Kinetic Energy Calculator
Energy is the capacity to do work or to produce heat. Kinetic energy is the energy due to motion. Potential energy is energy stored in matter. The joule (J) is the SI unit of energy and equals (kg? m2 s2) (kg ? . Units of Kinetic Energy The SI unit of kinetic energy is Joule which is equal to 1 kg.m 2.s The CGS unit of kinetic energy is erg.
Easily calculate the kinetic energy of an object in motion. Input supports metric and imperial measurement units. The calculator can also be used to solve for mass or velocity.
This kinetic energy calculator is useful for estimating the energy a body acquires through movement of any kind. For example, it can be used to calculate the kinetic energy of a person, vehicle car, truck, trainplane, football, as well as for falling bodies that crash into the ground. It can also be used to calculate the energy of different kinds of projectiles.
To calculate the kinetic energy you need to how to make bracelets with pictures only the body's mass and velocity. The kinetic energy calculator can also be used to solve for any of the other values: mass and velocity. The respective input fields will be hidden or displayed upon selecting what you want to use the calculator for.
When solving for mass you need to know velocity and kinetic energy, while when solving for velocity you need to know the object's mass and kinetic energy. When the output of the tool is mass or velocity it is in both standard metric units and imperial ones, with the units automatically being adjusted depending on how big or small the resulting value is.
The formula for kinetic energy KE expressed in terms of the body's velocity speed v and its mass m is the first equation below:. This formula is valid in classical mechanics and for non-rotating rigid point objects the object's mass is assumed to exist at a single point. If the object's speed is larger than a couple of percentages of the speed of light in vacuum it is a poor approximation according to relativistic mechanics.
This equation is used in coding this online kinetic energy calculator. Example 1: A car weighs kg 2. What is the car's kinetic energy? Example 2: A ball which weighs grams has a kinetic energy of J.
What is the velocity of the ball? First what to serve with spanish rice convert grams to 0. What is the plane's mass? Of course, while using our calculator you would not need to perform these unit conversions, as they are handled for you on the fly.
When solving for the object's mass we output both tonne metric ton and ton short ton. The first one is used by all countries in the world and is defined to be equal to kg by the international body of standardization.
The ton is currently only used in the United States and is equal to pounds lbs. Taylor and Ambler Thompson, p. Bureau international des poids et mesures pp. ISBN If you'd like to cite this online calculator resource and information as provided on the page, you can use the following citation: Georgiev G.
Calculators Converters Randomizers Articles Search. Kinetic Energy Calculator Easily calculate the kinetic energy of an object in motion.
Kinetic Energy. Kinetic energy. Body mass. Share calculator:. Embed this tool! Using the kinetic energy calculator This kinetic energy calculator is useful for estimating the energy a body acquires through movement of any kind.
Kinetic energy formulas The formula for kinetic energy KE expressed in terms of the body's velocity speed v and its mass m is the first equation below: whereas the second and third ones are the transformed equations for solving for mass or velocity. Kinetic energy calculation examples Example 1: A car weighs kg 2. Ton vs tonne, tons vs tonnes When solving for the object's mass we output both tonne metric ton and ton short ton.
Potential Energy and Kinetic Energy
The unit of energy in the metre - kilogram - second system is the joule. A two-kilogram mass (something weighing pounds on Earth) moving at a speed of one metre per second (slightly more than two miles per hour) has a kinetic energy of one joule. Energy has the same units as work and work is force times distance. One Joule is one Newton of force acting through one meter - Nm or Joule in SI-units. The Imperial units are foot-pound. 1 ft lb = N m (Joule). Dec 14, · Kinetic energy units The units of kinetic energy are precisely the same as for any other type of energy. The most popular and commonly used kinetic energy units are: Joule (J), equivalent to kg * m? / s? - SI unit.
In physics , the kinetic energy of an object is the energy that it possesses due to its motion. Having gained this energy during its acceleration , the body maintains this kinetic energy unless its speed changes.
The same amount of work is done by the body when decelerating from its current speed to a state of rest. In relativistic mechanics , this is a good approximation only when v is much less than the speed of light.
