Page 124 - Schaum's Outline of Theory and Problems of Applied Physics

CHAP. 9] CIRCULAR MOTION AND GRAVITATION 109

9.7. The coefficient of static friction between the tires of a truck whose velocity is 60 km/h and a road is 0.65. The smallest
turning radius of the truck is
(a) 9.4 m (c) 44 m
(b) 22 m (d) 565 m

9.8. A 500-g ball is whirled in a vertical circle at the end of a string 60 cm long. If the velocity of the ball at the bottom
of the circle is 4.0 m/s, the tension in the string there is
(a) 4.9 N (c) 13.3 N
(b) 8.4 N (d) 18.2 N

9.9. A car just leaves the road when it passes over a hump whose radius is 40 m. The car’s velocity is
(a) 20 m/s (c) 392 m/s
(b) 62 m/s (d) impossible to find without knowing the car’s mass
9.10. A woman whose mass is 60 kg on the earth’s surface is in a spacecraft at an altitude of two earth radii. Her mass
there is
(a) 6.7 kg (c) 20 kg
(b) 15 kg (d) 60 kg

9.11. A man whose mass is 80 kg on the earth’s surface is also in the spacecraft of Question 9.10. His weight there is
(a) 87 N (c) 261 N
(b) 196 N (d) 784 N

9.12. An astronaut weighs 3200 N on a planet whose mass is the same as that of the earth but whose radius is half that of
the earth. The astronaut’s weight on the earth is
(a) 400 N (c) 1600 N
(b) 800 N (d) 3200 N
2
9.13. A satellite orbits the earth in a circle of radius 8000 km. At that distance from the earth g = 6.2 m/s . The velocity
of the satellite is
(a) 0.90 km/s (c) 8.9 km/s
(b) 7.0 km/s (d) impossible to find without knowing the satellite’s mass

Supplementary Problems

9.1. Can a body move in a curved path without being accelerated?

9.2. In what ways, if any, do g and G change with increasing height above the earth’s surface?

9.3. The moon’s mass is approximately 1 percent of the earth’s mass. How does the gravitational pull of the earth on the
moon compare with the gravitational pull of the moon on the earth?

9.4. A hole is drilled to the center of the earth, and a stone whose mass is 1 kg at the earth’s surface is dropped into it.
What is the mass of the stone when it is at the earth’s center? What is its weight?

9.5. A lasso is whirled so that the loop at its end describes a horizontal circle 5 ft in radius. If each revolution of the lasso
requires 4 s, find the centripetal acceleration of the loop.

9.6. A 0.02-kg ball is whirled in a horizontal circle at the end of a string 0.5 m long whose breaking strength is 1 N.
Neglecting gravity, what is the maximum velocity the ball can have?