A 1200 kg safe is 2.0 m above a heavy-duty spring when the rope holding the safe breaks. The safe hits the spring and compresses it 54 cm . What is the spring constant.

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31-05-2017
Physics

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A 1200 kg safe is 2.0 m above a heavy-duty spring when the rope holding the safe breaks. The safe hits the spring and compresses it 54 cm . What is the spring constant.

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tiara143 tiara143 · Answer 1 · 2017-06-07T17:10:46+02:00

the spring constant is 200kN/m.

The work done on the spring by the the free falling safe is equal to the kinetic energy of the spring:

W1 = [tex] \frac{1}{2} [/tex]k[tex] x^{2} [/tex]

The work done on the safe by gravity is the potential energy of the spring:

W2 = (mass of safe) x g x (height)
= 1000kg x 9.8 m/s^2 x (2 + 0.54)m
=1000kg x 9.8 m/s^2 x (2.54)m
= 24,892 N-m

W2 = W1 =24892 N-m
⇒ [tex] \frac{1}{2} [/tex]k[tex] (0.5)^{2} [/tex] = 24892 N-m

Therefore, k = [tex] \frac{(24892)*2}{0.5*0.5} [/tex]= 199136 kN/m.

The spring constant is 199,136 N/m ≈ 200 kN/m