The diagrams show three unknown forces, F1, F2, and F3, pushing one, two, or thr

Question

The diagrams show three unknown forces, F1, F2, and F3, pushing one, two, or three boxes along a frictionless surface. Force F1 produces an acceleration a1 = 2.7 m/s2, force F2 an acceleration a2 = 1.6 m/s2, and force F3 an acceleration a3 = 1.0 m/s2. The short square boxes have mass m, and the tall rectangular boxes have mass 2m. Rank the following forces according to increasing magnitude, from smallest to largest. E.g., enter ABCDEF. If two forces are equal, enter the letters in alphabetical order. F1 F2 F3 contact force between boxes B and C contact force between boxes H and I contact force between boxes I and J

Explanation / Answer

Apply Newtons second law to the blocks

for accleration a1

F1 = m_A a1 = m *2.7

for accleration a2

F2 = (m_c + m_B) a2 = ( m+ 2m) 1.6 m/s^2 = m *4.8

for accleration a3

F3 = (m_H + m_I + m_J )a3= ( m+ 2m + m) 1 ms^2 = m *4

FBC = m_B*a2 = 2m*1.6 = 3.2m

FHI = m*a3 = m

FIJ = FHI + 2m*a3 = m + 2m = 3m

so the force from smallest to greatest is EAFDCB

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