8.2 Conservative and Non-Conservative Forces

A two-dimensional, conservative force is zero on the x- and y-axes, and satisfies the condition $\left(d F_{x} / d y\right) = \left(d F_{y} / d x\right) = \left(4 \text{N}/\text{m}^{3}\right) x y$. What is the magnitude of the force at the point $x = y = 1 \text{m}?$

Find the forces on the particle in the example when its kinetic energy is 1.0 J at $x = 0 .$

What is the physical meaning of a non-conservative force?

An external force acts on a particle during a trip from one point to another and back to that same point. This particle is only affected by conservative forces. Does this particle’s kinetic energy and potential energy change as a result of this trip?

A force $F \left(x\right) = \left(−5.0 x^{2} + 7.0 x\right) \text{N}$ acts on a particle. How much work does the force do on the particle as it moves from $x = 2.0 \text{m}$ to $x = 5.0 \text{m}?$

The potential energy function for either one of the two atoms in a diatomic molecule is often approximated by $U \left(x\right) = a / x^{12} - b / x^{6}$ where x is the distance between the atoms. (a) At what distance of separation does the potential energy have a local minimum (not at $x = \infty \left.\right) ?$ (b) What is the force on an atom at this separation? (c) How does the force vary with the separation distance?

A particle of mass $2.0 \text{kg}$ moves under the influence of the force $F \left(x\right) = \left(−5 x^{2} + 7 x\right) \text{N} .$ If its speed at $x = −4.0 \text{m}$ is $v = 20.0 \text{m}/\text{s},$ what is its speed at $x = 4.0 \text{m} ?$