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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:
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: = =
Lagrange wrote in his Mécanique analytique (published 1788, based on work done around 1755) that mechanics can be viewed as operating in a four-dimensional space— three dimensions of space, and one of time. [4] As early as 1827, Möbius realized that a fourth spatial dimension would allow a three-dimensional form to be rotated onto its ...
The value of work done (VOWD) is a project management technique for measuring and estimating the project cost at a point in time. It is mainly used in project environments of the Petroleum industry and is defined as the value of goods and services progressed, regardless of whether or not they have been paid for or received.
The gravitational potential (V) at a location is the gravitational potential energy (U) at that location per unit mass: =, where m is the mass of the object. Potential energy is equal (in magnitude, but negative) to the work done by the gravitational field moving a body to its given position in space from infinity.
Torque has the dimension of force times distance, symbolically T −2 L 2 M and those fundamental dimensions are the same as that for energy or work. Official SI literature indicates newton-metre, is properly denoted N⋅m, as the unit for torque; although this is dimensionally equivalent to the joule, which is not used for torque.
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Work: W: Transferred energy joule (J) L 2 M T −2: scalar Young's modulus: E: Ratio of stress to strain pascal (Pa = N/m 2) L −1 M T −2: scalar; assumes isotropic linear material spring constant: k: k is the torsional constant (measured in N·m/radian), which characterizes the stiffness of the torsional spring or the resistance to angular ...