Two different springs, A and B

PHYSICS · Multi-part · CBSE · Physics · Mechanical Properties of Solids · Mechanical Properties of Solids

Problem

Two different springs, A and B, obey Hooke’s law within the region tested. For each spring, the force required to produce an extension of

0.20\,\text{m}

is measured. Spring A:

F_{A}=12\,\text{N}

x=0.20\,\text{m}

Spring B:

F_{B}=8\,\text{N}

x=0.20\,\text{m}

The force–extension graphs of both springs are straight lines passing through the origin. (i) Derive the spring constant for each spring. (ii) Calculate the energy stored in each spring when stretched to

0.20\,\text{m}

. (iii) For a pulling force of

6\,\text{N}

, determine the extension produced in each spring and hence show which spring stores more elastic potential energy for this force. (iv) Explain briefly, with reference to the graphs you would draw, why the answer obtained in part (iii) is consistent with the areas under the respective force–extension lines.

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