An engine is attached to a wagon through a shock absorber of length… | JEE Main 2021 (1 Sep, Shift 2)

Q18JEE Main 2021 · 1 SEP · SHIFT 2Difficult

Spring & Elastic Energy

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 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 1.0 m. If 90% of energy of the wagon is lost due to friction, the spring constant is ____________ $\times$ 105 N/m.

Numerical answer type. Work it out, then open the answer.

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Answer: 16

$v = 72$ km/h $= 20$ m/s; $KE = \frac{1}{2}(40000)(20^2) = 8 \times 10^6$ J
Spring gets 10%: $8 \times 10^5 = \frac{1}{2}k(1.0)^2$
$k = 1.6 \times 10^6 = 16 \times 10^5$ N/m
So the answer is $16$ .

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