How Does Friction Affect Work When Moving a Board Across Different Surfaces?

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The discussion centers on calculating the net work done by friction when moving a board across two surfaces with different coefficients of kinetic friction. The board moves at a constant velocity, which implies that the net force is zero. To find the work done by friction, one approach suggested is to take the average coefficient of friction between the two regions. Another method involves integrating the frictional force over the distance the board travels. The conversation highlights the need for clarity on how to determine the frictional force and the application of integration in this context.
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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 to the right.(Image uploaded)

Q.Find the net work done by friction in pulling the board directly from region 1 to region 2. Assume that the board moves at constant velocity



Homework Equations


Work=ForceXDistance
F=muXN


The Attempt at a Solution


i don't know ow to find F and don't know integration. So I am stuck on this problem.
Please help?
 

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Welcome to PF.

What if you just took the average u? What would that be for the work?

It looks like the block is symmetrically moving across both regions. Starting wholly in one and ending wholly in the other.

Otherwise you can write an equation and integrate it over the distance from 0 to L.
 

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