Using Calculus to find Potential Energy

# Using Calculus to find Potential Energy - exerted by the...

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Using Calculus to find Potential Energy Our calculation of the gravitational potential energy was quite easy. Such an easy calculation will not always be the case, and calculus can be a great help in generating an expression for the potential energy of a conservative system. Recall that work is defined in calculus as W = F(x)dx . Thus the change in potential is simply the negative of this integral. To demonstrate how to calculate potential energy using vector calculus we shall do so for a mass-spring system. Consider a mass on a spring, at equilibrium at x = 0 . Recall that the force

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Unformatted text preview: exerted by the spring, which is a conservative force, is: F s = - kx , where k is the spring constant. Let us also assign an arbitrary value to the potential at the equilibrium point: U(0) = 0 . We can now use our relation between potential and work to find the potential of the system a distance x from the origin: U(x) - 0 = - (- kx)dx Implying that U(x) = kx 2 This equation is true for all x. A calculation of the same form can be completed for any conservative system, and we thus have a universal method for calculating potential energy....
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Using Calculus to find Potential Energy - exerted by the...

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