HCI 01 Measurement Solutions (Self-Review Questions)

1 Solutions to 2023 Measurement Self-Review Questions S1. Density,       3 33 6 10 0 1 0 10 0 1 0 k g m 10 0 1 0 . . . S2. (A) ohm, newton and volt are not base units. S3. Speed of car =   3 190 0 10 25 0 m s60 60 . . S4. 1 light-year = 81 53.0 10 (365 24 60 60) 9.46 10 m     Distance to star = 16 15 4.0 10 4.29.46 10   light-years S5. (C). Stopping the stopwatch requires judging the correct ti ming of the end of the sprint. The stopwatch may be stopped too early or too late by t he timekeeper (due to the fast speed). The other options constitute systematic errors. S6. Graph A B C D Precise   Not precise   Accurate   Not accurate   S7. 21 2 DFC A v  D Fv CA -122 ( 2 2 ) 11.411 m s(0.88)(1.2)(0.32)  D D CvF A vFC A v 11 11 22 22 1 2 0.01 0.1 0.02 11.411 2 22 0.88 1.2 0.32          v 1.416 v -111 1 m s The uncertainty must be expressed to 1 sf, which is in the ones place. Hence the value is expressed to the ones place too.

2 S8. fiΔv=v -v (note that this is a vector operation) S9. (a) (i) The velocity is at an angle to the horizontal. The diagram indicates it has both magnitude and direction. (ii) Less. All components of a vector are of a smaller ma gnitude than its original vector (the hypotenuse). (c) (i)  0115 60 7 5mshVc o s . (ii) 0115 60 13msvVs i n  vi Δv -vi (magnitude of 2.4 m s–1) vf (magnitude of 1.8 m s–1) 60o 15 m s-1 Vertical component Horizontal component