Section Study Guide. Teacher Notes and Answers. Circular Motion and Gravitation

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1 Section Study Guide Teacher Notes and Answers CIRCULAR MOTION 1. a. yes b. The car has a non-zero acceleration because the direction of motion is changing. c. The direction of centripetal acceleration is toward the center of the circle. In this case, the direction is toward the center of the Ferris wheel. d m/s 2 2. a. the wire b. centripetal force c. The centripetal force acts toward the center of the circular motion. d. inertia e m/s NEWTON S LAW OF UNIVERSAL GRAVITATION 1. a. 2 b. 4 c. d a. double one mass, double the force b. double both masses, quadruple the force c. double the radius, decrease the force to d. If measured in the opposite direction, the force will be in the opposite direction. 3. Because of inertia, objects tend to go in a straight line. A force is needed to change the direction of travel. MOTION IN SPACE 1. a. According to Copernicus, Earth and the other planets each move in a perfect circle around the sun. b. According to Kepler s First Law, Earth and the other planets each move in an elliptical orbit with the sun at one focus. 2. t 1 = t 2 3. T 2 r 3 4. Newton derived Kepler s laws from the universal law of gravitation. 5. T = s; v t = m/s TORQUE AND SIMPLE MECHANICS 1. a. F d, F e, F f, F g b. F e exerts the largest torque because it has the largest lever arm. 2. a J b. 120 N c. 110 m d. greater 3. a b c Holt Physics 1 Study Guide

2 Circular Motion 1. A Ferris wheel car is moving in a circular path at a constant speed. a. Is the car accelerating? b. How can the car have a non-zero acceleration if the speed is constant? c. What is the direction of centripetal acceleration? d. What is the magnitude of the centripetal acceleration if the tangential speed of the car is 2.0 m/s and the radius of the wheel is 83 m? 2. The hammer throw is a track-and-field event in which the thrower swings a heavy metal ball (the hammer ) on a wire in a circular motion, then releases the wire, sending the hammer flying. a. What provides the force to keep the hammer moving in a circle before the wire is released? b. What is the name for this force? c. In what direction does this force act? d. What is the term for the hammer s tendency to move in a straight line? e. Suppose the hammer has a mass of 7.26 kg, the wire is 1.00 m long, and the force keeping the hammer moving in a circle is N. What will the hammer s speed be when the thrower releases the wire? Holt Physics 2 Study Guide

3 Newton s Law of Universal Gravitation 1. Newton s universal law of gravitation states that F g = G m 1m 2. Consider a system of two masses, m 1 = m 2 = M, at a distance r = R o. The gravitational force on each of these masses would be F o = G MM R = G M 2. Find the ratio of the new 2 2 o R o gravitational force to the original force, F, for each of the following situations. o a. m 1 = M, m 2 = 2M, r = R o. b. m 1 = m 2 = 2M, r = R o. c. m 1 = m 2 = M, r = 2R o. d. m 1 = m 2 = M, r = R o. 2. For each situation in item 1, write a sentence that summarizes in words what has changed and how that change has affected the gravitational force. a. b. c. d. 3. Why is a force necessary to create circular motion? r 2 Holt Physics 3 Study Guide

4 Motion in Space 1. Claudius Ptolemy proposed that planets travel in small circles, called epicycles, while they simultaneously travel in larger circles around Earth. a. According to Nicolaus Copernicus, how do Earth and the other planets move? b. According to Kepler s first law, how do Earth and the other planets move? 2. Examine the diagram above. If the area A 1 equals the area A 2, what can you conclude about the relationship between t 1 and t 2? 3. Kepler s third law describes the relationship between a planet s orbital period, T, and the mean distance between the planet and the sun, r. Express this relationship as a proportion, in symbolic form. 4. How did Newton use Kepler s laws to support his theory of gravitation? 5. Earth travels around the sun in a nearly circular orbit at a mean distance of m. The sun s mass is kg. Calculate Earth s orbital period and orbital speed. Holt Physics 4 Study Guide

5 Torque and Simple Mechanics 1. Use the diagram at right to complete the following items. The arrows represent force vectors, and the dashed lines represent the lines of action of the forces. a. Identify the forces that exert a torque on the object. b. If each force has the same magnitude, which force exerts the largest torque? Explain your answer. 2. A pulley system with a mechanical advantage of 15 is used to lift a 1750 N piano to a third-floor balcony that is 7.0 m above the ground. a. If friction is negligible, how much work must be done? b. What applied force must the movers use? c. How much rope will the movers pull in? d. If friction is not negligible, is the input energy greater than or less than your answer to part a? 3. Calculate the efficiency of the following. a. W in = 1850 J, W out = 1700 J b. an object weighing 150 N is lifted 9.0 m using 1500 J of energy c. a force of 150 N is exerted along a 3.0 m inclined plane to raise an object weighing 425 N to a height of 1.0 m Holt Physics 5 Study Guide