5. Work and Energy: An elastic ball of radius r can be crudely approximated by a set of 5 equally spaced points, connected to their nearest neighbors by identical springs with spring constant k, arranged to form an octahedron. Consider squishing the 95339311 from its top, splaying the sides outward to a width w. a. Solve for the new height of the We\" after being squished, in terms of its width w and rest radius r. Show your work. h: b. By what percentage will the diameter have increased when the Wis completely squished at? Show your work. %lncreas'e = c. Show that the elastic potential energy stored in the W11 by squishing it from its top is given by the m k Us 2 W (W4 6rw3 + 221r2w2 20r3w + 123\"\") d. As the ball has mass, it will weigh down on itself and squish outjust sitting on a table. Explain how you could solve for how much the ball squishes in this case. Do not actually do this calculation- it's quite difcult. (Hint: look at the gravitational potential before and after squishing)