Part 1. A common belief is that a hole in a jet plane can suck a person out. On
ID: 1471431 • Letter: P
Question
Part 1. A common belief is that a hole in a jet plane can suck a person out. On an episode of the popular TV series Myth Busters, hosts Adam and Jaime attempted to determine whether this is possible. According to the hosts' experiment, such an event cannot happen (that is, they "busted" the myth). But did they need to perform the experiment? As a science advisor to the show, Adam and Jaime ask you to perform a crude calculation to test the myth. A typical jet plane travels at 552 mph at a cruising altitude of 25500 ft. The windows on a jet plane measure 14.0 in × 14.0 in. Calculate the force exerted on such a window as the plane flies at 25500 ft. above the sea level. (Assume the density and pressure of air at 25500 feet is 0.562 kg/m3 and 382 mbar but the interior of the plane remains pressurized to atmospheric pressure, that is, 1 atm.)
Part 2. Calculate the fractional difference between this force and the weight wman of a typical adult male (185 lb).
Part 3.How would you respond to Adam and Jaime?
Part 3 Choices:
A.There is no need to perform the experiment; it is impossible for a person to be sucked out of a plane.
B.My calculation does not prove that such an event cannot happen; you will need to perform the experiment.
Explanation / Answer
First thing to do is convert all given info into common units throughout and list the known values. I will convert to SI but come back to lbs for the answer.
velocity of the plane(v) = 542 mph = 242 m/s
sides of the window = 14 in = 0.356 m
pressure at 28500ft(P_o) = 324 mbar = 32400 Pa
pressure in airplane(P_a) = 1 atm = 101325 Pa
density of the air outside the plane() = 0.492 kg/m^3
Now we need to calculate the pressure difference between the inside and outside of the plane using the following formula:
P = 1/2 v^2+(P_a+P_o)
P = 1/2*(0.492 kg/m^3)*(242 m/s)^2+(101325 Pa - 32400 Pa)
P = 83331 Pa
We can now get the net force on the window by applying the equation:
P = F/A where, F = net force and A = area of the window
F = P*A = 83331 Pa * (0.356 m)^2
F = 10561 N
Convert Newtons to pound force:
10561 N = 2374 lbs of force on the window
Part b. Man - 183.91kg ( 1lbs = .45kg)
So w = 1839.1 N
The different is = 10561-1839.1
=8,721.9 N
Part c
B.My calculation does not prove that such an event cannot happen; you will need to perform the experiment.