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A finger pushes a chess piece horizontally to the right with a force of 0.06 N. The piece begins to slide to the right.

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3 Answers

Hi again, Sierra -- chess piece weighs 0.2N, which is the normal force on a flat board ...
friction is 50% of the normal or 0.1N ... since the pushing force of 0.06N < 0.1N friction,
the chess piece, to me,  seems "parked" ==> no acceleration ... All the best :)


I think what's not mentioned here is the static friction which would result in a static frictional force < the push force as indicated that the piece "slides to the right"? Hence, non-zero acceleration, and slowing down due to kinetic friction.
You may be correct in this example, Alex ... usually for most surfaces, "stiction" is stronger than sliding friction --  more force is needed to "get it going" than to "keep it going" against friction. My angle is that I don't accept the problem as stated ... a "0.6N or even 0.16N" push would seem more "real-world" for me :)
Sum of the forces in the x direction = Force of finger + Force due to friction = ma
Force of finger is +0.06N. (Choosing positive direction to the right)
Force due to friction is -0.5 * Normal Force (where friction force is resisting and opposite the motion and Normal Force is equal to mg) = -0.098N (The Normal Force = mg because sum of the forces in the y-direction = 0.  Hence: Normal Force + mg = 0 => Normal Force = -m(-g) = mg )
Sum of Forces (x-direction) = +0.06N - 0.098N = ma = 0.02kg * a => solve for a
a = -1.9m/s^2
 This means that as the finger pushes the piece to the right, friction is resisting movement so much that the piece is SLOWING down at a rate of 1.9m/s^2.  Eventually the piece will move to a square and stop.  Checkmate!
Force of friction =applied force * coefficient of friction = 0.06 N * 0.5 = 0.03 N
acceleration = force/mass = (0.03 N)/(0.02 kg) = 1.5 m/s^2 


Force due to friction is u*Normal Force.  The question IS ambiguous though.  Is it sliding to the right on its own? Or is it sliding to the right because of the finger?  I think it's the latter.