Problems

Problem 1 Lander is enjoying a nice BBQ with his friends. Trying to impress his friends he claims to be able to thoroughly cook a potato in fifteen minutes. Amazingly he is able to keep the grill at a constant temperature of 450° F. One of his friends who happens to be a finicky eater enjoys his potatoes cooked such that there is only a 15° F difference between the skin and the potatoes center. Will his friend be happy, and will the potato be soft enough to eat?

Problem 2 When comparing our results with the Gurney-Lurie charts, the potatoes were modeled as infinite perfect cylinders. Try modeling the potatoes first as perfect spheres and then as finite cylinders with an approximate length of 5 times the radius. Compare your results with the ones obtained. How big a difference is there? Which one of the results seems the most plausible? Was it a justified simplification to model the potatoes as infinite cylinders?

Problem 3 When Matt's family had baked potatoes for dinner a couple of days ago a potato took almost half an hour at 450° F to cook all the way through. The potato had approximately the same size as the ones used when performing the experiment and should according to the results be done after 15 to 20 minutes. Try to come up with a plausible explanation for the time deviation.