An engine is attached to a wagon through a shock absorber of length 1.5 m . The entire system with a total mass of 50000 kg was moving with a speed of 36 kmh - 1 , when the brakes are applied to bring it to rest. In this process, the spring of the shock absorber gets compressed by 1. 0 m . If 90 % of the energy of the wagon is lost due to friction, the spring constant is

Question

An engine is attached to a wagon through a shock absorber of length 1.5 m . The entire system with a total mass of 50000 kg was moving with a speed of 36 kmh - 1 , when the brakes are applied to bring it to rest. In this process, the spring of the shock absorber gets compressed by 1. 0 m . If 90 % of the energy of the wagon is lost due to friction, the spring constant is, 5.0 × 10 5 N/m, 4.0 × 10 5 N/m, 1.0 × 10 5 N/m, 2.0 × 10 5 N/m

MARKS App · Accepted Answer

Mass of the system ( m ) = 50000 kg Speed of the system ( v ) = 36 km/h = 3 6 × 5 1 8 m/s ∵ 1 km/h = 5 1 8 m/s = 10 m/s Compression of the spring ( x ) = 1.0 m KE of the system = 1 2 mv 2 = 1 2 × 5 0 0 0 0 × ( 1 0 ) 2 = 25000 × 100 J = 2.5 × 10 6 J Since, 90% KE of the system is lost due to friction, therefore kinetic energy transferred to shock absorber, = 10 % , K E t o t a l = 10 100 × 2.5 × 10 6 J = 2.5 × 10 5 J This K.E. is converted in to spring energy 2.5 × 10 5 = 1 2 k x 2 2.5 × 10 5 = 1 2 × k × 1 2 k = 5.0 × 10 5 N/m

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