Study Guide Solutions

Study Guide Solutions Table of Contents Chapter 1 A Physics Toolkit... 3 Vocabulary Review... 3 Section 1.1: Mathematics and Physics... 3 Section 1.2: Measurement... 3 Section 1.3: Graphing Data... 4 Chapter 2 Representing Motion... 4 Vocabulary Review... 4 Section 2.1: Picturing Motion... 4 Section 2.2: Where and When?... 4 Section 2.3: Position-Time Graphs... 5 Section 2.4: How Fast?... 5 Chapter 3 Accelerated Motion... 5 Vocabulary Review... 5 Section 3.1: Acceleration... 6 Section 3.2: Motion with Constant Acceleration... 7 Section 3.3: Free Fall... 8 Chapter 4 Forces in One Dimension... 9 Vocabulary Review... 9 Section 4.1: Force and Motion... 10 Section 4.2: Using Newton s Laws... 10 Section 4.3: Interaction Forces... 11 Chapter 5 Forces in Two Dimensions... 11 Vocabulary Review... 11 Section 5.1: Vectors... 11 Section 5.2: Friction... 15 Section 5.3: Force and Motion in Two Dimensions... 15 Chapter 6 Motion in Two Dimensions... 17 Vocabulary Review... 17 Section 6.1: Projectile Motion... 17 1

Section 6.2: Uniform Circular Motion... 18 Section 6.3: Relative Velocity... 19 Chapter 7 Gravitation... 19 Vocabulary Review... 19 Section 7.1: Planetary Motion and Gravitation... 19 Section 7.2: Using the Law of Universal Gravitation... 20 Chapter 9 Momentum and Its Conservation... 20 Vocabulary Review... 20 Section 9.1: Impulse and Momentum... 21 Section 9.2: Conservation of Momentum... 22 Chapter 10 Energy, Work, and Simple Machines... 23 Vocabulary Review... 23 Section 10.1: Energy and Work... 23 Section 10.2: Machines... 24 Chapter 11 Energy and Its Conservation... 24 Vocabulary Review... 24 Section 11.1: The Many Forms of Energy... 25 Section 11.2: Conservation of Energy... 26 2

Chapter 1 A Physics Toolkit Vocabulary Review 1. Physics 2. Scientific method 3. Significant digits 4. Inverse relationship 5. Line of best fit 6. Hypothesis 7. Independent variable 8. Scientific law Section 1.1: Mathematics and Physics 1. Experiments 2. Experimental data 3. Results 4. Theories 5. Equations 6. Units 7. Dimensional analysis 8. Graphs 9. C 10. E 11. A 12. F 9. Measurement 10. Linear relationship 11. Scientific theory 12. Accuracy 13. Dependent variable 14. Dimensional analysis 15. Quadratic relationship 16. Precision 13. H 14. D 15. B 16. I 17. G 18. Least 19. Three 20. With the number of significant digits required by the problem 21. 2 22. 1 23. 3 24. This can best be described as an observation because you have noticed a natural phenomenon. 25. The fact that exact units are mentioned makes this a quantitative measurement. 26. This statement describes the summing up of observations into a scientific law. 27. This is a hypothesis or prediction based on previous experience. 28. This is an example of reproducing results because you are doing the experiment a second time. 29. This is a scientific theory based on many observations and supported by experimental results. Section 1.2: Measurement 1. A 2. C 3. D 4. B 5. C 6. A 7. D 3

Section 1.3: Graphing Data 1. Quadratic 2. The independent variable is time and the dependent variable is distance. 3. Positive 4. 5. The graph is steeper at 2.0 s than at 1.0 s. 6. 15 m 7. ( ) 8. Inverse 9. Negative 10. Ohms/A 11. 5 A 12. 13. D 14. C 15. F 16. A 17. E 18. B Chapter 2 Representing Motion Vocabulary Review 1. Instantaneous velocity 2. Magnitude 3. Position 4. Time interval 5. Vector 6. Average velocity 7. Coordinate system 8. Origin 9. Position time graph 10. Motion diagram 11. Resultant 12. Particle model 13. Distance 14. Scalar 15. Instantaneous position 16. Displacement 17. Average speed Section 2.1: Picturing Motion 1. B 2. B 3. D 4. C 5. A Section 2.2: Where and When? 1. 4 m, -4 m, 5 m, 3 m, and 0 m 2. 1 m/s 3. -1 m/s 4. A, C, D 5. B 4

Section 2.3: Position-Time Graphs 1. Time 2. Position 3. 9.0 m 4. 4.0 s 5. 1.5 m/s 6. 7. ( ) ( ) Section 2.4: How Fast? 1. 2. At 15.0 m,. At 5.0 m,. 3. 4. At, At s, m 5. 6. 7. Average speed 8. +2.5 m/s 9. 10. ( ) ( ) 11. 12. ( ) ( ) Chapter 3 Accelerated Motion Vocabulary Review 1. Velocity-time graph 2. Instantaneous acceleration 3. Acceleration 4. Free fall 5. Average acceleration 6. Acceleration due to gravity 5

