3 boxes are stacked on top of each other, as shown. We push on block 2, the midd

Question

3 boxes are stacked on top of each other, as shown. We push on block 2, the middle block, with a force F = 6 Newtons.

The masses are m1=1kg, m2=2kg, m3=1kg.

The coefficients of friction are:
muk= 0.1 for the kinetic friction between box 1 and the ground (Sorry, Blackboard won't do Greek letters)
mus= 0.3 for the static friction between box 1 and box 2
mus= 0.2 for the static friction between box 2 and box 3

What happens?

answers are
Boxes 1 and 2 accelerate together, at a rate of 2 m/s2, and they slide out from under box 3.
Boxes 1 and 2 accelerate together, at a rate of 0.667 m/s2, and they slide out from under box
Boxes 1, 2, and 3 accelerate together, at a rate of 1.5 m/s2
Boxes 1, 2, and 3 accelerate together, at a rate of 0.5 m/s2
Box 2 slides over the edge of box 1 and falls on the floor.
None of the above

Explanation / Answer

Suppose that alll of the system moves together with acceleration of a:

F - k (m1+m2+m3)g = (m1+m2+m3) a

6 - 0.1*(1+2+1)*9.8 = (1+2+1)*a

>>> a = 0.52 m/s2

for the block 1:

s1 m1 g > k (m1+m2+m3)g + m1 a

0.3 * 1 * 9.8 > 0.1*(1+2+1) + 1*0.52

2.94 > 0.92

this is possible

for the block 3:

s3 m3 g > m3 a

0.2 * 1 * 9.8 > 1 * 0.52

1.96 > 0.52

this is possible

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Therefore I think that our supposition is correct and the correct answer is:

Boxes 1, 2, and 3 accelerate together, at a rate of 0.5 m/s2

(hope to be correct)

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