A spring with a constant of #4 (kg)/s^2# is lying on the ground with one end attached to a wall. An object with a mass of #3 kg# and speed of #3 m/s# collides with and compresses the spring until it stops moving. How much will the spring compress?

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Answer 1 · 2016-03-12T14:25:06

#color(green)(therefore "the spring is compressed by " 3/2 sqrt 3 " m"#

This is a routine case for using law of the conservation of energy

#color(red)("The kinetic energy possessed by the body when it collides transfers to the springs potential energy")#

#color(Blue)("KE of body = PE of spring")#

#1/2 mv^2 = 1/2kx^2#

#cancel(1/2) mv^2 = cancel(1/2)kx^2#

#m = 3, v = 3, k = 4 x = ?#

# 3 *3^2 = 4x^2#

#3^3 /2^2 = x^2#

#3 *3^2 /2^2 = x^2#

#x = sqrt(3 *3^2 /2^2 ) = 3/2 sqrt 3 #

#color(green)(therefore "the spring is compressed by " 3/2 sqrt 3 " m"#