To train astronauts for the high accelerations and weightlessness experienced du

Question

To train astronauts for the high accelerations and weightlessness experienced during space missions, NASA conducts special flights aboard a modified military refueling plane (the KC135A). A sample trajectory of one of these flights is shown below. To simulate weightlessness the plane turns sharply upward and travels at 45 degrees. Weightlessness begins when the plane is made to rapidly decelerate until the nose points 45 degrees below the horizontal. At the start of this deceleration, all objects not tied down in the plane are essentially "launched' into the air and the plane follows their trajectory so that relative to the plane all objects within experience zero acceleration. Zero-G! 1.8 G 1.8 G-1 A) What decelerations (horizontal and vertical) must the pilot cause to simulate weightlessness. Show that for zero g flight, the path of the trajectory must be parabolic (a second order polynomial). B) Generate a formula prescribing the trajectory of the plane for a simulate acceleration of fg where g is the acceleration due to gravity and f-0. Use Vo to represent the velocity entering the parabola C) If the magnitude of the plane's velocity is 800 ft/s entering the parabola, use your formula to determine the maneuver time for a fall of 12,000 feet Repeat for a simulation of the moon's gravity (1/6 g) andfor a simulation of the gravity on Jupiter (2.4g). D) Why are these called 'simulations?' Are the objects in the plane truly weightless?

Explanation / Answer

a. given nose angle = theta = 45 deg

for weightlessness, vertical acceleration = -g

horizontal acceleration = 0

total acceleration = -g

b. so, let trajectory be defined by y = f(x)

now, for weightlessness, y" = -g

hence

f"(t) = -g

hence

y = -gt^2 + At + B ( where A and B are constants)

now, y' = -2gt + A

y'(x = 0) = Vosin(phi) = A

hence

y = -gt^2 + Vosin(phi)t + B

let y = 0 when t = 0

then

y = -gt^2 + Vosin(phi)t

also, horizontal acceelration is 0

hence

x = Vocos(phi)*t

so, y = -gx^2/Vo^2cos^2(phi) + xsin(phi)/cos(phi) [ which is a parabola]

c. now from the figure

acceelration of 0.8 g is maintained for 20 seconds

then -g for 25 seconds

then -0.8 g for 20 seconds

so total flight time is 65 seconds

d. these simulations are called "Zero Gravity Flight Simulations"

as weight is defined as the force of gravity acting on the body

the person in this flight is not truly weight less as the earth still applies force on the person

its just that another force in that frame of reference adds up the force of gravity making normal force 0 for the person and giving the feeling of weightlessnes

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