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When a force is applied over a certain distance, that force does mechanical work, $W$. If the force is constant $F$ and the object it is exerted on is moved by a distance $\Delta x$, then $W=F\Delta x$.
The measurement of work and energy with the same unit reinforces the idea that work and energy are related and can be converted into one another. 1.0 J = 1.0 N∙m, the units of force multiplied by distance. 1.0 N = 1.0 kg∙m/s 2, so 1.0 J = 1.0 kg∙m 2 /s 2.
The work done, E w by a force, F moving through a distance, d is given by: \ ( {E_w} = Fd\) Units are joules, newtons and metres. If the force is overcoming frictional forces, all or some...
In equation form, the translational kinetic energy, \[KE = \dfrac{1}{2}mv^2,\] is the energy associated with translational motion. Kinetic energy is a form of energy associated with the motion of a particle, single body, or system of objects moving together.
If the force is measured in Newtons (N) and distance is in meters (m), then work is measured in Joules (J). If an object moves along a straight line from x = a to x = b under the influence of a variable force F (x), the work W done by the force is given by the definite integral.
The rate of doing work is equal to the rate of using energy since the force transfers one unit of energy when it does one unit of work. A horsepower is equal to 550 ft lb/s, and a kilowatt is 1000 watts.
In a typical dynamical system, the force F is composed of two terms: an external force F E and an internal force F I. The external force results from an external actor applying an arbitrary force–of his choice– to the system. The external force does work and changes the energy of the system at the whim of the actor.
