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to this page. CHAPTER 5. ANSWER KEY. BLM 5-1, Interpreting Vectors/Skill.
CHAPTER 5
ANSWER KEY
BLM 5-1, Interpreting Vectors/Skill Builder Goal: Students enhance their understanding of vectors.
Answers Adding Vectors Graphically
K 1. ∆d = 355 km[N3.1°E]; ∆d = 614 km K K 2. ∆d = 43 m[E25°N]; ∆d = 77 m; ∆d = 43 km[W25°S]; 0.0 m m 3. 1.9 [N22°E] s
Subtracting Vectors Graphically 1. 247 km[E6.6°S] 2. 3.1 km[E42°N] km [W0.14°N] 3. 46 h
BLM 5-2, Frames of Reference/ Information Handout
4. D’s frame of reference: m [W] Velocity of A = 5.6 s m Velocity of B = 4.8 [W] s m Velocity of C = 3.3 [W] s
BLM 5-3, The History of Vectors/Science Inquiry Goal: Students trace the history of vectors and the scientists who developed them.
Answers Scientist or Mathematician 1. Simon Stevin
2.
3.
Goal: Students develop the concept of a frame of reference.
Answers 1. A’s frame of reference: m Velocity of B = 0.82 [E] s m Velocity of C = 2.3 [E] s m Velocity of D = 5.6 [E] s 2. B’s frame of reference: m Velocity of A = 0.82 [W] s m Velocity of C = 1.48 [E] s m Velocity of D = 4.8 [E] s 3. C’s frame of reference: m Velocity of A = 2.3 [W] s m Velocity of B = 1.48 [W] s m Velocity of D = 3.3 [E] s
4.
5.
6.
Role in the development of vectors Introduced the parallelogram law for the addition of forces in his Statics and Hydrodynamics in 1586. Caspar Wessel Discovered a method for the graphical representation of complex numbers in 1797. Sir William Rowan Introduced the method of Hamilton quaternions in 1843, and greatly influenced further developments. His methed of quaternions provided a solution to the problem of multiplying vectors in a framework of a threedimensional space. Hermann Grassman Published a book in 1844 in which he attempted to build a kind of vector analysis for n dimensions. Oliver Heaviside Helped establish vector analysis as an independent branch of mathematics in the late nineteenth century. Josiah Willard Gibbs Influenced by Grassman, he developed an algebra of vectors in three-dimensional space. He applied this to the fields of crystallography and astronomy. Gibbs published papers on vector analysis in the 1880s, and summed up his work in Vector Analysis, published in 1901. Gibbs is considered the father of vector analysis.
Good sources are: 1. The Encyclopedia Americana, International Edition, Year 2000 edition by Grolier. 2. A History of Vector Analysis: The Evolution of the Idea of a Vectorial System by Michael J. Crowe (Dover, 1994) ISBN: 0486679101.
Copyright © 2004 McGraw-Hill Ryerson Limited. Permission to edit and reproduce this page is granted to the purchaser for use in her/his classroom. McGraw-Hill Ryerson shall not be held responsible for content if any revisions, additions, or deletions are made to this page.
CHAPTER 5
ANSWER KEY
BLM 5-4, Analyzing Distance and Displacement/Overhead Master Answers not applicable
BLM 5-5, Kinetic Energy/Reinforcement Goal: Students practise solving problems that involve kinetic energy.
Answers 1. 67 J 2. 2.86 × 108 J m 3. 6.3 s m 4. 3.63 × 106 s 5. 0.79 kg 6. 63 kg m 7. 32 s 8. (a) 2.5 × 104 J m (b) 3.97 s
BLM 5-6, Calculating Gravitational Potential Energy/Overhead Master Answers not applicable
BLM 5-7, Potential Energy Is Relative/ Skill Builder Goal: Students practise solving problems that involve gravitational potential energy.
Answers 1. 2. 3. 4. 5. 6. 7. 8.
8.2 J 2.9 J 8.2 J 3.2 kg 1.5 × 103 m 3.7 m 3.3 × 102 J 1.2 × 105 J
BLM 5-8, Chapter 5 Test/Assessment
Answers: 1. F: Scalar quantities have magnitude only. 2. F: The speed of an object is always greater than or equal to the magnitude of its velocity. 3. T 4. T 5. F: The amount of gravitational potential energy that an object has at one height relative to another height depends only on the vertical distance between the two heights. 6. (e) 7. (c) 8. (a) 9. (d) 10. (b) 11. position vectors 12. acceleration 13. four 14. mass, weight 15. vertical 16. (d) 17. (b) 18. (c) 19. (a) 20. (b) 21. (c) 22. (d) 23. (a) 24. (a) 25. (a) m 26. 27 s m 27. 6.2 s 28. 1.69 × 106 J 29. The diving board has elastic potential energy when it is bent. The diver has gravitational potential energy relative to the water. When the diver is gently bouncing down on the diving board, his gravitational potential energy is converted into kinetic energy, and the kinetic energy is then converted into elastic potential energy of the diving board. As the diver bounces upward, the elastic potential energy of the board is transformed into kinetic energy of the diver and then into gravitational potential energy of the diver. When the diver jumps up, some chemical potential energy in his body is converted into kinetic energy of the diver. The kinetic energy is then converted into gravitational potential energy. The gravitational potential energy is converted into kinetic energy of the diver. When the diver hits the water, he is slowed and some of the kinetic energy is converted into thermal energy of his skin and the water.
Goal: Students demonstrate their understanding of the information presented in Chapter 5. Copyright © 2004 McGraw-Hill Ryerson Limited. Permission to edit and reproduce this page is granted to the purchaser for use in her/his classroom. McGraw-Hill Ryerson shall not be held responsible for content if any revisions, additions, or deletions are made to this page.
