74. The greatest force a level road can exert on the tires of a certain 2000-kg car is 4 kN. What is the highest speed the car can round a curve of radius 200 m without skidding? 75. Find the minimum radius at which an airplane flying at 300 m/s can make a U-turn if the centripetal force on it is not to exceed 4 times the airplane's weight. 76. Some people believe that aliens from elsewhere in the uni- verse visit the earth in spacecraft that travel faster than jet airplanes and can turn in their own lengths. Calculate the centripetal force on a 100-kg alien in a spacecraft moving at 500 m/s (1 120 mi/h) while it is making a turn of radius 30 m. How many times the weight of the alien is this force? Do you think such stories can be believed? 77. The 200-g head of a golf club moves at 40 m/s in a circus lar are of 1.2 m radius. How much force must the player exert on the handle of the club to prevent it from flying out of her hands at the bottom of the swing? Ignore the mass of the club's shaft. 78. An airplane flying at a constant speed of 160 m/s pulls out of a dive in a circular arc. The 80-kg pilot presses down on his seat with a force of 3000 N at the bottom of the arc. What is the radius of the arc? 2.13 Newton's Law of Gravity 79. A track team on the moon could set new records for the high jump or pole vault (if they did not need space suits, of course) because of the smaller gravitational force. Could sprinters also improve their times for the 100-m dash? 80. If the moon were half as far from the earth as it is today, how would the gravitational force it exerts on the earth compare with the force it exerts today? 81. Compare the weight and mass of an object at the earth's surface with what they would be at an altitude of two earth's radii. 82. A hole is bored to the center of the earth and a stone is dropped into it. How do the mass and weight of the stoneat the earth's center compare with their values at the earth's surface? 83. Is the sun's gravitational pull on the earth the same at all seasons of the year? Explain. 84. The centripetal force that keeps the moon in its orbit around the earth is provided by the gravitational pull of the earth. This force accelerates the moon toward the earth at 2.7 x 10"m/s', so that the moon is continually "falling" toward the earth. How far does the moon fall toward the earth per second? Per year? Why doesn't the moon come closer and closer to the earth? 85. According to Kepler's second law, the earth travels fastest when it is closest to the sun. Is this consistent with the law of gravitation? Explain. 86. A 2-kg mass is I m away from a 5-kg mass. What is the gravitational force (a) that the 5-kg mass exerts on the 2-kg mass, and (b) that the 2-kg mass exerts on the 5-kg mass? (c) If both masses are free to move, what are their respective accelerations if no other forces are acting? 87. A dishonest grocer installs a 100-kg lead block under the pan of his scale. How much gravitational force does