Take the general case of an object of mass and velocity VA

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