Forces involving static friction

AI Thread Summary
The problem involves determining the shortest distance a railroad flatcar can stop without crates sliding, given a coefficient of static friction of 0.25 and an initial speed of 48 km/h. To solve it, one must first calculate the maximum acceleration using the static friction force, which is determined by the equation f = μF. The next step involves applying kinematics to relate the initial speed to the stopping distance. Understanding the relationship between force, mass, and acceleration is crucial for finding the solution. The key is to find the maximum acceleration that static friction can provide before the crates begin to slide.
america8371
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Homework Statement


The floor of a railroad flatcar is loaded with loose crates having a coefficient of static friction of 0.25 with the floor. If the train is initially moving at a speed of 48 km/h, in how short a distance can the train be stopped at constant acceleration without causing the crates to slide over the floor?


Homework Equations


f = \mu F
F = m a


The Attempt at a Solution


This is my first post so I hope did it correctly. Ok so I first tried to draw a force diagram but this is the first problem that has included a speed into it. I know its probably something simple that I'm just not thinking of but I'm having trouble seeing how I can relate speed to any of the equations in this section. Thanks in advance.
 
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The speed will come in when you apply kinematics to find the shortest distance. But first you must find the maximum acceleration.

Hint: What force accelerates the boxes? What's the maximum value of acceleration that that force can produce?
 
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