The maximum force a pilot can stand is about seven times his weight. What is the

Question

The maximum force a pilot can stand is about seven times his weight. What is the minimum
radius of curvature that a jet plane's pilot, pulling out of a vertical dive, can tolerate at a speed
of 250 m/s?
A) 4.25 m
B) 3.64 m
C) 1060 m
D) 911 m
Answer: C

13) A car traveling 20 m/s rounds an 80-m radius horizontal curve with the tires on the verge of
slipping. How fast can this car round a second curve of radius 320 m? (Assume the same
coefficient of friction between the car's tires and each road surface.)
A) 20 m/s
B) 40 m/s
C) 80 m/s
D) 160 m/s
Answer: B

14) A car is negotiating a flat curve of radius 50 m with a speed of 20 m/s. The centripetal force
provided by friction is 1.2 ? 104 N. What is the mass of the car?
A) 500 kg
B) 1000 kg
C) 1500 kg
D) 2000 kg
Answer: C

15) A car goes around a flat curve of radius 50 m at a speed of 14 m/s. What must be the
minimum coefficient of friction between the tires and the road for the car to make the turn?
A) 0.20
B) 0.40
C) 0.60
D) 0.80
Answer: B

16) A car is moving with a constant speed v around a level curve. The coefficient of friction
between the tires and the road is 0.40. What is the minimum radius of the curve if the car is to
stay on the road?
A) 0.40v2/g
B) v2/g
C) 2.5v2/g
D) 2v2/g
Answer: C

17) What minimum banking angle is required for an Olympic bobsled to negotiate a 100-m radius
turn at 35 m/s without skidding? (Ignore friction.)
A) 31e
B) 41e
C) 51e
D) 61e
Answer: C

18) A horizontal curve on a bobsled run is banked at a 45e angle. When a bobsled rounds this
curve at the curve's safe speed (no friction needed to stay on the run), what is its centripetal
acceleration?
A) 1.0 g
B) 2.0 g
C) 0.5 g
D) none of the above
Answer: A

Explanation / Answer

12) When he pulls out of the vertical dive, force acting on him = mV2/r + mg = 7mg (maximum)

=> r = V2/6g = 1060 m

13) When moving in a circle, forces acting on the car are mV2/r (centrifugal force) and the firctional force (mg)

Therefore, mV2/r = mg => = 0.5

=> when moving in a circle of radius 320 m, maximum speed = Sqrt (gr) = Sqrt (0.5*10*320) = 40 m/s

14) mV2/r (centrifugal force) = 1.2*104 N => m = 1.2*104*r/ V2 = 1500 KG

15) When moving in a circle, forces acting on the car are mV2/r (centrifugal force) and the firctional force (mg)

Therefore, mV2/r = mg => = V2/rg = 14*14/50*9.8 = 0.4

16) When moving in a circle, forces acting on the car are mV2/r (centrifugal force) and the firctional force (mg)

Therefore, mV2/r = mg => r = V2/g = V2/0.4*g = 2.5* V2/g

17) Minimum banking angle = tan-1(V2/rg) = 51 degrees

18) Using the same concept as above,

banking angle = tan-1(V2/rg)

=> 45 = tan-1(V2/rg)

=> tan 45 = V2/rg

=> 1 = V2/rg

=> V2/r = g = centripetal force

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