Question

the graph shows the variation with force f of the extension s of a spring.
the work done in changing the extension of the spring from 3.0 cm to 6.0 cm is
a 15 n cm.
b 30 n cm.
c 45 n cm.
d 60 n cm.

Explanation:

Step1: Recall work - energy theorem for spring

Work done on a spring is equal to the area under the force - extension graph.

Step2: Calculate area for \(s = 0\) to \(s = 3.0\ cm\)

The area of the triangle for \(s = 0\) to \(s = 3.0\ cm\) is \(A_1=\frac{1}{2}\times F_1\times s_1\). From the graph, when \(s_1 = 3.0\ cm=0.03\ m\), \(F_1 = 10\ N\). So \(A_1=\frac{1}{2}\times10\times0.03 = 0.15\ J = 15\ N\cdot cm\).

Step3: Calculate area for \(s = 0\) to \(s = 6.0\ cm\)

The area of the triangle for \(s = 0\) to \(s = 6.0\ cm\) is \(A_2=\frac{1}{2}\times F_2\times s_2\). When \(s_2 = 6.0\ cm = 0.06\ m\), \(F_2=20\ N\). So \(A_2=\frac{1}{2}\times20\times0.06=0.6\ J = 60\ N\cdot cm\).

Step4: Calculate work done for \(s\) from \(3.0\ cm\) to \(6.0\ cm\)

The work done \(W=A_2 - A_1\). \(W=60 - 15=45\ N\cdot cm\).

Answer:

C. 45 N cm