Answered: What was the speed of a 12 g bullet if…

What was the speed of a 12 g bullet if the block's mass is 2.5 kg and if the spring, with k = 58 N/m, was compressed by 40 cm? Express your answer in meters per second to two significant figures.

Physics for Scientists and Engineers: Foundations and Connections

1st Edition

ISBN:9781133939146

Author:Katz, Debora M.

Publisher:Katz, Debora M.

Chapter11: Collisions

Section: Chapter Questions

Problem 11PQ

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Concept explainers

Spring Potential Energy

The potential energy is the energy possessed by a body by virtue of its position or the energy held by the object due to its position relative to other objects, its force like stresses, charge, and other factors affecting the particles of the body. The potential energy is the measure of the net work done by or on the body. The spring potential energy is the potential energy stored due to the deformation of an elastic spring and this elasticity is due to the stretched spring. The elasticity is the ability of a solid-state matter to come back to its equilibrium position or original position after any kind of external force is acted on it. It is also known as Elastic potential energy. The potential energy here is caused due to the displacement of the spring from its equilibrium position to another position and this potential energy is equal to the net work done due to the stretching of the spring. It also resembles the same mechanics of the oscillation of a simple pendulum, where due to the external force, the object moves from its equilibrium position to its maximum ends and the periodic motion continues till it comes back to the equilibrium position to rest. 

Question

Solve the following:

You have been asked to design a "ballistic spring system" to measure the speed of bullets. A spring whose spring constant is kk is suspended from the ceiling. A block of mass MM hangs from the spring. A bullet of mass mm is fired vertically upward into the bottom of the block. The spring's maximum compression dd is measured from its initial suspended position.

What was the speed of a 12 g bullet if the block's mass is 2.5 kg and if the spring, with k = 58 N/m, was compressed by 40 cm?
Express your answer in meters per second to two significant figures.
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