Question

You have been asked to design a "ballistic spring system to measure the speed of bullets. A spring whose spring constant is k is suspended from the ceiling. A block of mass M hangs from the spring. A bullet of mass m is tired vertically upward into the bottom of the block. The spring's maximum compression d is measured from its initial suspended position. Find an expression for the bullet's speed uh- Express your answer in terms of the variables m, M, k, d, and constant 9. 90 ALD x x = 4 x x x x x-10 Submit Previous Answers Request Answer X Incorrect; Try Again; 7 attempts remaining The correct answer does not depend on: Part B What was the speed of a 14 g bullet if the block's mass is 2.5 kg and if the spring, with k = 59 N/m, was compressed by 45 cm ? Express your answer using two significant figures. 190 AEC O ? m/s Submit Request Answer

Answer 1

a)

velocity of bullet block system

0.5 k d^2 = 0.5 (m + M) V^2

V = $\sqrt$ (k d^2 / ( m+ M))

using conservation of momentum

momentum of bullet initially = momentum of bullet - block system

mv = (m+M) V

m v = (m + M) $\sqrt$ ( k d^2) / $\sqrt$ (m+M)

v = (1/m) $\sqrt$ ((m+M) k d^2)

=====

b)

v = (1/0.014)* $\sqrt$ ((2.5 + 0.014)* (59*0.45^2))

v = 391.465 m/s

======

Comment before rate in case any doubt, will reply for sure.. goodluck