An experiment is carried out to determine the spring constant k k\,k of a spring.
A student determines the length of the unstretched spring, l0l_0l0, by using a vertical metre rule. The scale reading at the top of the coil is 10.5 cm and at the bottom of the coil is 15.0 cm.
Calculate l0 l_0\,l0 in millimetres (mm).
Complete the table below of loads W W\,W and measured lengths l l\,l to find the extension e=l−l0e = l - l_0e=l−l0 of the spring.
W / Nl / mme / mm0.0045.00.00.5058.0—1.0071.0—1.5084.0—2.0097.0—2.50110.0— \begin{array}{|c|c|c|} \hline W\text{ / N} & l\text{ / mm} & e\text{ / mm} \\ \hline 0.00 & 45.0 & 0.0 \\ \hline 0.50 & 58.0 & \text{---} \\ \hline 1.00 & 71.0 & \text{---} \\ \hline 1.50 & 84.0 & \text{---} \\ \hline 2.00 & 97.0 & \text{---} \\ \hline 2.50 & 110.0 & \text{---} \\ \hline \end{array} W / N0.000.501.001.502.002.50l / mm45.058.071.084.097.0110.0e / mm0.0—————A graph of load WWW (on the yyy-axis) against extension eee (on the xxx-axis) is plotted. Since the connection is linear, determine the gradient G G\,G of this line using the coordinates (0.0,0.0)(0.0, 0.0)(0.0,0.0) and (65.0,2.50)(65.0, 2.50)(65.0,2.50). Show your working clearly.
The gradient G G\,G is numerically equal to the spring constant kkk. Write down the value for k k\,k to a suitable number of significant figures (2 or 3) with its unit.
245 exam-style questions on CIE IGCSE Physics 1.5 Forces, covering 1.5.1a Forces, resultant force and motion, 1.5.1b Load–extension graphs and the spring constant, 1.5.1c Friction and drag, 1.5.1d Force, mass and acceleration, 1.5.1e Motion in a circular path, 1.5.2a Moment of a force, 1.5.2b Principle of moments and equilibrium, and 1.5.3 Centre of gravity and stability. Each one has a worked solution and a mark scheme showing where the marks go.