(a) What is a vector quantity?
(b) Three vectors 3 ms\(^{-1}\) N 45° W, 12 ms\(^{-1}\)W and 5 ms\(^{-1}\)S act at a point.
(i) Sketch a vector diagram to illustrate the given information.
(ii) Calculate the resultant of the vectors.
(c) In a laboratory experiment to determine the force constant of a spiral spring, the mass or, the spring was varied and the corresponding extensions were measured and recorded as shown in the table below.
| Mass M/g | Weight W/N | Extension e/cm |
|
50 100 150 200 250 |
6.5 11.0 15.0 20.0 25.0 |
(i) Copy and complete the table. (Take g = 10 ms\(^{-2}\))
(ii) Plot a graph with weight, W, on the vertical axis and extension, e, on the horizontal axis.
(iii) Using the graph, determine the force constant of the spring.
(iv) Determine the natural length of the spring if its length was 38.0 cm when loaded with 250 g mass.
Explanation
(a) Vector quantity is any quantity that has both magnitude and direction, e.g. velocity.
(b)(i)
(ii)
| x | y |
|
-3 cos 45 = -2.121 -12.000 0.000 V_x = -14.121 |
+ 3 sin 45 = 2.121 0000 -5000 V_y = -2.879
|
R = \(\sqrt{V_x^2 + Vy^2}\)
= \(\sqrt{-14.121^2} + -2.879^2\) = 14.4m/s
Ta n \(\theta = \frac{2.879}{14.121} = 0.2039\)
\(\theta = tan^{-1} 0.2039 = 11.5^o\)
R = 14.4m/s S78.5\(^o\)W
(c)(i)
| Mass/g | Weight W/N | Ext.e/cm |
|
50 100 150 200 250 |
0.5 1.0 1.5 2.0 2.5 |
6,5 11.0 15.0 20.0 25.0 |
(iii) Force constant = slope
\(\frac{\Delta W}{\Delta e} = \frac{3.1 - 1.0}{30 - 11} = \frac{2.1}{9} = 0.1105\)
(iv) Nature length = 38.0 - 25 = 13cm