during a test of a bulletproof vest, a handgun is fired at point blank range. th

Question

during a test of a bulletproof vest, a handgun is fired at point blank range. the mass of the bullet is 2.12 g and it takes .341 s to travel through the gun barrell, during this time it has a constant acceleration of 334m/s^2. upon hitting it, the bullet causes the vest to move inward, eventually stopping without puncturing it. if the elastic fibers in the vest have a force constant of 2.37 x 10^5 n/m, how far does the vest move inward when it stops the bullet? the bullet travels horizontally after leaving the gun barrel; air reststance can be ignored; the motion of the elastic fibers in the vest can be considered simple harmonic.

Explanation / Answer

Given: mass of the bullet m = 2.12 g time taken to travel t = 3.41 sec force constant of vest k = 2.37*10^5 N/m from Newton second law of motion F = ma........(1) -kx = ma.....(2) from 1 and 2 we have x = ma/k     = (2.12*10^-3*334) / (2.37*10^5)     = 2.98*10^-6 m

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