A 10 kg runaway grocery cart runs into a spring with spring constant 250 N/m and compresses it by 60 cm. What was the speed of the cart just before it hit the spring?

How far must you stretch a spring with k = 1000 N/m to store 200 J of energy?

Protons and neutrons (together called nucleons) are held together in the nucleus of an atom by a force called the strong force. At very small separations, the strong force between two nucleons is larger than the repulsive electrical force between two protons—hence its name. But the strong force quickly weakens as the distance between the protons increases. A well-established model for the potential energy of two nucleons interacting via the strong force is

$U=U_0\left[1-e^{-x/x_0}\right]$

where x is the distance between the centers of the two nucleons, x0 is a constant having the value $x_o=2.0\times {10}^{-15}m$, and $U_o=6.0\times {10}^{-11}J.$

Quantum effects are essential for a proper understanding of nucleons, but let us innocently consider two neutrons as if they were small, hard, electrically neutral spheres of mass $1.67\times {10}^{-27}kg$ and diameter $1.0\times {10}^{-15}m$. Suppose you hold two neutrons $5.0\times {10}^{-15}m$ apart, measured between their centers, then release them. What is the speed of each neutron as they crash together? Keep in mind that both neutrons are moving.

A$1000kg$ safe is $2.0m$above a heavy-duty spring when the rope holding the safe breaks. The safe hits the spring and compresses it $50cm$. What is the spring constant of the spring?

a. If the force on a particle at some point in space is zero, must its potential energy also be zero at that point? Explain.

b. If the potential energy of a particle at some point in space is zero, must the force on it also be zero at that point? Explain.

Write a realistic problem for which the energy bar chart shown in FIGURE P10.65 correctly shows the energy at the beginning and end of the problem.