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Desert Eagle: Spring Constant of the Slide Spring

A Desert Eagle chambered for 44 mag in effect launches a bullet from a compressed slide spring (the bullet develops full velocity as the spring develops full compression). If the bullet is 180 grain (11.67 grams) and has a muzzle velocity of 1450 fps (442 m/s), assuming kinetic energy is conserved, what is the spring constant of the slide spring if the slide travels 13cm to cycle? (Note that it may cycle if it were lower - the greatest spring constant that will allow it to cycle is our goal here.)

Solution Preview

The parameters are given as: M= .00167 kg, V= 442 m/s, x= .13 m.
For energy to be conserved, the potential energy ...

Solution Summary

We find the solution by noting that for energy to be conserved, the potential energy in the compressed spring must equal the kinetic energy of the bullet when the spring has extended.