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A person pushes two boxes with a horizontal force F of magnitude of 100 N.
If the mass of box A is 9 kg and the mass of box B is 2 kg, calculate the magnitude of the action–reaction pair between the two boxes.

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Cricetus

The magnitude of the action–reaction pair between the two boxes (A and B) will be "18.2 N".

According to the question,

Mass of box A,

  • [tex]m_A = 9\ kg[/tex]

Mass of box B,

  • [tex]m_B = 2 \ kg[/tex]

Horizontal force,

  • [tex]F_{app} = 100 \ N[/tex]

From the Newton's law,

→ [tex]F_{app} = (\frac{F_{app}}{m_A+m_B} )a[/tex]

or,

→      [tex]a = \frac{F_{app}}{(m_A+m_B)}[/tex]

Bu substituting the values, we get

→         [tex]= \frac{100}{9+2}[/tex]

→         [tex]= \frac{100}{11}[/tex]

→         [tex]9.10 \ m/s^2[/tex]

We can see that between the two boxes, the action-reaction pair exist.

then,

→ [tex]F_{action-reaction} = m_b \ a[/tex]

→                          [tex]=2\times 9.10[/tex]

→                          [tex]= 18.2 \ N[/tex] (magnitude)

Thus the above solution is appropriate.

 

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