Box moving on a decelerating truck?

[dtseng96]

Homework Statement

A truck with a steel bed carries a wooden box, where μ_s = 2μ_k. The box of mass m is in the middle of the bed of length l. If the truck is moving forward with velocity v_o but is slowing down, determine the maximum distance the truck can take to stop before the box hits the cabin of the truck in terms of the variables given.

Homework Equations

F = ma, F_k = μ_kmg

The Attempt at a Solution

So my teacher said that the acceleration of the box relative to the truck is a_B = μ_kg, while the acceleration of the truck relative to the ground is a_T = -μ_kg. I'm having trouble understanding how my teacher got this... I do know that the acceleration of the block relative to the ground is a = μg, but I don't know how my teacher got the acceleration of the block relative to the truck. Can anyone help clarify my teacher's reasoning?


Any help is appreciated. Thank you so much!

In case you guys want to look at my teacher's actual solution, here it is. My question is about part b): https://dl.dropbox.com/u/12682457/m%20%26%20f%20%232%20copy.jpg

 

[Spinnor]

You wrote,

"...determine the maximum distance the truck can take to stop before the box hits the cabin..."

Shouldn't that be the minimum distance the truck can take to stop? If we decelerate slowly the box won't move relative to the truck.

Edit, ignore the above question, it now makes sense to me.

 

[Spinnor]

Does this look right?

 

[dtseng96]

@Spinnor: Yes, that does look correct to me! :) Except the question is looking for the maximum distance the truck travels :O

I discussed this again with my teacher, and apparently, there might be a mistake in my teacher's work. But yes, thank you for your solution! It gave me an idea of what the correct solution should look like...