A 3.628 ~kg freight car moving along a horizontal rail road spur track at 7.2 ~km / hour strikes a bumper whose coil springs experiences a maximum compression of 30 ~cm in stopping the car. The elastic potential energy of the springs at the instant when they are compressed 15 ~cm is

Step-by-step solution

( aligned 7.2 ~km / ram &= 7.2 5 18 ~m / s 7 / 2² &= 72 5 10 18 =2 ~m / s aligned ) firt case EC ( 1 2 k x²= 1 2 m v² ) ( 1 7 k (30 10⁻² )²= 1 2 3.628 (2)² ) (k= 4 3.628 9 10⁻² ) ( aligned EC & 1 2 k x²= 1 2 m v² & 1 2 k (30 10⁻² )²= 1 2 3.628 (2)² k &= 4 3.628 9 10⁻² aligned ) energy potential enrgy when conpressed at (15 ~cm ) ( aligned & 1 2 k (15 10⁻² )² =& 1 2 4 3.628 9 10⁻² 225 10⁻⁴ =& 1639 10⁻² 9 =& 182.206 10⁻² aligned ) ( aligned & 1 2 k (15 10² . &= 1 2 3.628 9 10⁻² 225 10⁻⁴ &= 1639 10⁻² 9 &=182.206 10⁻²