Section 3.1: Acceleration 2. C 3. B 4. D 5. C 6. A 7. Object B; the graph for Object B has a larger slope than that of Object A. 8. Object C has a negative slope, and it therefore decelerating. 9. Object B started from rest with a velocity of zero. Object C slows to a stop ( ) and remains stopped. 10. Object D begins with negative velocity, crosses the axis, and continues with positive velocity. This behavior indicates that it slows to a complete stop and then starts moving again. 11. Object A is moving forward (positive velocity) and object E is moving backwards (negative velocity). 6

Section 3.2: Motion with Constant Acceleration 7

Section 3.3: Free Fall 1. Air resistance 2. True 3. The same 4. True 5. True 6. 29.4 m/s 7. True 8. True 9. 9.80 m/s 2 10. True 8

Chapter 4 Forces in One Dimension Vocabulary Review 1. External world 2. Gravitational force 3. Newton s first law 4. Force 5. Field force 6. Interaction pair 7. Tension 8. Net force 9. Equilibrium 10. Drag force 11. Newton s second law 12. Apparent weight 13. Contact force 14. Newton s third law 15. Normal force 16. System 17. Inertia 18. Agent 19. Free-body diagram 20. Terminal velocity 21. Weightlessness 9

Section 4.1: Force and Motion 1. True 2. False 3. True 4. False 5. True 6. False 7. False 8. True 9. D 10. B 11. C 12. D 13. C 14. C 15. A 16. D Section 4.2: Using Newton s Laws 1. C 2. D 3. A 4. G 5. F 6. B 7. H 8. E 9. A 10. B 11. B 12. C 13. C 14. A 15. Direction opposite to 16. True 17. More 18. The drag force equals the force of gravity 10

Section 4.3: Interaction Forces Chapter 5 Forces in Two Dimensions Vocabulary Review 1. Component 2. Static Friction 3. Equilibrant 4. Kinetic friction Section 5.1: Vectors 1. True 2. Velocity 3. True 4. True 5. Coefficient of kinetic friction 6. Vector resolution 7. Coefficient of static friction 5. May or may not be 6. True 7. Tip 11

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Section 5.2: Friction 1. C 2. B 3. C 4. C 5. B Section 5.3: Force and Motion in Two Dimensions 15

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Chapter 6 Motion in Two Dimensions Vocabulary Review 1. E 2. A 3. C 4. D 5. B Section 6.1: Projectile Motion 1. To an observer at Position A, the ball would appear to move straight up and then straight down. 2. To an observer at Position B, the ball would appear to move in a straight line. 3. To an observer at Position C, the ball s path would appear as in the diagram (as a parabola). 17

4. Throughout its flight, a projectile is constantly being accelerated toward the ground, even when it is moving upward. Thus, the vertical vector of a projectile s flight first points upward and shrinks until the projectile reaches its maximum height, at which point the projectile has no vertical component to its motion. The vertical vector then points to the ground and grows larger until the projectile returns to Earth. The horizontal vector always points parallel to the ground and has the same magnitude throughout the projectile s flight. 5. Both stones will hit the ground at the same time because the horizontal component of their velocities is independent of the vertical component. They both start out with zero vertical velocity and they both undergo the same acceleration due to gravity. Section 6.2: Uniform Circular Motion 1. The object must be moving in a circle with a fixed radius and the object must be moving at constant speed. 2. While speed is a directionless quantity (scalar), velocity is a vector and therefore any change in direction indicates a change in velocity. 3. Newton s first law states that a body moving at a constant velocity will continue moving at a constant velocity unless an unbalanced force acts on that body. Since an object in uniform circular motion has a changing velocity, it must be experiencing a non-zero net force. 4. Newton s second law states that the net force acting on an object causing an acceleration in the same direction as the net force. As shown in #3, an object in uniform circular motion must be experiencing a non-zero net force. Therefore, there must be a non-zero acceleration in the same direction as the net force. 18

Section 6.3: Relative Velocity Chapter 7 Gravitation Vocabulary Review 1. Inertial mass 2. Kepler s Second Law 3. Gravitational Mass 4. Gravitational Field 5. Newton s Law of Universal Gravitation Section 7.1: Planetary Motion and Gravitation Note: Kepler s Laws will be discussed during second semester. They will not be on the first semester final exam. 1. Copernicus 2. Brahe 3. Brahe 4. Kepler 5. Newton 6. Kepler 7. Newton 8. Kepler 9. Third 10. First 11. First 12. Third 13. Second 14. 15. Planet B s average distance from the Sun 16. It is least at point 3 and greatest at point 1. 17. The magnitude of the force at point 3 is 18. 19. 20. 21. 22. 23. 19

