What Are the Mass and Friction Coefficient for the Blocks?

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The discussion revolves around analyzing the motion of two blocks with different masses and determining the dynamic friction coefficient between the larger block and the surface. When the smaller block's mass is 3kg, the larger block accelerates at 0.6 m/s², and at 4kg, it accelerates at 1.6 m/s². The relationship between the movements of the two blocks is established, with the smaller block moving twice as much as the larger block. Participants emphasize the importance of free body diagrams to understand the forces acting on the smaller block. The goal is to derive expressions for their motions and calculate the mass of the larger block and the friction coefficient.
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Figure attached below. You have a big block of mass M and a small block of mass m. When m=3kg, the acceleration of the large block is 0.6ms-2. When m=4kg, the acceleration of the large block is 1.6ms-2. The dynamic friction coefficient between the large block and the surface it slides on is μ. There is no friction between any other surface. Questions:

a) Express the relationship between the movement of block m and block M
b) Derive expressions for the motion of block m and block M.
c) Determine the mass of block M and the dynamic friction coefficient, μ, between it and the surface it slides on.

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Nice problem. So what have you got so far? How does the motion of mass m relate to the motion of mass M?
 
I know that x_m = 2 x_M, so that the small block moves two times as much as the big block. My problem is decomposing the forces.
 
Draw free body diagrams. Start with the mass m. What forces are acting on m?
 
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