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Force, acceleration, coefficient of kinetic friction

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See attached file for the graph.

In the figure below, m1 = 10.7 kg and m2 = 4.15 kg. The coefficient of kinetic friction is 0.271. If the system is set in motion with m2 moving downward, what will be the acceleration of the system?

I'm not sure how to factor in the coefficient of kinetic friction. Can you show me how to do this problem?

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Here is the solution (in the attached identical files: one pdf the other MS-word)

However some general guidelines to an "algorithmical" way to solve this kind of problems.

1. Choose direction of motion for ...

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