How does friction affect the acceleration of a moving box?

[hacker804]

Homework Statement

The following problem appeared in our test:
A box of mass m is moving with a constant velocity v along a smooth frictionless surface.When the box passes the boundary the frictional force acts on the box.The coefficient of kinetic friction between the box and the surface is μ_k and the box covers a distance x after crossing the boundary.
Find the dependence of acceleration on x.

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Homework Equations

∑F_x=ma_x

The Attempt at a Solution

I really did not know how to begin the solution.All I did know was that the acceleration would be equal to a=-μ_kg by Newton's Second law

 

[Orodruin]

Why don't you start from the realization you had about the acceleration? How do you relate the acceleration to the traveled distance?

 

[Chestermiller]

By any chance, do they give you the length of the box (like L)?

Chet

 

[haruspex]

the acceleration would be equal to a=-μ_kg by Newton's Second law

Not quite. You have canceled out the mass, without considering whether the masses on the two sides of the equation are the same. See Chet's hint/question.

 

[hacker804]

Actually I do not remember properly but I think the length of the block was L.

 

[haruspex]

Actually I do not remember properly but I think the length of the block was L.

I don't think it matters. The lower diagram implies x < L. If you have to allow for x > L as well it gets a little more complicated.
Let's assume x < L for now. Start again with ∑F_x=ma_x. What do you have for the force(s)?

 

[hacker804]

The only force is the frictional force F=-uk*mg

 

[Chestermiller]

What fraction of the mass is situated over the frictional surface, and what fraction of the mass is situated over the frictionless surface? What is the normal force over the frictional surface?

Chet