The traditional method of measuring a person\'s body-fat ratio is to weigh them on dry land and then weigh them while submerged in water. The body-fat ratio can be calculated using the difference in these weight measurements. Unfortunately, this method requires that the person become submerged in water, which is a problem for those suffering from hydrophobia (fear of water). As an angel investor, you give money to companies that you think have highly marketable products or services in exchange for partial ownership of the company. A company has mailed a proposal to you seeking money to market a new device for measuring a person\'s body-fat ratio with no need for the person to get wet.

1) Here's how: The person in the figure is standing on a weight scale in a sealed chamber. Initially the chamber is maintained at standard atmospheric pressure. However, the pressure is then lowered and the new weight is noted. Derive an expression for the density of the person in terms of his weight before (w1) and after (w2) the chamber is evacuated. Use ?1 and ?2 for the density of the air before and after the chamber is evacuated.

2) Consider a typical adult weighing 177.0 lb and possessing a density of 807.0 kg/m3. How low will the chamber need to drop in pressure at minimum to measure the person\'s density if the weight scale can only measure to the nearest 0.20 lb? (Assume air is an ideal gas and the chamber is maintained at standard temperature as the air is evacuated. The density of air at sea level is roughly 1.22 kg/m3.) (must be in atm)

3) According to research and marketing, a customer\'s discomfort becomes a problem once the pressure drops below 0.597 atm. Based on this result, would you seriously consider investing in the company? (a or b)

a) No, the product is not likely to be popular and, therefore, not marketable.

b) Yes, the product is safe and could be marketable.