You have been asked to design a \"ballistic spring system\" to measure the speed

Question

You have been asked to design a "ballistic spring system" to measure the speed of bullets. A bullet of mass m is fired into a block of mass M. The block, with the embedded bullet, then slides across a frictionless table and collides with a horizontal spring whose spring constant is k. The opposite end of the spring is anchored to a wall. The spring's maximum compression d is measured.

What was the speed of a 1.7 g bullet if the block's mass is 1.2 kg and if the spring, with k = 49 N/m , was compressed by 16 cm ?

What percentage of the bullet's energy is "lost"?

Explanation / Answer

Here, compressed length y = 0.16 m, mB = 0.0017 kg,

the speed of a 1.7 g bullet is calculated as follows:

vB = sqrt{[M +mB /mB2]*k}*y = 722.2 m/s

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the percentae of loss is,

  Percentage lost = 100*(1-[mB/(M+mB)]) = 99.85%

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