Minimum Coefficient of static friction to keep a block from sliding?

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SUMMARY

The discussion centers on calculating the minimum coefficient of static friction required to prevent a 5kg block from sliding on a 15kg block when a 40N horizontal force is applied. The initial calculation incorrectly assumed the entire system would accelerate uniformly, leading to an erroneous coefficient of static friction of 0.20. Upon reevaluation, incorporating the applied force into the friction equation, the correct minimum coefficient of static friction is determined to be approximately 0.61, confirming the necessity of accounting for all forces acting on the system.

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Brodo17
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A 5kg block is placed on top of a 15kg block that rests on a frictionless table. The surface between the top and bottom blocks is roughened so that there is no slipping between the blocks. A 40N horizontal force is applied to the top block. What is the minimum coefficient of static friction necessary to keep the top block from slipping on the bottom block?


F=ma
f=mew FN


Ok, in my first attempt I figured that if the blocks don't slide apart, then the entire sysstem would be accelerating. I said 40N = (20)a, and found that a=2m/s^2
Using this I said (5kg)(2m/s^2) = mew FN
10 / (9.8 X 5) = .20

However the answer says that it is actually .6

Then I though that maybe the system could not accelerate at all because the opposing frictional force will stop it from accelerating.
Im not even sure if I am on the right track though, and I cannot figure this out!

Thank you!
 
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"Using this I said (5kg)(2m/s^2) = mew FN"

You forgot the 40 N pulling force.

ehild
 
What do you mean I forgot about the 40N force? Where would I put it in my equation?

Actually, If I go
(5kg)(2) = mewFN + 40N
-30N = mewFN
-30 / (-9.8 x 5) = .61

Thanks
 

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