l. MULTIPLE CHOICE: Write the letter of the correct answer on the answer sheet. (9 pts} 1. Which of the following quantities is constant in uniform circular motion? A. Speed B. Velocity C. Acceleration D. All of the above For Items 2 and 3. consider a ball tied to a string with radius r moving in "CM with speed it. 2. If the speed of the ball is doubled while the string is kept at its original length. what happens to the centripetal force experienced by the ball? A. The force is halved C. The force is quadrupled B. The force is doubled D. The force is unchanged 3. How must the string be modied so that the centripetal acceleration ofthe ball is halved? A. Halve its length B. Double its length C. Quadruple its length D. Double its thickness For Items 4 and 5. consider two planets with masses m. and In: a distance rapart. The gravitational force between the planets is F. 4. The distance between the two planets is halved to 1151'. What is the new gravitational force behveen the planets? AJAF B. 1/2!\" C. 2F D. 4-? 5. The masses of both planets are doubled, and the distance between the planets is quadrupled to 4r. What is the new gravitational force between the planets? AJAF B. 55F C. 2F D. 4? 6. Which of the following statements about the Earth's orbit is TRUE? A. The Earth's orbit is circular with the Sun at one focus B. The Earth's orbit is circular with the Sun at the center C. The Earth's orbit is elliptical with the Sun at one focus D. The Earth's orbit is elliptical with the Sun at the center 7'. Which of Kepler's Laws implies that planets move the fastest when they are at the point in their orbit closest to the star they are orbiting? A. Kepler's First Law B. Kepler's Second Law C. Kepler's Third law D. Kepler's Laws do not say anything about planet speeds 8. Two planets A and B orbit the same star. The distance between A and the Star is thrice as much as the distance between B and the star. If planet B's period is T, what is planet A's period? A. 2.1T B. 3T C. 5.21' D. 9T 9. Two planets A and B orbit the same star with the same radius. The mass ofA is half that of B. If planet B's period is T, what is planet A's period? A.0.19T B. 1/3T C. 'l' D. 2.11' II. PROBLEM SOLVING: Solve for what is asked. Show your complete solutions. (16pts) 1. A 950-kg car is running around a circular track with radius 125 m at a speed of 18.0 m/s. a. What centripetal force is required so that the car stays in the circular track? (2 pts) b. What is the minimum required static friction between the car's wheels and the (2 pts) track so that the car does not skid? 2. A planet with mass 1.9 x 1027 kg orbits a star with mass 2.0 x 1030 kg. The radius of the planet's orbit is found to be 7.8 x 10 km a. What is the gravitational force of the planet on the star? (3 pts) b. What is the period of the planet's revolution in seconds? (3 pts) 3. In the middle of your space expedition, you find yourself stranded on a planet with mass 2.52 x 10"* kg and radius 4220 km. a. What is the acceleration due to gravity on the surface of this planet? (2 pts) b. If your mass is 60 kg, what is your weight on this planet? (2 pts) c. How high above the surface of the planet (in km) must you be so that the acceleration due to gravity you experience has a magnitude of 8.0 m/s?? (2 pts) Fo = 6 mim, E 9 = GM T 2 = 41253 w= mg GM FORMULA F. = umg (G = 6.67 x 10" fr