Solution Found!
You have been asked to design a “ballistic spring system”
Chapter 10, Problem 50P(choose chapter or problem)
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 speed \(v_{\mathrm{B}}\) in terms of \(m, M, k\), and \(d\).
b. What was the speed of a \(5.0 \mathrm{~g}\) bullet if the block's mass is \(2.0 \mathrm{~kg}\) and if the spring, with \(k=50 \mathrm{~N} / \mathrm{m}\), was compressed by \(10 \mathrm{~cm}\) ?
c. What fraction of the bullet's energy is "lost"? Where did it go?
Equation Transcription:
Text Transcription:
m
M
k
d
v_{\mathrm{B}}
m, M, k
d
5.0 g
2.0 kg
k = 50 N/m
10 cm
Questions & Answers
QUESTION:
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 speed \(v_{\mathrm{B}}\) in terms of \(m, M, k\), and \(d\).
b. What was the speed of a \(5.0 \mathrm{~g}\) bullet if the block's mass is \(2.0 \mathrm{~kg}\) and if the spring, with \(k=50 \mathrm{~N} / \mathrm{m}\), was compressed by \(10 \mathrm{~cm}\) ?
c. What fraction of the bullet's energy is "lost"? Where did it go?
Equation Transcription:
Text Transcription:
m
M
k
d
v_{\mathrm{B}}
m, M, k
d
5.0 g
2.0 kg
k = 50 N/m
10 cm
ANSWER:Step 1 of 5
In this problem, we have to find an expression for the bullet's initial speed and also the speed and find the fraction of the bullet's initial kinetic energy.