A spring with a constant of #8 (kg)/s^2# is lying on the ground with one end attached to a wall. An object with a mass of #8 kg# and speed of #6 m/s# collides with and compresses the spring until it stops moving. How much will the spring compress?

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Answer 1 · 2017-10-21T02:57:56

#6 m#

Kinetic energy of object #= (mv^2)/2#
#= (8 kg × (6 ms^-1)^2) / 2 = 144 J#

Potential energy stored in spring #= (kx^2)/2#
#= (8 kgs^-2 × x^2) / (2) = 4x^2kg.s^-2#

According to law of Conservation of Energy
Total energy of object = Total energy absorbed by spring

#144 J = 4x^2 kg . s^-2#

#x = sqrt((144) / 4) m = sqrt(36) m = 6 m#