A common belief is that a hole in a jet plane can suck a person out. On an episo

Question

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 522 mph at a cruising altitude of 31500 ft. The windows on a jet plane measure 14.0 in × 14.0 in. Calculate the force in lbs exerted on such a window as the plane flies at 31500 ft. above the sea level. (Assume the density and pressure of air at 31500 feet is 0.429 kg/m3 and 276 mbar but the interior of the plane remains pressurized to atmospheric pressure, that is, 1 atm.)

Calculate the fractional difference between this force and the weight wman of a typical adult male (185 lb).

How do you respond?

There is no need to perform the experiment; it is impossible for a person to be sucked out of a plane.

or

My calculation does not prove that such an event cannot happen; you will need to perform the experiment.

Explanation / Answer

here,

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) = 522 mph = 233.36 m/s

sides of the window = 14 in = 0.356 m

pressure at 31500 ft(P_o) = 276 mbar = 27600 Pa

pressure in airplane(P_a) = 1 atm = 101325 Pa

density of the air outside the plane(p) = 0.429 kg/m^3

the pressure difference between the inside and outside of the plane using the following formula

deltaP = 1/2 pv^2+(P_a+P_o)

deltaP = 1/2*(0.429 kg/m^3)*(233.6 m/s)^2+(101325 Pa - 27600 Pa)

deltaP = 73775.11Pa

We can now get the net force on the window by applying the equation:

deltaP = F/A where, F = net force and A = area of the window

F = deltaP*A = 73775.1 Pa * (0.356 m)^2

F = 9349.96 N

Convert Newtons to pound force:

10561 N = 2101.95 lbs of force on the window

the force in lbs is 2101.95 lbs

the fraction ofthi sforce to the weight of man , f = 2101.95/180

f = 11.68

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.