Questions -

Q1. On July 24, 2018, the high temperature recorded at PHX at approximately 3 pm was 117^oF and the barometric pressure was 29.74 inHg. Assume that the pressue reading is taken in a room where the pressure is equalized with the atmosphere, but the temperature is kept at 20^oC.

(a) What was the air density at PHX at 3 pm on July 24?

(b) The takeoff ground roll distance for an aircraft is approximately given as d_TO = (1.21/g)((W/S)/ρC_{L_max}(T/W))

where W = aircraft weight, S = wing planform area, C_{L_max} = maximum lift coefficient (a characteristic of the wing), and T = maximum engine thrust. The maximum available thrust for a turbofan engine is approximately directly proportional to air density. For an aircraft with a given takeoff weight, how much longer runway would be required on this hot day than would be required on a sea-level standard day (ρ = 1.225 kg/m³). Give this answer as a ratio or a percentage.

Q2. A tank is designed to contain 50 standard cubic feet of air when filled to a pressure of 3000 psig at an ambient temperature of 80^oF. Calculate the interior volume of the tank. One standard cubic foot of air occupies one cubic foot at standard temperature and pressure (T = 59^oF and p = 2116 lb/ft²).

Q3. When a person ice skates, the surface of the ice actually malts beneath the blades, so that there is a thin sheet of water between the surface of the blacks and the surface of the ice.

(a) If a skater of mass (m) 100 kg is moving at a constant velocity (V) of 4 m/s, and the blade has length (l) 30 cm and width (w) 5 mm, what is the frictional force acting on the bottom of the blade if the thickness (h) of the film of water is 0.1 mm?

(b) Suppose the skater suddenly puts both skates on the ice (blades pointed directly forward) and masts to a stop. Neglecting air resistance (drag), how far will the skater travel before coming to a stop? Assume the skater is moving at 4 m/s at the beginning of the coast.