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

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SUMMARY

The discussion focuses on calculating the net work done by friction when moving a uniform board across two regions with different coefficients of kinetic friction. The board moves at a constant velocity, which implies that the net force acting on it is zero. The key equations involved are Work = Force x Distance and F = μN, where μ represents the coefficient of friction and N is the normal force. Participants suggest averaging the coefficients of friction to simplify the calculation or using integration to derive the work done over the distance of the board.

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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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