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The simplest example is a massive point particle, the Lagrangian for which can be written as the difference between its kinetic and potential energies: (, ˙) =, where the kinetic energy is = ˙ and the potential energy is some function of the position, ().
The kinetic energy is equal to 1/2 the product of the mass and the square of the speed. In formula form: where is the mass and is the speed (magnitude of the velocity) of the body. In SI units, mass is measured in kilograms, speed in metres per second, and the resulting kinetic energy is in joules.
General. Energy is a scalar quantity and the mechanical energy of a system is the sum of the potential energy (which is measured by the position of the parts of the system) and the kinetic energy (which is also called the energy of motion): [1][2] The potential energy, U, depends on the position of an object subjected to gravity or some other ...
The energy entering through A 1 is the sum of the kinetic energy entering, the energy entering in the form of potential gravitational energy of the fluid, the fluid thermodynamic internal energy per unit of mass (ε 1) entering, and the energy entering in the form of mechanical p dV work: = (+ + +) where Ψ = gz is a force potential due to the ...
There are various types of potential energy, each associated with a particular type of force. For example, the work of an elastic force is called elastic potential energy; work of the gravitational force is called gravitational potential energy; work of the Coulomb force is called electric potential energy; work of the strong nuclear force or weak nuclear force acting on the baryon charge is ...
In physics, an elastic collision is an encounter (collision) between two bodies in which the total kinetic energy of the two bodies remains the same. In an ideal, perfectly elastic collision, there is no net conversion of kinetic energy into other forms such as heat, noise, or potential energy. During the collision of small objects, kinetic ...
In classical mechanics, a harmonic oscillator is a system that, when displaced from its equilibrium position, experiences a restoring force F proportional to the displacement x: where k is a positive constant. If F is the only force acting on the system, the system is called a simple harmonic oscillator, and it undergoes simple harmonic motion ...
For the case of a conservative force given by the gradient of some potential energy V, a function of the r k coordinates only, substituting the Lagrangian L = T − V gives ˙ ⏟ + ⏟ + = =, and identifying the derivatives of kinetic energy as the (negative of the) resultant force, and the derivatives of the potential equaling the non ...
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