Questions is...
a small is resting on a larger box, which is resting on a table. When an applied force is applied to the larger box, the two boxes move together. The small box does not slip.

If the acceleration of the pair of boxed has a magnitude of 2/5m/s^2, determine the smallest coefficient of friction between the boxes that will percent slippage.

I'm not sure where to even start... If the object is accelerating, wouldn't the small box slip off eventually? Or are we supposed to find static friction? ....

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Doc Al
Mentor
The only force accelerating the small box is static friction. What friction force is required? (Hint: Let "m" stand for the mass of the small box.)

Would I need to use a formula where the masses cancel? The only value the question gives us is the acceleration... which is 2.5m/s². Also the 9.8N/kg which is always assumed...

...I'm looking for µ, right?

Doc Al
Mentor
Would I need to use a formula where the masses cancel?
The mass will cancel, which is why I suggest labeling it "m" and continuing.

...I'm looking for µ, right?
That's right.

Hints: You'll need to combine two formulas: (1) Newton's 2nd law; (2) The formula for maximum static friction. (That second formula contains µ.)

alright,
so
F(s) = ma

F(N) - F(g) = 0
F(N) = F(g)
F(N) = mg

F(s) = µ(s) F(N)
ma = µ(s)mg
a/g = µ(s)
[2.5m/s²] / [9.8m/s²]= µ(s)
therefore, the smallest coefficient of friction between the boxes that will prevent slippage is 2.6x10^(-1)

something like that?

Doc Al
Mentor
Exactly like that.

wow thanks