The standard unit of kinetic energy is the joule , while the English unit of kinetic energy is the foot-pound. The dichotomy between kinetic energy and potential energy can be traced back to Aristotle 's concepts of actuality and potentiality. Willem 's Gravesande of the Netherlands provided experimental evidence of this relationship. By dropping weights from different heights into a block of clay, Willem 's Gravesande determined that their penetration depth was proportional to the square of their impact speed.
The terms kinetic energy and work in their present scientific meanings date back to the midth century. Early understandings of these ideas can be attributed to Gaspard-Gustave Coriolis , who in published the paper titled Du Calcul de l'Effet des Machines outlining the mathematics of kinetic energy. William Thomson , later Lord Kelvin, is given the credit for coining the term "kinetic energy" c.
Energy occurs in many forms, including chemical energy , thermal energy , electromagnetic radiation , gravitational energy , electric energy , elastic energy , nuclear energy , and rest energy.
These can be categorized in two main classes: potential energy and kinetic energy. Kinetic energy is the movement energy of an object. Kinetic energy can be transferred between objects and transformed into other kinds of energy. Kinetic energy may be best understood by examples that demonstrate how it is transformed to and from other forms of energy.
For example, a cyclist uses chemical energy provided by food to accelerate a bicycle to a chosen speed. On a level surface, this speed can be maintained without further work, except to overcome air resistance and friction.
The chemical energy has been converted into kinetic energy, the energy of motion, but the process is not completely efficient and produces heat within the cyclist. The kinetic energy in the moving cyclist and the bicycle can be converted to other forms. For example, the cyclist could encounter a hill just high enough to coast up, so that the bicycle comes to a complete halt at the top. The kinetic energy has now largely been converted to gravitational potential energy that can be released by freewheeling down the other side of the hill.
Since the bicycle lost some of its energy to friction, it never regains all of its speed without additional pedaling. The energy is not destroyed; it has only been converted to another form by friction. Alternatively, the cyclist could connect a dynamo to one of the wheels and generate some electrical energy on the descent.
The bicycle would be traveling slower at the bottom of the hill than without the generator because some of the energy has been diverted into electrical energy. Another possibility would be for the cyclist to apply the brakes, in which case the kinetic energy would be dissipated through friction as heat. Like any physical quantity that is a function of velocity, the kinetic energy of an object depends on the relationship between the object and the observer's frame of reference.
Thus, the kinetic energy of an object is not invariant. Spacecraft use chemical energy to launch and gain considerable kinetic energy to reach orbital velocity. In an entirely circular orbit, this kinetic energy remains constant because there is almost no friction in near-earth space.
However, it becomes apparent at re-entry when some of the kinetic energy is converted to heat. If the orbit is elliptical or hyperbolic , then throughout the orbit kinetic and potential energy are exchanged; kinetic energy is greatest and potential energy lowest at closest approach to the earth or other massive body, while potential energy is greatest and kinetic energy the lowest at maximum distance. Without loss or gain, however, the sum of the kinetic and potential energy remains constant.
Kinetic energy can be passed from one object to another. In the game of billiards , the player imposes kinetic energy on the cue ball by striking it with the cue stick. If the cue ball collides with another ball, it slows down dramatically, and the ball it hit accelerates its speed as the kinetic energy is passed on to it.
Collisions in billiards are effectively elastic collisions , in which kinetic energy is preserved. In inelastic collisions , kinetic energy is dissipated in various forms of energy, such as heat, sound, binding energy breaking bound structures. Flywheels have been developed as a method of energy storage.
This illustrates that kinetic energy is also stored in rotational motion. Several mathematical descriptions of kinetic energy exist that describe it in the appropriate physical situation. However, if the speed of the object is comparable to the speed of light, relativistic effects become significant and the relativistic formula is used. If the object is on the atomic or sub-atomic scale , quantum mechanical effects are significant, and a quantum mechanical model must be employed.
In classical mechanics , the kinetic energy of a point object an object so small that its mass can be assumed to exist at one point , or a non-rotating rigid body depends on the mass of the body as well as its speed. In formula form:. In SI units, mass is measured in kilograms , speed in metres per second , and the resulting kinetic energy is in joules.
When a person throws a ball, the person does work on it to give it speed as it leaves the hand. The moving ball can then hit something and push it, doing work on what it hits. Since the kinetic energy increases with the square of the speed, an object doubling its speed has four times as much kinetic energy. For example, a car traveling twice as fast as another requires four times as much distance to stop, assuming a constant braking force.
