A box is sliding with a speed of 4.50 on a horizontal surface when, at point P,

Question

A box is sliding with a speed of 4.50 on a horizontal surface when, at point P, it encounters a rough section. On the rough section, the coefficient of friction is not constant, but starts at 0.100 at P and increases linearly with distance past P, reaching a value of 0.600 at 12.5 past point P.
Use the work-energy theorem to find how far this box slides before stopping
What is the coefficient of friction at the stopping point?
How far would the box have slid if the friction coefficient didn't increase, but instead had the constant value of 0.100?

Explanation / Answer

Let coefficient of friction = 0.1+ kx at x= 12.5, u=0.6 =>k=0.04 => coefficient of friction =0.1 +0.04x 0.5*m*4.5^2 =m*(0.1 +0.04x)*gdx =>1.033 = 0.1x +0.02x^2 solving for x we get x=5.109 m distance box moves before stopping at stopping point ,u= 0.30436 for part 2 0.5*m*4.5^2 = 0.1*m*g*x => x=10.331 m

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