Question
(a) What is the maximum frictional force in the knee joint of a person who supports 66.0 kg of her mass on that knee? (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.
Question by OpenStax is licensed under CC BY 4.0
Final Answer

a) 10 N10 \textrm{ N}

b) 97 N97 \textrm{ N}

Solution video

OpenStax College Physics, Chapter 5, Problem 3 (Problems & Exercises)

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Video Transcript
This is College Physics Answers with Shaun Dychko. To find the maximum force of friction in a person’s joint, we will look up our coefficient of static friction and we’ll assume it’s static friction we’re looking for since that is the maximum possible friction force we can have between two surfaces. We’re looking for the entry in Table 5.1 that says “Bone lubricated by synovial fluid”, that is a joint in other words. So the static friction force will be the coefficient of static friction multiplied by the normal force and the normal force will be the person’s weight mg so we substitute that in for Fn. So that is 0.016 times 66 kilograms times 9.8 newtons per kilogram which gives 10 newtons. Now during exercise, we’re told that the normal force can be ten times the person’s weight. So we’re gonna plug ten times mg in for Fn now, we’re also going to change the coefficient of friction to be the coefficient of kinetic friction since we’re exercising in part b, we’ll assume that the joint is in motion. So the maximum kinetic friction force you’ll experience is the coefficient of kinetic friction times its normal force which is ten mg and that’s 0.015 times ten times 66 kilograms times 9.8 newtons per kilogram, which gives a kinetic friction force of 97 newtons.

Comments

Submitted by parm on Fri, 06/17/2022 - 13:25

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I'm sort of confused on why the answer calls for the kinetic coefficient of friction for the joint. I thought the question called for the max force of friction during strenuous exercise a joint can take? when I think of max I think of the limit before the static friction in the joint becomes kinetic. and wouldn't kinetic friction in the joint mean that the joint is buckling? and doesn't kinetic friction have no limit since its proportional to the normal force that is applied, such as when the increasing weight on a squat.

Hi parm, good questions. Your point about static vs kinetic friction is a good one. Yes, maximum static friction is always bigger than maximum kinetic friction. The way I read this question is that exercise implies movement - so I interpreted the friction as being kinetic in part (b). However some exercise is static in that the exercise might involve holding a challenging position. It would not be wrong to use static friction in part (b) of this solution - it's a matter of interpretation of the question. Part (a) was clearly about static friction since it involves "support", whereas part (b) is about "exercise", whatever that means.

The normal force will be the force required to prevent the person's feet (or other point of contact with the ground) from moving through the ground. It will be limited to their weight when they're stationary. It will be a bit more than their weight when they jump or land but in this scenario it's still limited by the strength of their muscles.

Hope this helps,
Shaun