?A spring has natural length \(20 cm\). Compare the work \(W_{1}\) done in stretching

Chapter 5, Problem 11

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QUESTION:

A spring has natural length \(20 cm\). Compare the work \(W_{1}\) done in stretching the spring from \(20 cm\) to \(30 cm\) with the work \(W_{2}\) done in stretching it from \(30 cm\) to \(40 cm\). How are \(W_{2}\) and \(W_{1}\) related?

Equation Transcription:

Text Transcription:

20 cm

W_1

30 cm

W_2

40 cm

Questions & Answers

QUESTION:

A spring has natural length \(20 cm\). Compare the work \(W_{1}\) done in stretching the spring from \(20 cm\) to \(30 cm\) with the work \(W_{2}\) done in stretching it from \(30 cm\) to \(40 cm\). How are \(W_{2}\) and \(W_{1}\) related?

Equation Transcription:

Text Transcription:

20 cm

W_1

30 cm

W_2

40 cm

ANSWER:

Step 1 of 4

From Hooke’s law we have,

Where, x is the distance from the natural position of the spring, which is  length.

The work done by the force  on the object is given by,

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