Question

Consider the diagram below where m1 = 10 kg, m2 = 5 kg and m3 = 10 kg. (a) Find the force if the acceleration of all boxes to the left is 10 m s−2 . (b) Find the forces between each box F12, F23, F21, and F32.

M13 1721 m2

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Answer #1

The acceleration of the entire system will be

a = \frac{F}{m_1 + m_2 + m_3}

Therefore

F_{12} = m_1a = \frac{m_1F}{m_1 + m_2 + m_3}

F_{23} = m_2a = \frac{m_2F}{m_1 + m_2 + m_3}

F_{32} = m_3a = \frac{m_3F}{m_1 + m_2 + m_3}

F_{21} = m_2a = \frac{m_2F}{m_1 + m_2 + m_3}

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