You use a spring to impart initial speed to a small ball that you will launch upward. The spring does not obey Hooke's Law perfectly, it follows

Ass P PY P X BU Bos S Ch & Ne GET C (9) Col 83 2.5 Sea & C bwckkh6a9 1 / 2 100% + Academic Conduct and U.S. copyright law. (9) [10 points] Consider a 1-dimensional potential given by the following. Because U(x) - 0 as x - co, it makes sense to define U (co) - 0. U (x) = _ A a 3 2a2 x 2 (a) What is the force equation associated with this potential energy function? Provide a symbolic expression. (b) Graph the potential energy function. A computer software generated graph is preferable, a very neatly hand drawn graph on graph paper is acceptable. Take a - 1.0 m and A = 64.0 J. Note that the potential energy blows up at x - 0 so you must restrict the range to see the function nicely. Try graphing the function from x - 0 to 16 m and U (x) from 0 to -4 J, or thereabouts. Label your axes. (c) Find locations of equilibrium and identify if they are stable or unstable. (d) Is this a conservative force? How do you know? (e) Place a particle of mass m = 0.2 kg at rest at the unstable equilibrium point closest to the origin. Displace slightly it in the direction of nearest stable equilibrium point. When it reaches the stable equilibrium point, what is the speed of the particle? MacBook Pro