Static and kinetic friction help?

AI Thread Summary
The discussion revolves around calculating the coefficients of kinetic and static friction for a 5 kg box being dragged with a 40 N force. The user calculated the coefficient of kinetic friction as 0.51 using a free body diagram and force summation, seeking validation for this result. For the static friction coefficient, the user is uncertain whether to use the full 40 N force or a lesser value, but is advised to use 40 N since it represents the force required to initiate movement. The calculations involve understanding the relationship between applied force, normal force, and frictional forces. The discussion emphasizes the importance of correctly applying the principles of physics in these calculations.
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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