Static and kinetic friction help?

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SUMMARY

The discussion focuses on calculating the coefficients of kinetic and static friction for a 5 kg box being dragged with a horizontal force of 40 N and accelerating at 3 m/s². The coefficient of kinetic friction was determined to be 0.51 using a free body diagram and force summation. For static friction, the applied force of 40 N is confirmed as appropriate for calculations, leading to the conclusion that the coefficient of static friction can be derived from the same force summation approach.

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  • Understanding of Newton's laws of motion
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  • Familiarity with friction coefficients
  • Basic algebra for force summation calculations
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AnnaRiddle
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I found a problem and I'm having one question, it goes like this:

A box of 5 kg is being dragged across the floor with a horizontal force of 40 N. If it starts at rest and it begins to accelerate at 3 m/s2 (constant acceleration), find:
A) The coefficient of kinetic friction
B) Supposing that this force (the 40 N) was just enough to start moving the box, find the coefficient of static friction

for A), I did my free body diagram and force summation, I found that my coefficient of kinetic friction is 0.51 (is it right?)

I'm not sure if my approach for B is correct. I used the same free body diagram but set my force summation equal to zero since the object has no acceleration in that case. (∑Fx = 40 N - μN = 0, where N= 49.05 N) I'm just unsure if I should use an applied force of less than 40 N (like 39 maybe?) or if I should still use 40.

Thanks!
 
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You should use 40.
 

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