Three blocks ib a frictionless horiztonal surface are in contact with each other

Question

Three blocks ib a frictionless horiztonal surface are in contact with each other as show in Fig. A forceF? is applied to block 1 (mass m1). Determine (a) Draw a free body diagram for each block. Determine (b) the acceleration of the system (in terms of m1, m2, and m3), (c) the net force on each block, and (d) the force of contact that each block exerts on its neighbor. (e) If m1=m2=m3= 10.0 kg and F= 96.0 N, give numerical answers to (b), (c), and (d). Explain how your answers make sense intuitively.

Im stuck on e. To find the acceleration I end up having 2 a's. a = F- F12/M1 where my F12 = (-M1)(a)+F. What do I do with that extra a? I could get it out by dividing but then I'd hve no a at all?

Thank you

Explanation / Answer

Please ask if you have any doubt.I will help you.

Lets concentrate on Block 1 :

F acts from Right and

F12 acts from left.

Supposing the whole system moves right with the same acceleration a ,

F = (m1+m2+m3) a gives a = 3.2 m/s2

Also ,the F12 will be exerted on Blocks (m2+m3) towards right by m1 .

F12 = (m3+m2) a = 64 N.

and similarly the F23 = (m3)a = 32N.

And you can clearly observe the net force acting on each block is given by

Block 1 : (m1)a = 32N

Block 2 : (m2)a = 32N

Block 3 : (m3)a = 32N

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