(a) What is a vector quantity?
(b) Three vectors 3 ms\(^{-1}\) N 45^\circ 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.
Verified Correct Answer: .
Physical Principles & Numerical Solution
(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
Source: Myschool Past Questions Archive (Record #53338)