An engine is attached to a wagon through a shock absorber of length 1.5 m. The system with a total mass of 50,000 kg is moving with a speed of 36 ^kmh(-1) when the brakes are applied to bring it 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, calculate the spring constant.

An engine is attached to a wagon through a shock absorber of length 1.

1.	An engine is attached to a wagon through a shock absorber of length 1.5 m. The system with a total mass of 50,000 kg is moving with a speed of 36 ^kmh(-1) when the brakes are applied to bring it 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, calculate the spring constant.
Answer» Solution :m = 50,00 kg v = 36 km/h ` = (36xx1000)/(60xx60)` = 10 m/s X = 1.0 m ` K = 1/2 mv^(2)` ` = 1/2 xx 50000 xx(10)^(2)` ` = 25000 xx100 J ` `= 2.5 xx10^(6)` J Since , 90 % of KE of the system is lost due to friction , therefore 10 % energy transferred to SHOCK ,absorber , is given by `Delta E = 1/2 kx^(2)` `DeltaE = 10 % of K ` ` :. 1/2 kx^(2) = 10/10 xx2.5 xx10^(6) J ` ` :. k = 5.0 xx10^(5) ` N/m