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## Homework Statement

A body of mass [itex]m_A=2 kg[/itex] is placed on a long board of mass [itex]m_B=8 kg[/itex] at distance [itex]d=1 m[/itex] from the rear edge of the board. The friction coefficient between the body and the board is [itex]μ=0.2[/itex]. A force of magnitude [itex]30 N[/itex] is applied to the front edge of the board and the body start moving towards the rear edge. How much time will it take to fall off the board?

## Homework Equations

The force of friction is given by [itex]F_f=F_n\cdot μ[/itex] where F_n is the normal force exerted by the object on the surface.

## The Attempt at a Solution

I tried to write down Newton's equation of motion (on the x-axis) for the body and the board as follows:

Board: [itex]F=(m_A+m_B)a_1[/itex]

Body: [itex]F\frac{m_A}{m_A+m_B}-F_f=m_A a_2[/itex] where [itex]F_f=m_Agμ[/itex].

With these equations the problems doesn't come out right...