24. The planet s mean distance from the Sun as well as the mass of the Sun 25. It was a thin rod with small lead spheres at each end. The rod was suspended by a thin wire attached at its center so that the rod could spin freely. He then placed two larger lead spheres in fixed positions near the smaller spheres. The gravitational attraction between the lead spheres allowed Cavendish to obtain a value for the universal gravitational constant. 26. ( )( )( ) ( ). This is the same number as the universal gravitational constant. The universal gravitational constant is the force of gravity between two 1.00 kg objects that are separated by exactly one meter. Section 7.2: Using the Law of Universal Gravitation 1. Horizontal, vertical 15. No; the inertial mass is a function of an 2. 9.80 m/s 2 object s resistance to an exterior force, not 3. Horizontal to its position relative to other objects. 4. Air resistance 16. C 5. Orbit 17. E 6. The radius of the satellite s orbit 18. D 7. The same 19. F 8. True 20. B 9. Would change 21. A 10. Inverse-square relationship 22. Gravitational 11. True 23. Force; space 12. N/kg 24. Space 13. Toward Earth s center 25. Mass 14. Gravitational mass determines the force of 26. General relativity attraction between two masses and inertial mass determines an object s resistance to any type of force. Chapter 9 Momentum and Its Conservation Note: Anything that mentions angular was not discussed in class, and will not be on any test. Vocabulary Review 1. Angular momentum 2. Law of conservation of momentum 3. Angular impulse angular momentum theorem 4. Law of conservation of angular momentum 5. Closed system 6. Impulse 7. Isolated system 8. Momentum 9. Impulse-momentum theorem 20

Section 9.1: Impulse and Momentum 1. 8.0 N 2. 6.0 s 3. Impulse 4. 5. ( )( ) 6. 7. 8. 9. ( ) ( ) 10. ( ) ( ) 11. ( ) ( ) 12. ( ) ( ) 13. Increase the size of the force, or increase the amount of time the force is acting. 21

14. Injuries occur as a result of the large force between the driver s body and the steering wheel during an accident. An air bag increases the time of the collision. Since the same impulse is required to stop the driver s body, a longer collision time results in a lower force, and less chance of injury. 15. True 16. Angular 17. True 18. Increases 19. True 20. Constant 21. Faster Section 9.2: Conservation of Momentum 1. They have equal magnitude but are opposite in direction. 2. They have equal magnitude but are opposite in direction. 3. They are equal in both magnitude and direction. 4. Closed system 5. Internal forces 6. External forces 7. Isolated system 8. Law of conservation of momentum 9. Change 10. Conditions 11. Interaction 12. Zero 13. Zero 14. Less than zero 15. Greater than zero 16. C 17. C 18. D 19. B 20. A 21. C 22. Since skater N has initial momentum only in the -direction, and skater E has initial momentum only in the -direction, the final momentum in each direction is equal to the initial momentum of each skater. ( ) ( ) ( ) ( ) ( ) ( ) 22

( ) ( ) The skaters move at, north of east. Chapter 10 Energy, Work, and Simple Machines Vocabulary Review 1. Efficiency 2. Machine 3. Compound machine 4. Resistance force 5. Watt 6. Effort force 7. Work-energy theorem 8. Energy 9. Kinetic energy 10. Power 11. Mechanical advantage 12. Joule 13. Ideal mechanical advantage 14. Work Section 10.1: Energy and Work 1. C 2. B 3. E 4. D 5. F 6. A 23

7. True 8. Positive 9. True 10. Decreases 11. Is constant 12. True 16. 0.50 m 17. 30.0 N 18. The area represents the work done on the crate. 19. ( )( ) 20. From 0.0 m to 0.40 m, the area under the graph is ( )( ). Using the equation for work, ( )( ). The answers are the same. 21. First, find the area under the graph from 0.50 m to 0.70 m, consisting of a rectangle and a triangle on top of it formed by the sloped line. ( )( ) 22. D 23. B 24. C 25. E 26. A ( )( ) Add these areas to the area of the rectangle from problem #21 to find the total word done. Section 10.2: Machines We did not discuss machines, and you will not be tested on it. Chapter 11 Energy and Its Conservation Vocabulary Review 1. Conservation of energy 2. Reference level 3. Mechanical energy 4. Kinetic energy 5. Gravitational potential energy 6. Inelastic collision 24

7. Rotational kinetic energy 8. Thermal energy 9. Elastic collision 10. Elastic potential energy Section 11.1: The Many Forms of Energy 1. B 2. C 3. A 4. A 5. and 6. 7. B 8. A 9. A 10. B 11. C 12. B 13. C 14. B 15. D 16. A 17. B 18. True 19. True 20. Increases 21. True 22. Gravitational potential energy 23. Elastic 24. B 25. C 25

26. D Section 11.2: Conservation of Energy 1. a. ( )( )( ) b. If you want to go twice as fast, you need four times as much kinetic energy ( is proportional to ). Since potential energy is converted to kinetic energy as the skater goes down the ramp, the skater needs four times as much starting potential energy. Since gravitational potential energy is directly proportional to height, the ramp must be four times as high. c. Use conservation of mechanical energy. The gravitational potential energy change is equal to the kinetic energy change. Since the skater starts with 380 J of potential energy (see part a) and no kinetic energy, and finishes with no potential energy, the skater must finish with 380 J or kinetic energy. 2. The path that an object follows in reaching the ground does not affect the final kinetic energy of the object. 3. Some of the original mechanical energy in the system is converted to another form of energy within members of the system or transmitted to energy outside the system. For example, some of the energy is lost to friction or air resistance; some energy is converted to thermal energy or sound energy. 4. D 5. A 6. B 7. C 26