An engine is attached to a wagon through a shock absorber of length 1.5 m. The system with a total mass of 40,000 kg is moving with a speed of `72 kmh^(1)` when the brakes tare 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 1.0 m. If 90% of energy of the wagon is lost due to friction, the spring constant is ________ `xx 10^5` N/m.

Answer

16

Explanation

Work ` = Delta K.E.`
`W_("friction") + W_("spring") = 0 - (1)/(2) mv^(2)`
`- (90)/(100) ((1)/(2) mv^(2)) + W_("spring") = - (1)/(2) mv^(2)`
`W_("spring") = - (10)/( 100) xx (1)/(2) mv^(2) rArr - (1)/(2) kx ^(2) = - (1)/(20) mv^(2)`
`rArr k = (40000 xx (20) ^(2))/( 10 xx (1)^(2))`
`rArr 16 xx 10 ^(5) N//m`