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

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SUMMARY

The discussion centers on calculating the minimum stopping distance for a truck traveling at 15 m/s, carrying a crate with a static friction coefficient of 0.40. To prevent the crate from sliding, the frictional force must be sufficient to decelerate the crate alongside the truck. The solution involves applying Newton's Laws to determine the necessary deceleration and subsequently the stopping distance, utilizing the frictional force derived from the coefficient of friction.

PREREQUISITES
  • Understanding of Newton's Laws of Motion
  • Knowledge of static friction and its coefficient
  • Ability to perform Free Body Diagrams (FBD)
  • Basic kinematic equations for motion
NEXT STEPS
  • Calculate the frictional force using the formula: F_friction = μ * N, where μ is the coefficient of friction and N is the normal force.
  • Determine the deceleration of the truck using the frictional force as the net force acting on the crate.
  • Apply kinematic equations to find the stopping distance, specifically using the equation: d = v^2 / (2a), where v is the initial velocity and a is the deceleration.
  • Explore the implications of different coefficients of friction on stopping distances in various scenarios.
USEFUL FOR

Physics students, mechanical engineers, and anyone studying dynamics and friction in motion scenarios will benefit from this discussion.

aeromat
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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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