What is the maximum compression of the spring?

Question

A 1500-kg car moving at 25 m/s hits an initially uncompressed horizontal spring with spring constant of 2.0 * 10^6 N/m. What is the maximum compression of the spring? (Neglect the mass of the spring)

Answer 1

The KE of the car is "turned into" PE of the spring.

An equation and a bit of chugging...

1/2 m v^2 = 1/2 k * x^2 where we want x

1500 * 25^2 = 2000000 * x^2 so x=.68 meters (2 sig. figs.)

-Fred