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$\bullet$ Friction at the hip joint. Fig-ure 5.51 shows the bone structureat the hip joint. The bones are nor-mally not in direct contact, butinstead are covered with cartilageto reduce friction. The spacebetween them is filled with water-like synovial lluid, which furtherdecreases friction. Due to thisfluid, the coefficient of kineticfriction between the bones canrange from 0.0050 to $0.020 .$ Thewide range of values is due to thefact that motion such as runningcauses more fluid to squirt between the bones, thereby reduc-ing friction when they strike each other.) Typically, approxi-mately 65$\%$ of a person's weight is above the hip-we'll callthis the upper weight. (a) Show that when a person is simplystanding upright, each hip supports half of his upper weight.(b) When a person is walking, each hip now supports up to2.5 times his upper weight, depending on how fast he is walk-ing. (Recall that when you walk, your weight shifts from oneleg to the other and your body comes down fairly hard on eachleg. $.$ For a 65 kg person, what is the maximum kinetic frictionforce at the hip joint if $\mu_{k}$ has its minimum value of 0.0050$?$(c) As a person gets older, the aging process, as well asosteoarthritis, 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 . Whatwould be the greatest friction force for the walking person inpart $(b) ?$ The increased friction causes pain and, in addition,wears down the joint even more.

a) $\frac{w}{2}$b) 20.7 $\mathrm{N}$c) 310.5 $\mathrm{N}$

Physics 101 Mechanics

Chapter 5

Applications of Newton's Law

Motion Along a Straight Line

Motion in 2d or 3d

Newton's Laws of Motion

Applying Newton's Laws

Rutgers, The State University of New Jersey

University of Michigan - Ann Arbor

University of Sheffield

McMaster University

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okay, Very wordy problem here, but it's not super involved is also see S O for part A. Let's start by dealing free body diagram here. So you have the way of the person's upper body double use of you acting downwards. And then you have normal force from each hip acting directly upwards. So that's a very simple situation. And that is exactly what's happening with the person standing upright. And so the use Newton's second lively was off, forcing. Why direction? And because there's no because it is an equilibrium, uh, met force Zero. So that just means that two times normal force one one each from each help minus w Cebu equaled Sarah and so w serve you. The weight of the upper body is just twice the normal force, meaning that or, in other words, the normal force is half off the weight of the upper body says we want to have shown on the problem. Uh, okay, and that's for you and part B. And we have that maximum normal force is 2.5 times the weight of the upper body, and we know that weight of the upper body 65% the mass of the massive ah, 65% of the total weight of a person's that would be 25 multiplied by 250.65 that 65% times mg mass attention fashion due to craft. Okay, Therefore very simply kinetic friction is equal. Teo Contraction forces people Tio confessions connect fiction times, normal forest And so that's 0.5 times 2.5 times 2.65 times mg and mg. Now this M is just 65 kilograms. She is 9.8 meters per second squared. Okay? And you write that down. You work that out and you get 5.2 suits and finally in part. See, we have that maximum Connecticut perfect friction coefficient is 0.3. And so it's the same equation we using here because, um, you care turns. And so it's 0.3 times. Of all the stuff Red 0.3 times, 2.5 times is 0.65 times, 65 times 9.8 and we get ah, maximum force of 310 newts. Yeah,

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