In special relativity, an object with mass cannot move at the speed of light. As an object approaches the speed of light, its energy and momentum accelerate exponentially. Since the speed of light in a vacuum is constant in all reference frames, relativistic adjustments for energy and mass must be applied.
The conservation of mass and energy are well-established physical principles.
Special relativity must be used in order for these rules to be true in all reference frames. It is worth noting that for objects moving at speeds much below the speed of light, the formulas for relativistic energy and mass provide values that are comparable to their Newtonian counterparts.
The relativistic kinetic energy equation indicates that when an object’s velocity approaches the speed of light, its energy approaches infinity. As a result, accelerating an item over this limit is impossible.
In simple words, when an object approaches the speed of light, its relativistic kinetic energy increases to infinity, indicating that nobody with mass can reach the speed of light. On the other hand, Newtonian kinetic energy (0.5mv2) increases without limit as an object’s speed increases.
The relativistic energy expression includes both rest mass energy and the kinetic energy of motion. The kinetic energy is then given by
The above formula illustrates that when an object’s velocity approaches the speed of light, the work required in accelerating it from rest approaches infinite. As a result, accelerating an item over this limit is impossible.
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Relativistic Kinetic Energy Relation Derivation
The formula for relativistic kinetic energy is E = (γ – 1)mc², where E is the kinetic energy, m is the mass of the object, c is the speed of light, and γ is the Lorentz factor, which takes into account the effects of special relativity.
If a body’s speed is a significant fraction of the speed of light, its kinetic energy must be calculated using relativistic mechanics. In special relativity theory, the expression for linear momentum is altered.
We use the equation for linear momentum using m as an object’s rest mass, v and v as its velocity and speed, and c as the speed of light in a vacuum.
Since Kinetic energy is the integral of momentum with respect to velocity.
By solving the above integral, we get
Eo = mc2
Relativistic Kinetic Energy in Simple Terms
Relativistic kinetic energy is the energy that an object possesses due to its motion, taking into account the effects of special relativity. According to special relativity, as an object moves faster and faster, its mass increases and time slows down for it. As a result, the amount of kinetic energy it possesses also increases.
In simple terms, relativistic kinetic energy can be thought of as the energy that an object has because it is moving very fast. The faster an object moves, the more kinetic energy it has. However, at very high speeds, the object’s mass also increases, which means that even more energy is required to keep it moving at that speed.
The effects of special relativity on kinetic energy are not usually noticeable in everyday situations, they are important in high-energy physics, where particles are accelerated to very high speeds in particle accelerators. Understanding relativistic kinetic energy is also important in the study of astrophysics, where objects such as stars and black holes can move at speeds close to the speed of light.
Daily Life Significance of Relativistic Kinetic Energy
In our daily lives, the effects of relativistic energy are typically not noticeable, as the speeds at which we move are much lower than the speed of light. However, there are a few examples of how relativistic energy can have practical applications in our lives:
- GPS: The Global Positioning System (GPS) relies on special and general relativity to operate accurately. The GPS system uses satellites to triangulate the position of a GPS receiver on the ground. However, because the satellites are moving at high speeds in orbit around the Earth, their clocks tick at a slightly different rate than clocks on the ground. This difference in clock rates is corrected by using the principles of relativity, allowing the GPS system to operate with high accuracy.
- Medical Imaging: In medical imaging, such as in PET (Positron Emission Tomography) scans, the decay of radioactive isotopes produces high-energy particles that move at relativistic speeds. These particles can be detected and used to create images of the body, helping doctors to diagnose and treat medical conditions.
- Particle Accelerators: Particle accelerators, such as the Large Hadron Collider (LHC) in Switzerland, use the principles of relativistic energy to accelerate particles to very high speeds, approaching the speed of light. These particles then collided with each other, allowing physicists to study the fundamental properties of matter and the universe.
What is Kinetic Energy?
The K.E. of a moving object is half of the product of its mass and the square of its velocity.
The greater the moving body’s speed and mass, the greater its K.E.
The term “kinetic” is derived from the Greek word “kinesis,” which means “motion.”
Kinetic energy is always positive since an object’s mass can never be zero and the square of velocity is positive. Furthermore, kinetic energy is the energy held by a body as a result of its motion.
