Question 1. Disk in a gas.
Imagine a disk of radius r moving with constant velocity v (perpendicular to the plane of the disk) in a certain contained volume of gas of density n that is in thermal equilibrium at temperature T . What is the drag force on the disk? The answer does not have to be rigorous. Assume that:
- the gas molecules collide with the disk elastically,
- the speed of the disk is slow compared with the average molecular speed, and
- the disk is large compared to a molecule but small compared to the molecules’ mean free path.
Hint: Finding the leading term in the force to within a numerical factor is suﬃcient.
Question 2. Minimum energies.
Figure 1: Wok on a table (above) and a planetary system (below) -see question 2
a) A wok, the famous Asian round-bottomed cooking vessel, can be modeled as a uniform hollow semi-sphere. Initially, you have a wok on your table with the open side down. What is the minimum energy needed to ﬂip the wok such that in the end it has the open side up? Assume that the wok is made of a metal sheet with surface density σ and that the gravitational acceleration is g.