Exam2_solution-Sp03

# Exam2_solution-Sp03 - Physics 221. Exam 2 (Midterm) Spring...

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Physics 221. Exam 2 (Midterm) Spring 2003 51. This booklet is version A. Enter A on question 51. The situation below refers to the next two questions: Two particles A and B move along the x -axis according to the graph shown below. x (m) 0 1 2 3 4 5 A B t (s) 52. Which of the following statements about the x -component of their accelerations between t = 0 and t = 5 s is true? a. a x ,A > 0 , a x ,B > 0 b. a x ,A > 0 , a x ,B = 0 c. a x ,A = 0 , a x ,B > 0 d. a x ,A < 0 , a x ,B > 0 e. a x ,A < 0 , a x ,B = 0 Particle B moves at constant speed (x(t) has a constant slope), so a x,B = 0. Particle A starts off with a certain positive velocity (positive slope) and slows down (slope decreases) between 0 and 2 s (approx.). This corresponds to a negative acceleration. After t =2 s, it starts moving in the negative x-direction (i.e., negative velocity) and speeds up, so the acceleration is still negative. Mathematically, the second derivative of this curve is always negative . 3. When is their relative velocity equal to zero? a. At some point between t = 0 and t = 1 s. b. At some point between t = 1 and t = 2 s. c. At some point between t = 2 and t = 3 s. d. At some point between t = 3 and t = 4 s. e. At some point between t = 4 and t = 5 s. Page 1 of 22

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Physics 221. Exam 2 (Midterm) Spring 2003 Their relative velocity will be zero whenever their velocities are equal. This is, whenever the slopes of the curves are equal. This happens sometime between 1 and 2 s (see dotted red line in figure). 54 . Two vectors A and B have the same magnitude. Vector A is in the positive x - direction. Vector B is in the negative y -direction. Which of these figures correctly depicts the angle between vectors A and ( A - B )? (Ignore length of vectors in the figure). A A A B A B A B e. c. 60° 45° b. d. 45° 60° 90° a. A B A B A A A B B A y B x A 55 . Force vector F A has the magnitude of 5.0 N and an angle of 300° with respect to the positive x -axis (counter-clockwise). Force vector F B has a magnitude of 5.0 N and an angle of 60° with respect to the positive x -axis (counter-clockwise). What is the magnitude of the third force vector, which must be added to F A and F B in order to make the net force equal to zero? (All forces act on the same object). a. 2.5 N b. 5.0 N c. 7.5 N d. 10.0 N e. None of the above Page 2 of 22
Physics 221. Exam 2 (Midterm) Spring 2003 y F B 60° x F C 60° F A You can see the result right away from the symmetry of the problem (all three vectors are separated by angles of 120°) or you can do the calculation. F c,y = 0 (due to the symmetry) F c,y = (5 N) cos 60° (5 N) cos 60° = 5 N 56. Let A = i + 2 j + α k and B = 3 i j + β k . Find the values of and that will make A × B = 0. a. = 2, = 0 b. = 0, = 2 c. = 2, = 2 d. = 3, = 2 e. There are no values of and that will make A × B = 0. A × B = 0 means that the vectors are parallel to each other. In this case, there should be some scalar k such that A = k B . This is clearly impossible considering the first two components.

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## This note was uploaded on 03/26/2008 for the course PHYS 221 taught by Professor Herrera-siklody during the Spring '08 term at Iowa State.

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Exam2_solution-Sp03 - Physics 221. Exam 2 (Midterm) Spring...

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