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Solved: CALC Varying Coefficient of Friction. A box is
Chapter 6, Problem 73P(choose chapter or problem)
Problem 73P
CALC Varying Coefficient of Friction. A box is sliding with a speed of 4.50 m/s on a horizontal surface when, at point P, it encounters a rough section. The coefficient of friction there is not constant; it starts at 0.100 at P and increases linearly with distance past P, reaching a value of 0.600 at 12.5 m past point P. (a) Use the work–energy theorem to find how far this box slides before stopping. (b) What is the coefficient of friction at the stopping point? (c) How far would the box have slid if the friction coefficient didn’t increase but instead had the constant value of 0.100?
Questions & Answers
QUESTION:
Problem 73P
CALC Varying Coefficient of Friction. A box is sliding with a speed of 4.50 m/s on a horizontal surface when, at point P, it encounters a rough section. The coefficient of friction there is not constant; it starts at 0.100 at P and increases linearly with distance past P, reaching a value of 0.600 at 12.5 m past point P. (a) Use the work–energy theorem to find how far this box slides before stopping. (b) What is the coefficient of friction at the stopping point? (c) How far would the box have slid if the friction coefficient didn’t increase but instead had the constant value of 0.100?
ANSWER:
Solution 73P
Introduction
First we have to find out the functional form of the coefficient of friction with distance (). Then we can find out the force as a function of
. From this we can calculate the work done by friction. Equating this work done by the friction with the initial kinetic energy we will get the distance the box can travell.
Step 1
Let us first find out the coefficient of friction as a function of . Since the coefficient of friction is changing linearly, we can write that
Now the given boundary conditions are
At ,
, hence we have
Also at m,
, hence we have
So the coefficient of friction can be written as
