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## Homework Statement

A stack of two blocks sits on a frictionless surface; however, between the two blocks is a kinetic coefficient of friction μ

_{k}. External force F is applied to the top block. During the time the force is applied, the top block is displaced by x1, and the bottom block is displaced by x2. Assume enough force is applied that x1 > x2. What is the final velocity of the center of mass of the system in terms of the values above and g?

## Homework Equations

F

_{net}= ma and the standard kinematics equations

## The Attempt at a Solution

Since force is constant, acceleration is constant and x1 = 1/2at

^{2}where a = F/m - u

_{k}g. Solving for t, we get t = √(2x1/(F/m - u

_{k}g). Also, v

_{final}= 2v

_{avg}= 2 * (x1/t + x2/t) / 2 = something with u

_{k}and g in it.

The smarter method is just to use F = ma and a

_{cm}= F/2m. The final position of the center of mass is x1+x2/2 and using v

^{2}

_{f}- v

^{2}

_{i}= 2ad we get v

_{cm}= √F/2m * (x1 + x2) which doesn't involve u

_{k}or g at all.

I'm wondering whether there's a the top method is wrong or if there's a simplification step that would link the two answers.