A spring with a constant of #1 (kg)/s^2# is lying on the ground with one end attached to a wall. An object with a mass of #8 kg# and speed of #9 m/s# collides with and compresses the spring until it stops moving. How much will the spring compress?
Before the reaction energy is kinetic, since the object is moving, and energy is given by
After the reaction, the energy is potential, stored in the spring, and given by
Since these two equations must be equal (conservation of energy above),
The question is asking you about how much the spring compresses, so you rearrange to make
Put in the values you know and solve