The lubrication of bone joints is a subject of ongoing medical research. two bones connected at a joint do not touch. the bones are covered in articular cartilage, and are surrounded by lubricating synovial fluid. rheumatoid arthritis results in overproduction of synovial fluid, swollen joints, and difficult and painful movement. other joint disorders degrade the synovial fluid, directly increasing the friction between the bones, resulting in painful motion.

part a

to measure the effective coefficient of friction in a bone joint, a healthy joint (and its immediate surroundings) can be removed from a fresh cadaver. the joint is inverted, and a weight is used to apply a downward force on the head of the femur into the hip socket. then, a horizontal force is applied and increased in magnitude until the femur head rotates clockwise in the socket. the joint is mounted in such a way that will cause clockwise rotation, not straight-line motion to the right. the friction force will point in a direction to oppose this rotation.

draw vectors indicating the normal force

(magnitude and direction) and the frictional force
(direction only) acting on the femur head at point a.

assume that the weight of the femur is negligible compared to the applied downward force.

draw the vectors starting at the black dot. the location, orientation and relative length of the vectors will be graded.