An engine is attached to a wagon through a shock absorber of length 1.5m. The system with a total mass of 40,000kg is moving with a speed of 75 kmh^-1 when the brakes are applied to bring it to rest. In the process of the system being  brought to rest, the spring of the shock absorber gets compressed by 1.0m. If 90% of energy of the wagon is lost due to friction, the spring constant is________× 10⁵ N/m.

<p>By work energy theorem</p><p>Work done = change in K.E.</p><p>Work done by friction work done by spring</p><p><span contenteditable="false"> <math> <mrow> <mo>=</mo> <mn>0</mn> <mo>−</mo> <mfrac> <mrow> <mn>1</mn> </mrow> <mrow> <mn>2</mn> </mrow> </mfrac> <mi>m</mi> <msup> <mrow> <mi>V</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msup> </mrow> </math> </span> &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &lt;!- [if gte mso 9]-&gt; &lt;!- [endif]-&gt;&nbsp;</p><p>As 90% of K.E. is losed by friction so that</p><p><span contenteditable="false"> <math> <mrow> <mo>−</mo> <mfrac> <mrow> <mn>9</mn> <mn>0</mn> </mrow> <mrow> <mn>1</mn> <mn>0</mn> <mn>0</mn> </mrow> </mfrac> <mrow> <mo> (</mo> <mrow> <mfrac> <mrow> <mn>1</mn> </mrow> <mrow> <mn>2</mn> </mrow> </mfrac> <mi>m</mi> <msup> <mrow> <mi>V</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msup> </mrow> <mo>)</mo> </mrow> <mo>−</mo> <mfrac> <mrow> <mn>1</mn> </mrow> <mrow> <mn>2</mn> </mrow> </mfrac> <mi>K</mi> <msup> <mrow> <mi>x</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msup> <mo>=</mo> <mo>−</mo> <mfrac> <mrow> <mn>1</mn> </mrow> <mrow> <mn>2</mn> </mrow> </mfrac> <mi>m</mi> <msup> <mrow> <mi>V</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msup> </mrow> </math> </span> &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&lt;!- [if gte mso 9]-&gt; &lt;!- [endif]-&gt;&nbsp;</p><p>-K -&gt;<strong>&nbsp;</strong><strong>-</strong>16 × 10⁵</p><p>K = 16 × 10⁵</p>

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