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(20 points) You are at the center of a boat and have been rowing the boat for a long time. You weigh only 80 kg and your 120 kg buddy Bubba has been riding at the front of your 60 kg, 4 m long boat. You come to a stop in the water and then switch places. A) What is the center of mass before you switch places

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Answer:

Explanation:

From the given information:

Let the first weight be [tex]m_ 1[/tex] = 80 kg

The weight of the buddy be [tex]m_2[/tex] = 120 kg

The weight of  Bubba be [tex]m_3[/tex] = 60 kg

Also, since you and Budda are a distance of 4m to each other, then the length to which both meet buddy will be:

[tex]x_1 = x_3 = \dfrac{4}{2} \\ \\ = 2[/tex]

The length of the boat be [tex]x_2[/tex] = 4 m

∴

We can find the center of mass of the system by using the formula:

[tex]X_{CM} = \dfrac{m_1x_1+m_2x_2+m_3x_3}{m_1+m_2+m_3} \\ \\ X_{CM} = \dfrac{(80 \times 2)+(120\times4)+(60\times2)}{80+120+60} \\ \\ X_{CM} = \dfrac{160+480+120}{260} \\ \\ \mathbf{X_{CM} = 2.923}[/tex]

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