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

• jcfor3ver
In summary, the problem involves a uniform board with length and mass being pulled from one region with coefficient of kinetic friction μ1 to another region with coefficient μ2. The positive direction is shown in the figure. The work done in this scenario would fall between mg*μ1*L and mg*μ2*L, with the exact value being determined by a graph of force vs distance.

## 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.

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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