1. Two objects attract each other with a gravitational force of 16 units. If the distance between the two objects is reduced in half, then what is the new force of attraction between the two objects? 2. Two objects attract each other with a gravitational force of 18 units. If one object's mass is doubled and the distance is tripled, then what is the new force of attraction between the two objects? 3. What will happen to the orbit of the planets of the solar system if our star (the Sun) shrinks into a black hole? 4. The starship Enterprise is located 2.44 x 107 m away from a planet with a mass of 3.32 x 1023 kg. If the starship has a mass of 95 kg, how much gravitational force is it experiencing? 5. If Spock (72 kg) weighs himself and finds that he weighs 133 N, how far away from the surface of the earth (5.98 x 1024 kg) is he? 6. Scotty beams Captain Kirk (86 kg) down to a planet that is the same size as Uranus, which has a radius of 2.61 x 107 m, and finds that he weighs 1250 N. What is the mass of that planet? 7. The gravitational force between two objects is 18 N. How does the gravitational force change when: a. the mass of one is doubled? b. the masses of both are doubled? c. the distance between them is doubled? d. the distance between them is cut in half? 8. Two objects of mass 50 kg each are 75 m apart. a. What force does one exert on the other? b. If there is a gravitational attraction between all objects, why aren't the two objects accelerating towards each other? 9. Two spheres of equal mass have a force of gravity of 3.5 x 10-6 N exerted on each other and the distance between them is 4 m. a. What is the mass of each sphere? b. If you wanted to change the gravitational force between them, what would create the greatest change: the distance between them or their masses? Explain. 10. The radius of the earth is about 6400 km. What would be the earth's gravitational attraction on 75 kg astronaut in an orbit 6400 km above the earth's surface? (Mass of Earth = 5.972 1024 kg) Circular Motion 11. A 2.5 kg stone is attached to a string 1.00m long, and is twirled in a circle at a rate of 15 revolutions in 20 seconds. a. What is the centripetal speed? b. What is the centripetal acceleration? c. What is the centripetal force? 12. An object is moving with uniform circular motion, at a speed of 5.00 m/s. The centripetal acceleration that is acting on it is 20.0 m/s2. a. What is the radius of the circle? b. What is the period? 13. An amusement park ride consists of a turntable of 2.0 m radius turning at 0.70 rev/s about a vertical axis. If a 70 kg child sits at the outer edge of the turntable, what force is necessary to keep the child from sliding off? 14. A 2500 kg car enters a curve with a radius of 45 m with a speed of 35 m/s. a. What is the centripetal force that maintains the car's circular motion through the curve? b. Describe the motion of the car if the car suddenly hit a patch of black ice while taking the curve. 15. A student is riding on a carousel at a speed of 4 m/s, has a radius of 5 m and the centripetal force is 240 N. a. What is the student's mass? b. What would happen to the centripetal force acting on the student if they moved closer to the axis of rotation? Explain. 16. A 905 kg test car travels around a r = 3.25 km circular track. The race track can apply a maximum centripetal force of 2140 N. a. What is the maximum speed the test car can enter the curve safely? b. If engineers had miscalculated the mass of the test car, what would they need to change in order to complete the track successfully