A jet flying 400m/s banks to make a horizontal circular turn. The radius of the

Question

A jet flying 400m/s banks to make a horizontal circular turn. The radius of the turn is 5000m. The mass of the jet is 25000kg. 8 5. What must be the angle of the turn (deg)? a. 93 b. 83 C. 73 d. 63 e. 53 6. What should be the lift force to keep the plane in a circular turn? a. 2.5 10 N b. 4.5*10 N c. 3.3 10 N d. 8.5 10N 7. On a banked race track, the smallest circular path on which cars can move has a radius of 235m. The larger outer circle is 320m. The height of the outer wall is 25m. At what minimum speed can a car move on the racetrack without relying on friction? a. 42m/s b. 33m/s c. 29m/s d. 26m/s e. 15m/s 8. At what angle is the track banked (in deg)? a. 9 b. 16 c. 22 Ld. 25 e. 34 A satellite is in a circular orbit around an unknown planet. The satellite has a speed of 250km/s

Explanation / Answer

(5)

tan theta = v^2/ rg

theta = tan^-1( v^2/ rg)

= tan^-1 ( 400)^2/ 5000(9.8)

=73 degree

(6)

Fx = mv^2/r = 25000( 400)^2/ 5000 = 800000 N

Fy = mg = 25000( 9.8) = 245000 N

lifiting force = sqrt Fx^2 + Fy^2 = sqrt ( 800000)^2 + ( 245000)^2 = 836674.966 N

rounding to two significant digits F = 8.5* 10^5 N

7)

tan theta = h/ r2- r1 = 25/320-235 = 0.294

v_ min = sqrt r1 g tan theta

= sqrt ( 235) (9.8 ( 0.294)

=26 m/s

(8)

tan theta = h/ r2- r1 = 25/320-235 = 0.294

theta = tan^-1 ( 0.294) = 16 degree

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