Concepts & Calculations

Note: Each of these problems consists of Concept Questions followed by a related quantitative Problem. The Concept Questions involve little or no mathematics. They focus on the concepts with which the problems deal. Recognizing the concepts is the essential initial step in any problem-solving technique.

| 64 | Concept Questions (a) Considering the fact that , which is the larger unit for measuring area, 1 ft2 or 1 m2? (b) Consider a 1330-ft2 apartment. With your answer to part (a) in mind and without doing any calculations, decide whether this apartment has an area that is greater than or less than 1330 m2.
Problem In a 1330-ft2 apartment, how many square meters of area are there? Be sure that your answer is consistent with your answers to the Concept Questions.

| 65 | Concept Question The corners of a square lie on a circle of diameter D. Each side of the square has a length L. Is L smaller or larger than D? Explain your reasoning using the Pythagorean theorem. Problem The diameter D of the circle is 0.35 m. Each side of the square has a length L. Find L. Be sure that your answer is consistent with your answer to the Concept Question.

| 66 | Concept Question Can the x or y component of a vector ever have a greater magnitude than the vector itself has? Give your reasoning. Problem A force vector has a magnitude of 575 newtons and points at an angle of 36.0° below the positive x axis. What are (a) the x scalar component and (b) the y scalar component of the vector? Verify that your answers are consistent with your answer to the Concept Question.

| 67 | Concept Questions The components of vector are Ax and Ay (both positive), and the angle that it makes with respect to the positive x axis is . (a) Does increasing the component Ax (while holding Ay constant) increase or decrease the angle ? (b) Does increasing the component Ay (while holding Ax constant) increase or decrease the angle ? Account for your answers.
Problem (a) The components of displacement vector are and . Find . (b) The components of displacement vector are and . Find . (c) The components of displacement vector are and . Find . Be sure that your answers are consistent with your answers to the Concept Questions.

| 68 | Concept Questions Vector points due west, while vector points due south. (a) Does the direction point north or south of due west? (b) Does the direction of point north or south of due west? Give your reasoning in each case. Problem Vector has a magnitude of 63 units and points due west, while vector has the same magnitude and points due south. Find the magnitude and direction of (a) and (b) . Specify the directions relative to due west. Verify that your answers agree with your answers to the Concept Questions.

| 69 | Concept Questions A pilot flies her route in two straight-line segments. The displacement vector for the first segment has a magnitude of 244 km and a direction 30.0° north of east. The displacement vector for the second segment has a magnitude of 175 km and a direction due west. The resultant displacement vector is = and makes an angle with the direction due east. Make a drawing to scale showing the vectors and placed tail to head and the resultant vector . Without doing any calculations decide whether (a) the magnitude of is greater or smaller than the magnitude of , (b) the magnitude of is greater or smaller than the magnitude of , and (c) the angle is greater than, smaller than, or equal to 30.0°.
Problem Using the component method, find the magnitude of and the directional angle . Check to see that your answers are consistent with your answers to the Concept Questions.

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