Solution Found!
Take the general case of an object of mass and velocity VA
Chapter 1, Problem 30P(choose chapter or problem)
(III) Take the general case of an object of mass \(m_{A}\) and velocity \(v_{A}\) elastically striking a stationary \(\left(v_{B}=0\right)\) object of mass \(m_{B}\) head-on.
(a) Show that the final velocities \(v_{A}^{\prime} \text { and } v_{B}^{\prime}\) are given by
\(v_{A}^{\prime}=\left(\frac{m_{A}-m_{B}}{m_{A}+m_{B}}\right) v_{A} v_{B}^{\prime}=\left(\frac{2 m_{A}}{m_{A}+m_{B}}\right) v_{A}\)
(b) What happens in the extreme case when \(m_{A}\) is much smaller than \(m_{B}\)? Cite a common example of this.
(c) What happens in the extreme case when \(m_{A}\) is much larger than \(m_{B}\)? Cite a common example of this. What happens in the case when \(m_{A}=m_{B}\)? Cite a common example.
Equation Transcription:
Text Transcription:
mA
vA
(vB=0)
mB
v'A and v'B
v_A^\prime=(\frac{m_A-m_B m_A+m_B) v_A v_B^\prime
mA
mB
mA
mB
mA= mB
Questions & Answers
QUESTION:
(III) Take the general case of an object of mass \(m_{A}\) and velocity \(v_{A}\) elastically striking a stationary \(\left(v_{B}=0\right)\) object of mass \(m_{B}\) head-on.
(a) Show that the final velocities \(v_{A}^{\prime} \text { and } v_{B}^{\prime}\) are given by
\(v_{A}^{\prime}=\left(\frac{m_{A}-m_{B}}{m_{A}+m_{B}}\right) v_{A} v_{B}^{\prime}=\left(\frac{2 m_{A}}{m_{A}+m_{B}}\right) v_{A}\)
(b) What happens in the extreme case when \(m_{A}\) is much smaller than \(m_{B}\)? Cite a common example of this.
(c) What happens in the extreme case when \(m_{A}\) is much larger than \(m_{B}\)? Cite a common example of this. What happens in the case when \(m_{A}=m_{B}\)? Cite a common example.
Equation Transcription:
Text Transcription:
mA
vA
(vB=0)
mB
v'A and v'B
v_A^\prime=(\frac{m_A-m_B m_A+m_B) v_A v_B^\prime
mA
mB
mA
mB
mA= mB
ANSWER:
Solution 30P:
We have to derive the relation between the initial velocities of the two colliding bodies and their final velocities in terms of their masses.
Step 1 of 7
Concept:
Law of conservation of linear momentum: When no external force acts on the system, then the final momentum of the system is equal to their initial momentum.