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 # 3 m/s# collides with and compresses the spring until it stops moving. How much will the spring compress?

1 Answer
Feb 13, 2016

Answer:

#Delta x=sqrt 18 m#

Explanation:

#"The kinetic energy of an object with ,mass of m and velocity of v is given as:"#
#E_k=1/2*m*v^2#
#E_k=1/2*4*3^2#
#E_k=18 J" Object has a kinetic energy of 18 J"#
#"The kinetic energy of object changes to potential energy on spring, if object stops:"#
#"The potential energy of compressed spring is given by:"#
#E_p=1/2*k*Delta x^2#
#E_p=1/2*2*Delta x^2#
#E_p=Delta x^2#
#E_p=E_k " Energy not lost"#
#18=Delta x^2#
#Delta x=sqrt 18 m#