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# Kinetic energy

This page covers the following topics:

Kinetic energy is the energy an object has due to its motion and thus its speed. It can be calculated using KE = 1/2 × mass × velocity² and is given in Joules, J.

Although momentum is always conserved in collisions, this is not always the case for the kinetic energy of the objects involved. An elastic collision is one in which kinetic energy is conserved and an inelastic collision is one in which kinetic energy is not conserved and is transformed to other forms of energy. It can be found whether a collision is elastic or inelastic by calculating the kinetic energy of the objects before and after the collision using KE = (1/2)mv².

The photoelectric theory is observed when light falls onto metal surfaces and electrons are ejected immediately. Light is released as packets of energy called photons and the energy of a photo is E = hf = hc/λ, where h = the Planck constant (6.63 × 10⁻³⁴ Js), f = frequency of photon, c = speed of light (3 × 10⁸ m/s) and λ = the wavelength of the photon. A photon collides with an electron; the energy provided by the photon is used to break the bonds holding the electron in the metal and the remaining is converted to kinetic energy as the electron moves away. This is represented by the equation: hf = φ + (1/2)mv²max, where φ = the work function, ie. the minimum energy required for an electron to be released. The work function is directly proportional to the threshold frequency, which is the minimum frequency at which an electron would be released. The kinetic energy in the equation is the maximum, since the electrons found deeper into the metal than the very surface ones use more energy in being released.

Particles in a gas are in constant motion, thus they have kinetic energy, which can be calculated by the basic kinetic energy formula: KE = 1/2 × m × v². Due to the collisions that occur inside the gas, the particles do not all share the same speed, but rather exhibit a distribution of speeds and thus a distribution of kinetic energies. The average kinetic energy of the particles in a sample of gas may be calculated.The root-mean-square speed is the speed for which the kinetic energy would be equal to the average kinetic energy of the sample. By the Kinetic Molecular Theory, the average molecular kinetic energy is directly proportional to absolute temperature, therefore can be calculated using the following formula: KE = 3/2 × k × T, where k is the Boltzmann constant (1.38 × 10⁻²³ JK⁻¹) and T is the temperature in Kelvin. These two equations for the average molecular kinetic energy can be equated to solve problems in which some of the variables are known. The internal energy of a gas is the sum of its kinetic energy and potential energy.

Rotational kinetic energy is a part of the total kinetic enerrgy of an object and it is defined as the kinetic energy possessed by an object due to its rotational motion. The rotational kinetic energy can be calculated using the formula E = 1/2 × I × ω², where I is the moment of inertia of the object and ω is the angular speed. The moment of inertia of an object is a measure of how difficult it is to alter its rotational speed and can be calculated using I = mr², where m is the mass of the object and r is the distance from the axis of rotation. A flywheel is a very heavy wheel that takes a lot of force to spin around and to stop from spinning, meaning that it has a high angular momentum and moment of inertia. So, when the flywheel is spinning at a great speed, it tends to keep spinning, thus resulting in storage of energy in the form of kinetic energy due to its movement. This energy can then be used in another point in the system.

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