Explain about force and potential energy in two dimensions.
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Explain about force and potential energy in two dimensions.
Force is a vector quantity and can be decomposed into its components along chosen directions in either two or three dimensions. A two dimensional force can be perceived as a force in which the component along one of our chosen directions is zero.
Let us choose our two dimensional coordinate axes as the x and y axes.
A force in the xy plane can then be decomposed into its x and y components. Thus the force can be written as,
In the same way, if a force of magnitude acts along the x axis and a force of magnitude acts along the y axis, the the resultant force acts in the direction of . The resultant of all force on an object might act in such a direction in which no actual force is exerted. This is due to the vector nature of force.
Potential energy on the other hand is a scalar quantity. So the total potential energy is the arithmetic sum of the potential energy due to all the forces acting on an object.
Potential energy is related to force in the following manner,
where is the elementary distance moved by the object under the action of force.
Since consists of and in the x and y directions respectively the potential energy can be written as,
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