How does friction affect the stopping distance of a moving crate?

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Friction plays a crucial role in determining the stopping distance of a crate in a truck moving at 15 m/s. The coefficient of static friction is 0.40, which helps calculate the frictional force that prevents the crate from sliding. To solve the problem, one must first determine the force required to keep the crate stationary relative to the truck. This force is then used as a decelerating force to calculate the minimum stopping distance. Understanding the dynamics of both the truck and the crate is essential for an accurate solution.
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Homework Statement


A crate is carried in a truck traveling horizontally at 15m/s. If the coeff of static friction between the crate and the truck is 0.40, determine the min. stopping distance for the truck such that the crate will not slide on the truck.


Homework Equations


Newton's Laws


The Attempt at a Solution


Ok, what I have so far is this:
I know that there is a frictional force preventing the box from moving. However, I don't understand how this makes sense when I have to use a 15m/s velocity movement forward from the truck. Does this require separate FBD's for both the truck and box?
 
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First you will need to find the amount of force that is needed to keep that crate in place using the coefficient of friction from the bed of the truck. Then you will need to use that force as a decelerating force which will be used to find the stopping distance.

I would think you could use only one FBD on this problem because the reference frame can be from the box. Try it and see what happens.
 
Ok in the x-direction, are the forces the following:

[Ff = 0] ?
 
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