Frictional Force in a Knee Joint| Further Applications of Newton’s Laws: Friction, Drag, and Elasticity| College Physics| Problem 5.3

(b) During strenuous exercise, it is possible to exert forces to the joints that are easily ten times greater than the weight being supported. What is the maximum force of friction under such conditions? The frictional forces in joints are relatively small in all circumstances except when the joints deteriorate, such as from injury or arthritis. Increased frictional forces can cause further damage and pain.

SOLUTION:

Shown below is the table for the coefficient of static and kinetic friction copied from the book. The coefficients of static and kinetic friction with the system bone lubricated by the synovial fluid are 0.016 and 0.015, respectively.

PART A

To solve for the friction, we use the formula $f\le \mu N$ where $\mu$ is the coefficient of friction, and N is the normal force. We know that the normal force is equal to the weight of the body which means, for this case, the formula for friction is $f\le \mu mg$. We want the maximum friction to be developed, so we have

$f_{max}=\mu mg$

$f_{max}=0.016\left(66.0\:kg\right)\left(9.80\:m/s^2\right)$

$f_{max}=10.3488\:N$

PART B

This time, we shall use the kinetic coefficient of friction, and the normal force is now 10 times as large. So, we have

$f=10\cdot \mu _k\cdot N$

$f=10\left(0.015\right)\left(66.0\:kg\right)\left(9.80\:m/s^2\right)$

$f=97.02\:N$