Solving 3 Block and Pulley Homework

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The discussion revolves around a physics homework problem involving two blocks connected by a pulley system, with friction affecting their motion. For the first question, the user attempts to calculate the frictional force needed to accelerate both blocks together but struggles to determine the friction force between them. The maximum static friction force is identified as fs = m1 * g * μ, but the user seeks clarification on the forces acting on block 1. The second question concerns finding the minimum mass of block 3 required for block 1 to begin moving relative to block 2, which remains unresolved. Overall, the user expresses confusion and requests assistance in understanding the problem.
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Homework Statement


A block of mass m1 is on top of a block of mass m2. Block 2 is connected by an ideal rope passing through a pulley to a block of unknown mass m3 as shown. The pulley is massless and frictionless. There is friction between block 1 and 2 and between the horizontal surface and block 2. Assume that the coefficient of kinetic friction between block 2 and the surface, μ, is equal to the coefficient of static friction between blocks 1 and 2.

Q1 : The mass of block 3 has been changed such that block 1 and block 2 are moving together with a given acceleration of magnitude a. What is the magnitude and the direction of the force of friction exerted by block 2 on block 1?

Q2: What is the minimum value of m3 for which block 1 will start to move relative to block 2?

Homework Equations

The Attempt at a Solution



For part 1, I thought that the force needed to move both block 1 and block 2 would be F= (m_1+m_2)a, but I couldn't think of how I should compute the friction force between block 1 and block 2. I know that the maximum friction force for block 1 is fs=m_1*g*mu

For part 2, I still couldn't get my head around it...

Please help! I'm generally confused with this problem.
 
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For part 1, can you list all forces acting on block 1, and the necessary force to accelerate it?
Part 2 will follow from part 1.
 

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