Question

To simulate car accidents, auto manufacturers study the collisions of moving cars with mounted springs of different spring constants. Consider a typical simulation with a car of mass 1000 kg moving with a speed 18.0 kmh^-1 on a smooth road and colliding with a horizontally mounted spring of spring constant 6.25 × 10^-3 Nm^-1 . What is the maximum compression of the spring?

Answer 1

At maximum compression x_m , the K.E. of the car is converted entirely into the P.E. of the spring.

∴ \(\frac{1}{2} kx^2_m\) = \(\frac{1}{2} mv^2\) or \(x_m\) = 2m.