Q.A spring of force constant $k = 200\ \text{N/m}$ is compressed by $0.1\ \text{m}$ from its natural length. Find the elastic potential energy stored in the spring, and the speed with which a block of mass $0.5\ \text{kg}$ placed against the spring leaves it when released, on a frictionless horizontal surface.

Potential energy is energy a body possesses because of its position or configuration, defined for a conservative force so that the work that force does equals the negative of the resulting change in potential energy, $W_{\text{conservative}} = -\Delta U$. For gravity near the Earth's surface this gives $U = mgh$; for an ideal spring obeying Hooke's law, integrating the restoring force $F(x)=kx$ gives the elastic potential energy stored at an extension (or compression) $x$ from natural length, $U(x) = \tfrac12kx^2$. This energ …