Copyright © 2017 Pearson Education, Inc. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 1 – 1 Chapter 1: Introduction to Physics Answers to Even-Numbered Conceptual Questions 2. The quantity T + d does not make sense physically, because it adds together variables that have different physical dimensions. The quantity d/T does make sense, however; it could represent the distance d traveled by an object in the time T. 4. The frequency is a scalar quantity. It has a numerical value, but no associated direction. 6. (a) 107 s; (b) 10,000 s; (c) 1 s; (d) 1017 s; (e) 108 s to 109 s. Solutions to Problems and Conceptual Exercises 1. Picture the Problem: This problem is about the conversion of units. Strategy: Multiply the given number by conversion factors to obtain the desired units. Solution: (a) Convert the units: 91 gigadollars$152,000,000 0.152 gigadollars1 10 dollars (b) Convert the units again: 4121 teradollars$152,000,000 1.52 10 teradollars1 10 dollars   Insight: The inside back cover of the textbook has a helpful chart of the metric prefixes. 2. Picture the Problem: This problem is about the conversion of units. Strategy: Multiply the given number by conversion factors to obtain the desired units. Solution: (a) Convert the units: 651.0 10 m85 m 8.5 10 mm   (b) Convert the units again: 61.0 10 m 1000 mm85 m 0.085 mmm 1 m   Insight: The inside back cover of the textbook has a helpful chart of the metric prefixes. 3. Picture the Problem: This problem is about the conversion of units. Strategy: Multiply the given number by conversion factors to obtain the desired units. Solution: Convert the units: 98Gm 1 10 m0.3 3 10 m/ss Gm   Insight: The inside back cover of the textbook has a helpful chart of the metric prefixes.Chapter 1: Introduction to Physics James S. Walker, Physics, 5th Edition Copyright © 2017 Pearson Education, Inc. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 1 – 2 4. Picture the Problem: This problem is about the conversion of units. Strategy: Multiply the given number by conversion factors to obtain the desired units. Solution: Convert the units: 12 95teracalculation 1 10 calculations 1 10 s136.8 s teracalculation ns136,800 calculations/ns 1.368 10 calculations/ns   Insight: The inside back cover of the textbook has a helpful chart of the metric prefixes. 5. Picture the Problem: This is a dimensional analysis question. Strategy: Manipulate the dimensions in the same manner as algebraic expressions. Solution: 1. (a) Substitute dimensions for the variables: 222121 [L][L] [T] [L] The equation is dimensionally consistent.2 [T]x at 2. (b) Substitute dimensions for the variables:        LT1T Not dimensionally consistentLTvtx   3. (c) Substitute dimensions for the variables:         222 LT T T Dimensionally consistentLTxta    Insight: The number 2 does not contribute any dimensions to the problem. 6. Picture the Problem: This is a dimensional analysis question. Strategy: Manipulate the dimensions in the same manner as algebraic expressions. Solution: 1. (a) Substitute dimensions for the variables:        L1T YesL T 1 Txv   2. (b) Substitute dimensions for the variables:              21 T TLT1 NoL T 1 T Tav   3. (c) Substitute dimensions for the variables:          222L21T T YesL T 1 Txa    4. (d) Substitute dimensions for the variables:                 22 2 2222LTL T LL NoLL T L Tva    Insight: When squaring the velocity you must remember to square the dimensions of both the numerator (meters) and the denominator (seconds).Chapter 1: Introduction to Physics James S. Walker, Physics, 5th Edition Copyright © 2017 Pearson Education, Inc. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 1 – 3 7. Picture the Problem: This is a dimensional analysis question. Strategy: Manipulate the dimensions in the same manner as algebraic expressions. Solution: 1. (a) Substitute dimensions for the variables:      LT L YesTvt 2. (b) Substitute dimensions for the variables:      2211222LT L YesTat 3. (c) Substitute dimensions for the variables:      2LL2 2 T NoTTat 4. (d) Substitute dimensions for the variables:                 22 2 2222LTL T LL YesLL T L Tva    Insight: When squaring the velocity you must remember to square the dimensions of both the numerator (meters) and the denominator (seconds). 8. Picture the Problem: This is a dimensional analysis question. Strategy: Manipulate the dimensions in the same manner as algebraic expressions. Solution: 1. (a) Substitute dimensions for the variables:      2211222LT L NoTat 2. (b) Substitute dimensions for the variables:      2LLT YesTTat 3. (c) Substitute dimensions for the variables:      22L2T NoLTxa 4. (d) Substitute dimensions for the variables:        222L L L2 2 L YesTTTax   Insight: When taking the square root of dimensions you need not worry about the positive and negative roots; only the positive root is physical. 9. Picture the Problem: This is a dimensional analysis question.