Consider the hip joint. The bones are normally not in direct contact , but instead are covered with
cartilage to reduce friction. The space between them is filled with synovial fluid, which reduces the
friction further. Due to this fluid, the coefficient of kinetic friction between the bones can range
from 0.00500 to 0.0200. (The wide range of values is due to the fact that motion such as running
causes more fluid to squirt between the bones, thereby reducing friction when they strike each other.)
Approximately 65% of a perosn’s weight is above the hip - we will call this the upper weight.
(a) Show that when a person is simply standing upright, each hip supports half of the upper weight.
(b) When a person is walking, each hip now supports up to 2.5 times the upper weight, depending
on how fast the person is walking. (Recall that when you walk, your weight shifts from one leg
to the other and your body comes down fairly hard on each leg.) For a 65 kg person, what is the
maximum kinetic friction force at the hip joint if µk has a minimum value of 0.0050?
(c) As a person gets older, the aging process, as well as osteoarthritis, can alter the composition of
the synovial fluid. In the worst case, this fluid could disappear, leaving bone-on-bone contact with
a coefficient of kinetic friction of 0.30. What would be the greatest friction force for the walking
person in part (b)? The increased friction causes pain and, in addition, wears down the joint
even more