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.
(a) Find an expression for the bullet's initial speed in terms of m, M, k, and d.
vi =
(b) What was the speed of a 6.9 g bullet if the block's mass is 2.0 kg and if the spring, with k = 59 N/m, was compressed by 10 cm?
__________ m/s
(c) What fraction of the bullet's energy is "lost"?