Dragging a Board problem, fairly simple yet somehow I am getting it wrong?

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SUMMARY

The discussion centers on calculating the work done on a uniform board being dragged across a boundary with differing coefficients of kinetic friction. The initial frictional force is determined by the coefficient of kinetic friction in region 1 (μ1), while the final frictional force is dictated by region 2 (μ2). The net work done is calculated using the equation Wnet = -[(M*g*μ1*L)+(M*g*μ2*L)], but the user struggles with the correct interpretation of the work done as the board transitions from one region to another. A graphical representation of force versus distance is recommended to visualize the work done during the transition.

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Homework Statement



A uniform board of length and mass lies near a boundary that separates two regions. In region 1, the coefficient of kinetic friction between the board and the surface is , and in region 2, the coefficient is . The positive direction is shown in the figure.



Homework Equations



Wnet= -[(M*g*mu1*L)+(M*g*mu2*L)]



The Attempt at a Solution





^^^^^^ wouldn't that be my solution above? computer is teling me that I am wrong.
 
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Initially the board is in μ1 territory and it gets pulled into μ2 territory, right?
Is it stretched out perpendicular to the boundary?
If so, initially the force of friction is mg*μ1. After pulling the full length of the board, the force of friction is mg*μ2. So the work should be somewhere between mg*μ1*L and mg*μ2*L.

I would suggest sketching a graph of force vs distance. The area under this graph will be the work done.
 
where is the figure?
 

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