Question

(ii) state two measurements that should be recorded in order to plot a suitable graph so as to verify hookes law (2 marks)
(iii) describe how the measurements made in (ii) can be used to determine the spring constant. (2 marks)
(b) a helical spring stretches by 0.6 cm when supporting a weight of 40 g. determine the extension when the same spring supports a weight of 65 g. (3 marks)

Explanation:

(ii) Step1: Identify key quantities for Hooke's law

Hooke's law relates force (weight) and extension.

(ii) Step2: State required measurements

Measure weight (force) applied and spring extension.

(iii) Step1: Recall Hooke's law formula

$F = kx$ where $F$=force, $k$=spring constant, $x$=extension.

(iii) Step2: Explain graph use for $k$

Plot $F$ vs $x$; $k$ is the slope of the straight line.

(b) Step1: Apply proportionality (Hooke's law)

Since $F \propto x$, $\frac{F_1}{x_1} = \frac{F_2}{x_2}$ (mass ∝ force here).

(b) Step2: Substitute values

$F_1=40g, x_1=0.6cm, F_2=65g$. $x_2 = x_1 \times \frac{F_2}{F_1} = 0.6 \times \frac{65}{40}$

(b) Step3: Calculate $x_2$

$x_2 = 0.6 \times 1.625 = 0.975cm$

Answer:

(ii) Weight (force) applied to the spring and extension of the spring
(iii) Plot force vs extension; spring constant is the slope of the linear graph
(b) 0.975 cm