Units of Kinetic Energy
- Joules (MKS system).
- Erg (CGS system, 1 erg = 10-7Joules).
- Electron volt (atomic/subatomic scale).
Kinetic Energy Types
Translation K.E
Translational K.E= (1/2)(mass)(velocity)2.
Mass is the amount of matter contained within an object and velocity is the speed of a moving object in a particular direction.
Rotational K.E
Rotational K.E = (1/2)(Moment of Inertia)(angular velocity)2.
Moment of inertia is the angular mass or rotational inertia of a rigid body and angular velocity is a vector measure of rotation rate.
Kinetic Energy Definitions in Simple Words
- Kinetic energy is defined as the energy possessed by a body by virtue of its motion.
- The translational K.E of a body is equal to one-half the product of its mass, m, and the square of its velocity, v, or (1/2)mv2.
- The rotational K.E of a body is equal to one-half the product of its moment of Inertia, I, and the square of its angular velocity, ω, or (1/2)Iω2.
What is Work?
Work is a force that acts in the direction of motion on an item.
It is the product of force (F) and displacement (S) in the force’s direction.
It is a scalar quantity with the unit of Joule.
Work done equals force multiplied by displacement.
What is 1 Joule?
1 Joule is the amount of work done when a force of 1 Newton is applied over a distance of 1 meter.
Joule = N.M
Joule= kg*m2/sec2
Derivation of Equation of Kinetic Energy
Consider a body with mass “m” and velocity “v” travelling over a rough surface.
Due to frictional force, the body comes to a stop after travelling a distance “S.”
As long as the body has K.E. and is capable of doing work against opposing force F, it will continue to do so until it stops and loses all of its K.E. Kinetic energy equals the work done by the body in this situation.
The initial velocity (vi) of the body is v and the final velocity (vf) is zero.
K.E=Work = FS
F=ma and a= -F/m (acceleration is negative as motion is opposed)
2aS =vf2-vi2 (Newton’s law of motion)
2(-F/m)S= (0)2-(v)2
-2FS/m=-v2
FS =(1/2)(m)v2 = K.E
Quick Links
- Difference Between Kinetic and Potential Energy.
- Instantaneous Velocity| Easy Key Points
- Mechanical Energy| 7 Easy Daily Life Examples
- Room Temperature| Comfortable Temperature
- Kinetic energy formula
- Can force be negative?
- Velocity time graph
Summary
- The relativistic kinetic energy equation indicates that when an object’s velocity approaches the speed of light, its energy approaches infinity.
- The motion must occur at nearly the speed of light for relativistic effects to be evident.
- Because the speed of light exceeds a billion kilometres per hour, such motion is well beyond our comprehension.
More Links
Momentum Equation| Definition and Examples
Velocity Formula & Definition
Linear Motion or Rectilinear Motion
Can Momentum be Negative?
Quarks in Physics
Frequently Asked Questions (FAQs)
1. What is a state function?
A state function is a property that depends on the state of a system and is independent of the path taken to get it. Pressure and temperature, for example, are state functions.
2. What is air?
Air is a homogeneous mixture of different gasses. The air in the atmosphere is composed of nitrogen, oxygen (which is required for animal and human life), carbon dioxide, water vapour, and trace amounts of other elements (argon, neon, etc.). At higher elevations, air contains ozone, helium, and hydrogen.
3. What is Angular displacement?
The shortest angle between the starting and end locations of an item travelling in a circular motion around a fixed point is defined as angular displacement. Because it is a vector quantity, angular displacement has a magnitude and a direction associated with it.
4. Linear motion?
Linear motion (also known as “rectilinear motion”) is a one-dimensional motion along a straight line that can be represented mathematically with only one spatial dimension. Linear motion is defined as movement along a straight path, whereas nonlinear motion is any movement that is not in a straight line.
5. Uniform circular motion?
Uniform circular motion is described as the constant-speed movement of an item in a circle. An object in uniform circular motion moves at a constant pace. Despite this, it is speeding as a result of its shift in course.
Author
Umair Javed
Umair has been working at Whatsinsight since 2020 as a content writer.
He has a Masters degree in Materials Science.