Answer: You have been asked to design a “ballistic spring

Chapter 10, Problem 61GP

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Problem 61GP

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.

Hint: This is a two-part problem. The bullet’s collision with the block is an inelastic collision. What quantity is conserved in an inelastic collision? Subsequently the block hits a spring on a frictionless surface. What quantity is conserved in this collision?

b. What was the speed of a 5.0 g bullet if the block’s mass is 2.0 kg and if the spring, with k = 50 N/m, was compressed by 10 cm?

c. What fraction of the bullet’s initial kinetic energy is “lost”? Where did it go?