A spring with a constant of #5 (kg)/s^2# is lying on the ground with one end attached to a wall. An object with a mass of #9 kg# and speed of #7 m/s# collides with and compresses the spring until it stops moving. How much will the spring compress?

1 Answer
Feb 12, 2016

Answer:

#Delta x=21*sqrt(5)/5m#

Explanation:

#E_k=1/2*m*v^2" the kinetic energy of an object with 9 kg mass"#
#E_k=1/2*9*7^2#
#E_k=1/2*9*49#
#E_p=1/2*k*Delta x^2#
#"the potential energy of a spring compressed with Delta x"#
#E_k=E_p#
#cancel(1/2)*9*49=cancel(1/2)*5*Delta x^2#
#Delta x^2=(9*49)/5#
#Delta x=sqrt ((9*49)/5)#
#Delta x=3*7*sqrt (1/5)#
#Delta x=21*sqrt(5)/5m#