When a fighter pilot pulls out from the bottom of a powerful dive, his body move

Question

When a fighter pilot pulls out from the bottom of a powerful dive, his body moves at high speed along a segment of an upward bending approximately circular path. However, while his body moves up, his blood tends to move straight ahead (this is due to the law of inertia), and begins to fill the easily expandable veins in his legs. This can deprive his brain of blood, and cause a blackout if the radial acceleration (that is the centripetal acceleration) is 4g or more, and lasts several seconds Could the same thing happen to you on a roller coaster? Imagine that you are on a roller coaster with a big, circular loop. The radius of the loop is 10m, and your speed is 24 m/s. a) Calculate your centripetal acceleration while passing the lowest point of the loop b) Calculate how long it will take you to go through the lowest of the loop (from, say, the 4.5 o'clock position to the 7.5 o'clock position, if that makes sense). Look in sec. 6.1 for the equations to use, along with a bit of thinking Are you at risk of a blackout? (don't just say yes or no, but explain why you said yes or no) c)

Explanation / Answer

Given,

R = 10 m ; v = 24 m/s ;

a)We know that

a = v^2/R

a = 24^2/10 = 57.6 m/s^2

Hence, a = 57.6 m/s^2

b)1/4 circle means the angle subtended = 45 deg = 0.785 rad

0.785 rad = 2 x 3.14 x 0.785 = 355.1 m

t = d/v = 355.1/24 = 14.8 s

Hence, t = 14.8 s

c)in terms of g,

a = 57.6/9.81 g = 5.87 g

This is greater than 4g

Yes we are at the rish of bloackout.

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