A bottle of mass mb = 0.1 kg and volume V = 0.1 m3 is attached to the bottom of a vertical thin rod of length ` = 1 m and mass mr = 2 kg, that is hinged at the top end. The bottle is full of hydrogen (mO = 1.67x10-27 kg) and is at atmospheric pressure and temperature T0 = 20 0C.
(a) What are the number of moles and the initial rms velocity of the hydrogen?
(b) The temperature of the oxygen in the bottle is now increased to T = 100 0C. What is the new pressure inside the bottle?
(c) At this temperature, the cork at the end of the bottle, mass mc = 0.05 kg, pops off causing the cork to fly off in one direction (assumed to be in the horizontal direction). If the cork was held in by a kinetic friction fk = 100 N, and it takes Δt = 0.01 s for the cork to pop off, what is the speed of the cork as it flies off? (Hint: Use impulse.)
(d) While the cork is flying off, what must be conserved? Be specific. After the cork flies off, the rod/bottle system begins to swing with an angular speed of ω. Determine ω for the rod/bottle system. (You may ignore the mass of the air inside the bottle.)
(e) To what height will the rod/bottle system swing up to? (Hint: Don't forget about the center of mass of the rod.)