A jet fighter flying at 300 m/s (just below the speed of sound) makes a turn of

Question

A jet fighter flying at 300 m/s (just below the speed of sound) makes a turn of radius 2.05 km What is its centripetal acceleration in gs? Suppose the pilot makes an emergency turn to avoid an approaching missile, subjecting himself to a centripetal acceleration of 10 gs, while flying at 430 m/s (supersonic). What is the radius of his turn? This must be short-lived because fighter planes can only briefly endure such large accelerations without serious damage, and the pilot will soon black out at 10 gs.) A rotating space station is said to create "artificial gravity" -a loosely-defined term used for an acceleration that would be crudely similar to gravity. The outer wall of the rotating space station would become a floor for the astronauts, and centripetal acceleration supplied by the floor would allow astronauts to exercise and maintain muscle and bone strength more naturally than in non-rotating space environments. If the space station is 240 m in diameter, what angular velocity would produce an "artificial gravity" of 9.80 m/s^2 at the rim? Consider the dependence of centripetal acceleration on tangential speed and radius of the circular path. Rpm A 23.0-kg child is riding a playground merry-go-round that is rotating at 45.0 rpm. What centripetal force must she exert to stay on if she is 1.50 m from its center? Consider the relationship between angular speed and centripetal acceleration. How does force relate to acceleration? N What centripetal force does she need to stay on an amusement park merry-go-round that rotates at 3.00 rpm if she is 5.60 m from its center? Compare each force with her weight force from part(a)/weight = force from part(b)/weight =

Explanation / Answer

1. Centripetal accleration a = v^2/r

v is angular velocity

r is radius

a = 300^2/(2050)

a = 44 m/s^2

as g = 9.81 m/s^2

a = 44/9.81 = 4.48 g or 4.5 g

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2. a = v^2/r

but v = r W

so

a = g= r W^2

W^2 = g/r = 9.81/(120)

W = 0.285 rad/s

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3. a = r W^2

here r = 1.5 m

W = 45*2pi/60 = 4.71 rad/s

Force F = mv^2/r or m r W^2

Fc = 23 * 1.5* 4.71^2

Fc = 765.35 N

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b. Fc = 23 * 5.6 * (3*2pi/60)^2

Fc = 12.71 N

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ratio of parta /partb = 765.35/12.71

= 60.21

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