− 2 ( a ) ∆d
a 11. (a) Using the scale indicated in the question: A = 29.0 m/s [35° N of E] The north and east components of this vector are, respectively: A (sin 35°) = 29.0 m/s (sin 35°) = 17 m/s A (cos 35°) = 29.0 m/s (cos 35°) = 24 m/s Notice that the answers are written to two significant digits because the angle is stated to two significant digits. (b) The vectors can be added by using a vector scale diagram (adding the vectors head-to-tail), by using components, or by applying trigonometry (the laws of sines and cosines). (c) Scale: 1.0 cm = 5.0 cm B + A = 3.9 cm × 5.0 cm = 20 cm [65° N of E]
A − B = 3.3 cm × 5.0 cm = 17 cm [2° S of E]
Copyright © 2003 Nelson
Unit 1 Are You Ready?
Technical Skills and Safety
12. (a) The total time is 6(0.10 s) = 0.60 s. (b)
As shown in the illustration, the x-component of each displacement vector is about 1.0 cm in the diagram, or 5.0 cm using the scale indicated. We can conclude that the motion in the x direction is constant-speed motion. (c) The y-component of the displacements constantly changes, becoming smaller as the puck rises, and then becoming larger as the puck descends. (d) The displacement (or change of position) from the initial position to the final position is: ∆d = 6.15 cm × 5.0 cm/cm = 31 cm [right] ∆t = 0.60 s vav = ? vav = = ∆d ∆t 31 cm [right]
0.60 s vav = 52 cm/s [right] The average velocity of the puck is 52 cm/s [right]. 13. (a) Using a stopwatch, determine the total time for a certain number of complete revolutions of the stopper (e.g., 20 cycles). Then apply the following relationships: number of cycles frequency: f = total time period: T = total time
number of cycles (b) The string should be strong, the stopper should be securely attached to the string, and the lab partner should hold the string securely while twirling the stopper a safe distance away from objects or people. (c) Typical sources of error are: •...