Physics Problem: Two Blocks Connected by String. Find the mass.

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Here is a problem from an "online site".

A block of mass M rests on a block of mass M1 = 5.00 kg which is on a tabletop (see figure below). A light string passes over a frictionless peg and connects the blocks. The coefficient of friction mu-k at both surfaces equals 0.330. A force of F = 67.0 N pulls the upper block to the left and the Lowe block to the right. The blocks are moving at a constant speed.

1) Determine the mass of the upper block.
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@11:11 it seems there is sign error on the second m2

stewartcopeland
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Can you solve this using the Lagrangian Method?

dimitrispapadimitriou