As a consequence of this quadrupling, it takes four times the work to double the speed. The kinetic energy of an object is related to its momentum by the equation:. The kinetic energy of any entity depends on the reference frame in which it is measured. However, the total energy of an isolated system, i. Thus, the chemical energy converted to kinetic energy by a rocket engine is divided differently between the rocket ship and its exhaust stream depending upon the chosen reference frame.
This is called the Oberth effect. But the total energy of the system, including kinetic energy, fuel chemical energy, heat, etc. Different observers moving with different reference frames would however disagree on the value of this conserved energy. The kinetic energy of such systems depends on the choice of reference frame: the reference frame that gives the minimum value of that energy is the center of momentum frame, i. This minimum kinetic energy contributes to the invariant mass of the system as a whole.
The work done in accelerating a particle with mass m during the infinitesimal time interval dt is given by the dot product of force F and the infinitesimal displacement dx. However, also see the special relativistic derivation below. Since this is a total differential that is, it only depends on the final state, not how the particle got there , we can integrate it and call the result kinetic energy.
Assuming the object was at rest at time 0, we integrate from time 0 to time t because the work done by the force to bring the object from rest to velocity v is equal to the work necessary to do the reverse:.
This equation states that the kinetic energy E k is equal to the integral of the dot product of the velocity v of a body and the infinitesimal change of the body's momentum p. It is assumed that the body starts with no kinetic energy when it is at rest motionless.
A system of bodies may have internal kinetic energy due to the relative motion of the bodies in the system. For example, in the Solar System the planets and planetoids are orbiting the Sun. In a tank of gas, the molecules are moving in all directions. The kinetic energy of the system is the sum of the kinetic energies of the bodies it contains. A macroscopic body that is stationary i. These all contribute to the body's mass, as provided by the special theory of relativity.
When discussing movements of a macroscopic body, the kinetic energy referred to is usually that of the macroscopic movement only. However, all internal energies of all types contribute to a body's mass, inertia, and total energy. In fluid dynamics , the kinetic energy per unit volume at each point in an incompressible fluid flow field is called the dynamic pressure at that point.
The speed, and thus the kinetic energy of a single object is frame-dependent relative : it can take any non-negative value, by choosing a suitable inertial frame of reference.
For example, a bullet passing an observer has kinetic energy in the reference frame of this observer. The same bullet is stationary to an observer moving with the same velocity as the bullet, and so has zero kinetic energy. In any other case, the total kinetic energy has a non-zero minimum, as no inertial reference frame can be chosen in which all the objects are stationary.
This minimum kinetic energy contributes to the system's invariant mass , which is independent of the reference frame. The total kinetic energy of a system depends on the inertial frame of reference : it is the sum of the total kinetic energy in a center of momentum frame and the kinetic energy the total mass would have if it were concentrated in the center of mass.
Substituting, we get: . Thus the kinetic energy of a system is lowest to center of momentum reference frames, i. In any different frame of reference, there is additional kinetic energy corresponding to the total mass moving at the speed of the center of mass.
The kinetic energy of the system in the center of momentum frame is a quantity that is invariant all observers see it to be the same. It sometimes is convenient to split the total kinetic energy of a body into the sum of the body's center-of-mass translational kinetic energy and the energy of rotation around the center of mass rotational energy :. Thus the kinetic energy of a tennis ball in flight is the kinetic energy due to its rotation, plus the kinetic energy due to its translation.
If a body's speed is a significant fraction of the speed of light , it is necessary to use relativistic mechanics to calculate its kinetic energy. In special relativity theory, the expression for linear momentum is modified. Integrating by parts yields. This formula shows that the work expended accelerating an object from rest approaches infinity as the velocity approaches the speed of light.
Thus it is impossible to accelerate an object across this boundary. The mathematical by-product of this calculation is the mass-energy equivalence formula—the body at rest must have energy content. This is done by binomial approximation or by taking the first two terms of the Taylor expansion for the reciprocal square root:. When objects move at a speed much slower than light e.
The next term in the Taylor series approximation. This can also be expanded as a Taylor series , the first term of which is the simple expression from Newtonian mechanics: . This suggests that the formulae for energy and momentum are not special and axiomatic, but concepts emerging from the equivalence of mass and energy and the principles of relativity.
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