A plastic tube has an inner diameter of d = 13.4 mm, and it can withstand a gauge pressure of Pmax = 324 kPa before bursting. A particular section this tube is sealed off at one end but open at the other. The tube is placed vertically on a table with its open end facing upward, and a rubber stopper (m = 350 g) is placed inside. The rubber has been lubricated, so friction with the inner walls of the tube is negligible. Suppose that you slowly push the rubber stopper deeper and deeper into the tube until the tube is just about to burst. What is the largest downward force F you can apply to the stopper without bursting the tube? The symbolic answer should be stated in terms of d, Pmax, Patm, m, and g, though not all of these quantities may be needed. Draw a free body diagram of this scenario.

A plastic tube has an inner diameter of d = 13.4 mm, and it can withstand a gauge pressure of Pmax = 324 kPa before bursting. A particular section this tube is sealed off at one end but open at the other. The tube is placed vertically on a table with its open end facing upward, and a rubber stopper (m = 350 g) is placed inside. The rubber has been lubricated, so friction with the inner walls of the tube is negligible. Suppose that you slowly push the rubber stopper deeper and deeper into the tube until the tube is just about to burst. What is the largest downward force F you can apply to the stopper without bursting the tube? The symbolic answer should be stated in terms of d, Pmax, Patm, m, and g, though not all of these quantities may be needed. Draw a free body diagram of this scenario.