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 #2/5 kg# and speed of #1/4 m/s# collides with and compresses the spring until it stops moving. How much will the spring compress?

1 Answer
Apr 30, 2016

Answer:

#0.16m#

Explanation:

According to the law of conservation of energy, the total energy before and after a reaction must be equal.

Kinetic energy before this reaction is #1/2mv^2#, where #m# is mass and #v# is velocity. Potential energy stored in the spring is #1/2kx^2#, where #k# is the spring constant and #x# is the distance it compresses.

Therefore, according to conservation,

#1/2mv^2=1/2kx^2#

#mv^2=kx^2#

Now we can put in what we know of the values and rearrange to find #x#,

#2/5*(1/4)^2=1*x^2#

#1/40=x^2#

#x=sqrt(1/40)approx0.16m#