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Solved: You have been asked to design a “ballistic spring
Chapter 10, Problem 51P(choose chapter or problem)
Problem 51P
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 fired vertically upward into the bottom of the block and stops in the block. The spring’s maximum compression d is measured.
a. Find an expression for the bullet’s speed vB in terms of m, M, k, and d.
b. What was the speed of a 10 g bullet if the block’s mass is 2.0 kg and if the spring, with k = 50 N/m, was compressed by 45 cm?
Questions & Answers
QUESTION:
Problem 51P
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 fired vertically upward into the bottom of the block and stops in the block. The spring’s maximum compression d is measured.
a. Find an expression for the bullet’s speed vB in terms of m, M, k, and d.
b. What was the speed of a 10 g bullet if the block’s mass is 2.0 kg and if the spring, with k = 50 N/m, was compressed by 45 cm?
ANSWER:
Step 1 of 3
Part (a)
The equation for the kinetic energy of the bullet block system after collision is as follows:
The equation for the potential energy stored in the spring if the compression produced in the spring is d as follows:
The kinetic energy of the bullet block system after collision is equal to the potential energy stored in the spring by the law of conservation of energy.
The equation for the velocity of the bullet block system after collision is as follows:
