^{2} /c^{2}) -1]**

- KE is the Kinetic Energy
- m is the mass of the object
- m
_{0}is the rest of mass - v is the speed of the object
- c is the speed of the light

**Note:** When the object's velocity is at least 1% of the speed of light, this relativistic kinetic energy is applicable.

### Relativistic Kinetic Energy Examples

**Question 1:** Calculate the Relativistic KE of an object having mass 25 kgs and velocity 35 m/s?

**Solution:**

Consider the problem, we have

Mass of the object ,m = 25 kg

The speed of the object v = 35 m/s

We know that,Relativistic Kinetic Energy Formula: **KE = m _{0}c^{2}*[√(1-v^{2} /c^{2})-1]**

m_{0} = 25.0 / √(1-35^{2}/299792458^{2}))

Relativistic Kinetic Energy KE = 25.00000000000017 * (299792458^{2}) * √(1-35^{2}/299792458^{2})-1

Therefore, Relativistic Kinetic Energy of an object is 15466.189740488153 J

### FAQs on Relativistic Kinetic Energy Calculator

**1. What are the four different kinds of kinetic energy?**

Radiant, thermal, sound, electrical, and mechanical kinetic energy are the five basic categories.

**2. What is the formula for calculating relativistic kinetic energy?**

The Relativistic kinetic energy is derived by subtracting potential energy from total energy.The following is the equation for relativistic kinetic energy: **KE = m _{0}c^{2}*[√(1 - v^{2} /c^{2}) -1]**

- KE is the Kinetic Energy
- m is the mass of the object
- m
_{0}is the rest of mass - v is the speed of the object
- c is the speed of the light

**Note:** When the object's velocity is at least 1% of the speed of light, this relativistic kinetic energy is applicable.

**3. How to calculate the relativistic KE using the formula?**

The steps for calculating the KE of a moving object are listed below. Check the output by going through these simple steps.

- Get the mass and velocity of the object.
- Calculate the velocity square and multiply the square value by the mass of the object.
- By divide the value by two to get the relativistic kinetic energy.