Problem

$\bullet$ At a construction site, a pallet of br…

05:29

Problem 32 Hard Difficulty

$\bullet$ Friction at the hip joint. Fig-
ure 5.51 shows the bone structure
at the hip joint. The bones are nor-
mally not in direct contact, but
instead are covered with cartilage
to reduce friction. The space
between them is filled with water-
like synovial lluid, which further
decreases friction. Due to this
fluid, the coefficient of kinetic
friction between the bones can
range from 0.0050 to $0.020 .$ The
wide range of values is due to the
fact that motion such as running
causes 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 call
this the upper weight. (a) Show that when a person is simply
standing upright, each hip supports half of his upper weight.
(b) When a person is walking, each hip now supports up to
2.5 times his upper weight, depending on how fast he is walk-
ing. (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 $\mu_{k}$ has its 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.

Answer

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

Related Courses

Physics 101 Mechanics

Discussion

You must be signed in to discuss.

Top Physics 101 Mechanics Educators

Christina K.

Rutgers, The State University of New Jersey

Watch More Solved Questions in Chapter 5

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Problem 7

Problem 8

Problem 9

Problem 10

Problem 11

Problem 12

Problem 13

Problem 14

Problem 15

Problem 16

Problem 17

Problem 18

Problem 19

Problem 20

Problem 21

Problem 22

Problem 23

Problem 24

Problem 25

Problem 26

Problem 27

Problem 28

Problem 29

Problem 30

Problem 31

Problem 32

Problem 33

Problem 34

Problem 35

Problem 36

Problem 37

Problem 38

Problem 39

Problem 40

Problem 41

Problem 42

Problem 43

Problem 44

Problem 45

Problem 46

Problem 47

Problem 48

Problem 49

Problem 50

Problem 51

Problem 52

Problem 53

Problem 54

Problem 55

Problem 56

Problem 57

Problem 58

Problem 59

Problem 60

Problem 61

Problem 62

Problem 63

Problem 64

Problem 65

Problem 66

Problem 67

Problem 68

Problem 69

Problem 70

Problem 71

Problem 72

Problem 73

Problem 74

Problem 75

Problem 76

Problem 77

Problem 78

Problem 79

Problem 80

Problem 81

Problem 82

Problem 83

Problem 84

Problem 85

Problem 86

Problem 87

Problem 88

Problem 89

Problem 90

Problem 91

Video Transcript

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,

We have video lessons for 97.51% of the questions in this textbook