Page 125 - Schaum's Outline of Theory and Problems of Applied Physics

110 CIRCULAR MOTION AND GRAVITATION [CHAP. 9

9.7. How much centripetal force is needed to keep a 4-lb iron ball moving in a horizontal circle of radius 5 ft at a velocity
of 15 ft/s?

9.8. A 5000-kg airplane makes a horizontal turn 1 km in radius at a velocity of 50 m/s. How much centripetal force is
required?

9.9. A motorcycle begins to skid when it makes a turn of 15-m radius at a velocity of 12 m/s. What is the highest velocity
at which it can make a turn of 30-m radius?
9.10. What is the minimum coefficient of static friction required for a car traveling at 60 km/h to make a level turn 40 m in
radius?
9.11. The coefficient of static friction between a car’s tires and a certain concrete road is 1.0 when the road is dry and 0.7
when the road is wet. If the car can safely make a certain turn at 25 mi/h on a dry day, what is the maximum velocity
on a rainy day?

9.12. A crate is on the floor of a truck moving at 15 m/s. If the coefficient of friction between the crate and the truck floor
is 0.4, what is the minimum radius of a turn the truck can make without the crate slipping?

9.13. An airplane whose velocity is 500 km/h banks at an angle of 40 . If the rudder is not used, what is the radius of the
◦
turn the airplane makes?
9.14. A highway curve 250 m in radius is banked at an angle of 14 . For what velocity is the curve designed?
◦
9.15. Find the minimum velocity at which a car will leave the road when passing over a hump whose radius is 12 m.

9.16. A string 1 m long is used to swing a 500-g ball in a vertical circle. What is the tension in the string at the top of the
circle when the ball is moving at 5 m/s?

9.17. The 200-g head of a golf club is moving at 45 m/s in a circular arc 1 m in radius. Ignoring the mass of the club’s shaft,
how much force must the player exert on the handle of the club to keep it from flying out of his hands at the bottom
of the swing?

9.18. A woman swings a pail of water at constant velocity in a vertical circle 100 cm in radius. (a) If the water is not to
spill, what is the minimum velocity the pail can have? (b) How much time per revolution is this equivalent to?

9.19. What is the gravitational attraction between an 80-kg man and a 50-kg woman who are 2 m apart?

9.20. What is the gravitational attraction between two 3200-lb elephants when they are 20 ft apart?

9.21. The acceleration of gravity on the surface of Mars is 0.4g. How much will a person whose weight on the earth’s
surface is 180 lb weigh on the surface of Mars?

9.22. A man weighs 180 lb on the earth’s surface. (a) What would he weigh at a distance from the center of the earth of
three times the radius of the earth? (b) What would his mass there be?

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9.23. A 10-kg monkey is 10 m above the earth’s surface. (a) What is its weight there? (b) What is its mass there?
9.24. Find the weight of an 80-kg person at the earth’s surface and at an altitude of 2000 km.
9.25. At what altitude will a person’s weight be half what it is at the earth’s surface?

9.26. Find the velocity in meters per second that an artificial earth satellite must have to pursue a circular orbit at an altitude
of half an earth radius.

9.27. Find the radius of a satellite orbit whose period is 12 h.