A spring with a constant of #6 (kg)/s^2# is lying on the ground with one end attached to a wall. An object with a mass of #1 kg# and speed of #4 m/s# collides with and compresses the spring until it stops moving. How much will the spring compress?

1 Answer
Feb 17, 2016

Answer:

#x=sqrt 6/3 m#

Explanation:

#"The Kinetic Energy of Object is :"E_k=1/2*m*v^2#
#E_k=1/2*1*4^2=1/2*16J#
#"The kinetic energy of object turns a potential energy on spring , if spring compresses"#
#E_p=1/2*k*Delta x^2#
#E_k=E_p#
#cancel(1/2)*16=cancel(1/2)*6*Delta x^2#
#Delta x^2=16/6#
#x=sqrt(16/6)#
#x=4*1/sqrt 6#
#x=4*sqrt 6/6#
#x=(2*sqrt 6)/3 m#