A spring with a constant of #4 (kg)/s^2# is lying on the ground with one end attached to a wall. An object with a mass of #2 kg# and speed of #3 m/s# collides with and compresses the spring until it stops moving. How much will the spring compress?
1 Answer
The spring will compress
Explanation:
You can calculate this using Hooke's law:
You can calculate
To find the acceleration (or deceleration, in this case) with the information you have, use this convenient rearrangement of the laws of motion:
where
Substitute in the values you know
Notice that the acceleration is negative. This is because the object is slowing down (decelerating).
Substitute this equation for
Substitute this equation for
As you're working in SI units, this distance has units of meters.
The spring will compress