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John’s mass is 95.6 kg, and Barbara’s is 55.3 kg. He is standing on the x axis at xJ = +10.9 m, while she is standing on the x axis at xB = +2.50 m. They switch positions. How far and in which direction does their center of mass move as a result of the switch? Distance moved by center of mass =

Answer :

Answer:Shifted towards Left by distance of 2.243 m

Explanation:

Given

Mass of john [tex]m_1=95.6 kg[/tex]

Mass of barbara [tex]m_2=55.3 kg[/tex]

John is standing at [tex]x=10.9 m[/tex]

Barbara is standing at [tex]x=2.50 m[/tex]

[tex]x_{com}=\frac{m_1x_1+m_2x_2}{m_1+m_2}[/tex]

[tex]x_{com}=\frac{95.6\times 10.9+55.3\times 2.5}{95.6+55.3}[/tex]

[tex]x_{com}=\frac{1180.29}{150.9}[/tex]

[tex]x_{com}=7.821 m[/tex]

Now if they change their Position then

[tex]x'_{com}=\frac{95.6\times 2.5+55.3\times 10.9}{95.6+55.3}[/tex]

[tex]x'_{com}=\frac{841.77}{150.9}[/tex]

[tex]x'_{com}=5.578[/tex]

Thus we can see that center of mass shifted towards left by a distance of [tex]2.243 m[/tex] because heavier is shifted towards left

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