A spring with a constant of #9 (kg)/s^2# is lying on the ground with one end attached to a wall. An object with a mass of #2 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
Mar 4, 2016

Answer:

#Delta x=7/3sqrt2" " m#

Explanation:

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#E_k=1/2*m*v^2" The Kinetic Energy of Object"#
#E_p=1/2*k*Delta x^2#
#"The Potential Energy of Spring Compressed"#
#E_k=E_p" Conservation of Energy"#
#cancel(1/2)*m*v^2=cancel(1/2)*k*Delta x^2#
#m*v^2=k*Delta x^2#
#2*7^2=9*Delta x^2#
#Delta x=sqrt(2*7^2/9)#
#Delta x=7/3sqrt2" " m#