I am not an expert but I believe that equation only applies to gravity. It would be mu (the friction coefficient) times the force applied to the box (which, because your mass is 1 in this case, is equal to the acceleration before friction). The g you used in your post, that is equal to 9.81 m/s^2 is calculated from newton's equation F=GM/r^2. That is not the force being applied to the box. I hope that helps!
By box I meant the object. I ususually think of these objects as boxes.
Net force equals mass times acceleration.
There are two general strategies that can be used to solve this exercise.
One uses the starting point that Mister T suggests -- Express acceleration in terms of the applied force. If you can solve the equations of motion for the acceleration, you can extract the force from that.
The other uses the notion of work and kinetic energy. You are told the distance covered and you can compute the energy that must be lost...
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