Answer :
Answer with Explanation:
We are given that
Mass of one body=4.5 kg
Initial velocity of one body=8.9 m/s
Initial velocity of another body=0
Final velocity of one body=[tex]\frac{1}{5}\times 8.9=1.78 m/s[/tex]
a.We have to find the mass of the other body.
Energy and momentum are conserved in this system
[tex]p_i=P_f[/tex]
[tex]m_1v_{1i}+0=m_1v_{1f}+m_2v_{2f}[/tex]
[tex]v_{2f}=\frac{m_1v_{1i}-m_1v_{1f}}{m_2}[/tex] (equation I)
From conservation of kinetic energy
[tex]\frac{1}{2}m_1v^2_{1i}=\frac{1}{2}m_1v_{1f}^2+\frac{1}{2}m_2v^2_{2f}[/tex]
[tex]m_2=\frac{m_1v^2_{1i}-m_1v^2_{1f}}{v^2_{2f}}[/tex] (equation II)
Substitute equation I in equation II
[tex]m_2=\frac{m_1v^2_{1f}-m_1v^2_{1f}}{(\frac{m_1v_{1i}-m_1v_{1f}}{m_2})^2}[/tex]
[tex]m_2=\frac{(m_1v_{1i}-m_1v_{1f})^2}{m_1v^2_{1i}-m_1v^2_{1f}}[/tex]
Substitute the given values then we get
[tex]m_2=\frac{(4.5\times 8.9-4.5\times 1.78)^2}{4.5\times (8.9)^2-4.5\times (1.78)^2}[/tex]
[tex]m_2=3 kg[/tex]
Hence, the mass of other body=3 kg
b.We have to find the speed of two body center of mass .
The center of mass speed is given by
[tex]v_{com}=\frac{p_i}{m_1+m_2}[/tex]
Substitute the values then we get
[tex]v_{com}=\frac{m_1v_1+0}{m_1+m_2}[/tex]
[tex]v_{com=\frac{4.5\times 8.9}{4.5+3}=5.34 m/s[/tex]
Hence, the speed of the two body center of mass is given by =5.34 m/s