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For convenience, consider contact with the spring occurs at t = 0, then the integral of the product of the distance x and the x-velocity, xv x dt, over time t is 1 / 2 x 2. The work is the product of the distance times the spring force, which is also dependent on distance; hence the x 2 result.
There are several ways of doing mechanical work, each in some way related to a force acting through a distance. [34] In basic mechanics, the work done by a constant force F on a body displaced a distance s in the direction of the force is given by = If the force is not constant, the work done is obtained by integrating the differential amount ...
Power is the rate with respect to time at which work is done; it is the time derivative of work: =, where P is power, W is work, and t is time.. We will now show that the mechanical power generated by a force F on a body moving at the velocity v can be expressed as the product: = =
The length of this vector gives the straight-line distance from x to y. Displacement has the dimensions of length. ... Force, energy, work. Force is a vector with ...
Action at a distance also acts as a model explaining physical phenomena even in the presence of other models. Again in the case of gravity, hypothesizing an instantaneous force between masses allows the return time of comets to be predicted as well as predicting the existence of previously unknown planets, like Neptune.
The work done by a conservative force is equal to the negative of change in potential energy during that process. For a proof, imagine two paths 1 and 2, both going from point A to point B. The variation of energy for the particle, taking path 1 from A to B and then path 2 backwards from B to A, is 0; thus, the work is the same in path 1 and 2 ...
Work is defined as a force applied over a distance. The SI unit of work is the Joule, equivalent to a force of 1 Newton exerted along a distance of 1 metre. In gas flow across a constant section this equates to a volume flowing against a pressure: [note 1] Work = Pressure x Volume and Power = Work / time
If a 100 kg object is dragged for 10 m along a surface with the coefficient of friction μ = 0.5, the normal force is 981 N and the work done (required energy) is (work=force x distance) 981 × 0.5 × 10 = 4905 joules. Now give the object 4 wheels.