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Energy can broadly be classified into kinetic, due to a body's motion, and potential, due to a body's position relative to others. Thermal energy, the energy carried by heat flow, is a type of kinetic energy not associated with the macroscopic motion of objects but instead with the movements of the atoms and molecules of which they are made.
The left side is the work dissipated into the heat bath, and the right side could be interpreted as the fluctuation in the work due to thermal noise. Consider dragging an overdamped particle in a viscous fluid with temperature T {\displaystyle T} at constant force f {\displaystyle f} for a time t {\displaystyle t} .
The work done is given by the dot product of the two vectors, where the result is a scalar. When the force F is constant and the angle θ between the force and the displacement s is also constant, then the work done is given by: = If the force is variable, then work is given by the line integral:
Classical mechanics is the branch of physics used to describe the motion of macroscopic objects. [1] It is the most familiar of the theories of physics. The concepts it covers, such as mass, acceleration, and force, are commonly used and known. [2] The subject is based upon a three-dimensional Euclidean space with fixed axes, called a frame of ...
In physics, Hooke's law is an empirical law which states that the force (F) needed to extend or compress a spring by some distance (x) scales linearly with respect to that distance—that is, F s = kx, where k is a constant factor characteristic of the spring (i.e., its stiffness), and x is small compared to the total possible deformation of the spring.
The kinetic energy of an object is equal to the work, force times displacement , needed to achieve its stated velocity. Having gained this energy during its acceleration, the mass maintains this kinetic energy unless its speed changes. The same amount of work is done by the object when decelerating from its current speed to a state of rest. [2]
The potential energy of an object can be defined as the object's ability to do work and is increased as the object is moved in the opposite direction of the direction of the force. [ nb 1 ] [ 1 ] If F represents the conservative force and x the position, the potential energy of the force between the two positions x 1 and x 2 is defined as the ...
In mechanics, a constant of motion is a physical quantity conserved throughout the motion, imposing in effect a constraint on the motion. However, it is a mathematical constraint , the natural consequence of the equations of motion , rather than a physical constraint (which would require extra constraint forces ).