A spring with a constant of #2 (kg)/s^2# is lying on the ground with one end attached to a wall. An object with a mass of #4 kg# and speed of #1 m/s# collides with and compresses the spring until it stops moving. How much will the spring compress?

1 Answer
Jan 3, 2018

Answer:

The spring will compress by #=1.4m#

Explanation:

Mass of the object is #m=4kg#

Speed of the object is #v=1ms^-1#

The kinetic energy of the object is

#KE=1/2mv^2=1/2*4*1^2=2J#

This energy will be stored in the spring

#E=1/2kx^2#

The spring constant is #k=2kgs^-2#

Let the compression of the spring be #=xm#

Therefore,

#2=1/2*2*x^2#

#x^2=(2*2)/2=2m^2#

The compression is

#x=sqrt2=1.4m#