Work, Energy, and Power

Which of the following forces is a conservative force?

A block is moved from point A to point B in a gravitational field. If the work done by gravity on the block is $W$, what is the change in potential energy, $\Delta U$, of the block?

A force field is given by $\vec{F}(x, y) = (2x, 3y)$. Is this force conservative? If so, find the potential energy function U(x, y).

The zero point for potential energy is:

A mass $m$ is raised from a height $h_1$ to a height $h_2$ near the Earth's surface. If the zero point for gravitational potential energy is chosen to be at $h_1$, what is the change in potential energy?

A particle is subject to a gravitational force from a much larger mass. Which location would be the most convenient to set the zero point of potential energy?

A ball falls from a height $h$ to the ground. What happens to its potential energy as it falls?

A particle moves from point A to point B under the influence of a conservative force. The force is given by $F(x) = -kx$, where $k$ is a constant. What is the work done by the force in moving the particle from $x = 0$ to $x = x_0$?

A force acting on a particle is given by $F(x) = 3x^2$. Find the potential energy function $U(x)$, assuming $U(0) = 0$.

On a potential energy graph, what does a point of stable equilibrium correspond to?