What is Conservative force; potential energy?

Definition 13.5 University Physics — Year 1 · Chapter 13 — Work, Energy, and Potential Energy

A force is conservative if its work between two points does not depend on the path followed. Equivalently, there exists a function of position, the potential energy $E_p$ , such that

W_{A\to B} = E_p(A) - E_p(B) = -\Delta E_p , \qquad \delta W = -\dd E_p ,

$E_p$ being defined up to an additive constant (a choice of origin).

Examples

Example 13.11 (Energy lost to friction)

A block slides down a slope of angle $\alpha$ and height $h$ with kinetic friction $\mu_d$ : $W_{\text{nc}} = -\mu_dmg\cos\alpha \times h/\sin\alpha = -\mu_dmgh\cot\alpha$ , so $\tfrac12 mv^2 = mgh(1 - \mu_d\cot\alpha)$ . For $h = 2.0\,\mathrm{m}$ , $\alpha = 30^\circ$ , $\mu_d = 0.20$ : $v = 5.1\,\mathrm{m}/\mathrm{s}$ instead of $6.3\,\mathrm{m}/\mathrm{s}$ ; a third of the potential energy became heat.

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Examples

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