Question

A 2000 Kg car is driving 15 m/s. It drives head-on into a giant spring attached
to a brick wall. The spring compresses 8 meters after the impact. What is the
spring coefficient of the giant spring? *

Answer 1

Answer:

The spring constant is k=7031.25

Explanation:

We start by using the conservation of mechanical energy:

Ui + Ki = Uf + Kf

the Ui (initial potential energy) is zero since the spring is relaxed.

In the final situation, the Kf (final kinetic energy is zero since the car and spring are NOT in motion)

Then we have:

$K_i=U_f\\\frac{1}{2} m*v^2=\frac{1}{2} k*(\Delta x)^2\\\frac{1}{2} 2000*15^2=\frac{1}{2} k*(8)^2\\k=7031.25$