Question

A common belief is that a hole in a jet plane can suck a person out. On an episode of a popular TV series, the hosts attempted to determine whether this is possible. According to the hosts' experiment, such an event cannot happen. Did they need to perform the experiment? As a science adviser to the show, the hosts ask you to perform a crude calculation to test the myth. A typical jet plane travels at 532 mph at a cruising altitude of 29500 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 29500 ft above the sea level. Assume the density and pressure of air at 29500 ft are 0.470 kg/m³ and 308 mbar, respectively, but that the interior of the plane remains pressurized to atmospheric pressure, 1 atm. Calculate the fractional difference between this force and the weight man of a typical adult male (185 lb)."

A) Choose the correct response about the need for the experiment:
a) Yes
b) No

Answer 1

The force exerted on a window of a jet plane flying at a cruising altitude of 29500 ft can be calculated using the formula F = P.A, where F is the force exerted, P is the pressure, and A is the area of the window. The force is approximately 1745.041 N. The fractional difference between this force and the weight of a typical adult male is approximately 112.5%.

Step-by-step explanation:

Based on the information given, we can perform a calculation to determine the force exerted on a window of a jet plane flying at a cruising altitude of 29500 ft. To calculate the force, we need to use the formula F = P.A, where F is the force exerted, P is the pressure, and A is the area of the window. First, we need to convert the altitude to meters. 29500 ft is approximately 8992 meters. Next, we can calculate the pressure using the formula P = ρ.g.h, where P is the pressure, ρ is the density of air, g is the acceleration due to gravity, and h is the height. Using the given density of air at 29500 ft (0.470 kg/m³) and the height (8992 m), we can calculate the pressure to be 4293.728 N/m². Finally, we can calculate the force exerted on the window by multiplying the pressure (4293.728 N/m²) by the area of the window (14.0 in × 14.0 in). Converting the area to square meters, we get 0.4057 m², and multiplying it by the pressure gives us a force of approximately 1745.041 N.

To calculate the weight of a typical adult male, which is the weight man mentioned in the question, we can convert the weight from pounds to Newtons using the conversion factor 1 lb = 4.448 N. Given that the weight is 185 lb, we can calculate the weight man to be approximately 821.68 N. To find the fractional difference between the force exerted on the window and the weight man, we can divide the difference between the two values by the weight man and multiply by 100. Subtracting the force exerted on the window (1745.041 N) from the weight man (821.68 N) gives us a difference of approximately 923.361 N. Dividing this difference by the weight man and multiplying by 100 gives us a fractional difference of approximately 112.5%.