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$\bullet$ $\bullet$ The effect of jogging on the knees. High-impact activities such as jogging can cause considerable damage to the cartilage at the knee joints. Peak loads on each knee can be eight times body weight during jogging. The bones at the knee are separated by cartilage called the medial and lateral meniscus. Although it varies considerably, the force at impact acts over approximately 10 $\mathrm{cm}^{2}$ of this cartilage. Human cartilage has a Young's modulus of about 24 MPa (although that also varies). (a) By what percent does the peak load impact of jogging compress the knee cartilage of a 75 kg person? (b) What would be the percentage for a lower-impact activity, such as power walking, for which the peak load is about four times body weight?

a) 24$\%$b) 12$\%$

Physics 101 Mechanics

Chapter 11

Elasticity and Periodic Motion

Equilibrium and Elasticity

Periodic Motion

Cornell University

University of Washington

University of Winnipeg

Lectures

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Hi there, Troy G. Here for numerator. So be an interesting problem having to do with the link elasticity in the compression of of knee cartilage in terms of power walking and jogging again we're using Young's module is helps us understand lengthy elasticity. Stress force over area on the top, divided by strange experience. What is the change in shape off of a material divided by its original links of Delta L over L on the bottom and Young's is a calculable measured quantity for many materials, including the cartilage in the knee. Here. For this problem, we're told that when jogging or walking for part B, the area of impact on our cartilage is about 10 square centimeters. Recall that there is 10 to the fourth square centimeters in a square meter because it's 100 by 100 centimeter, so that converts into 1.0 times 10 to the negative third meters square were given the Youngs module ISS for the knee cartilage is 24 Mega Pascal's good s. I prefixed their mega 10 to the sixth, so why don't we communicate that in terms of Pascal's as 2.4 times 10 to the positive seven. There were also given this interesting tidbit of information at the beginning of the problem, that the impact force is about eight times the body weight of the person jogging. So we know, of course, that, um, the body weight, that gravitational force of a person's masses, that person's mass multiplied by the acceleration due to gravity downward. And here's our eight times. So for a 75 kilogram person is given in the problem. That means the the downward force again. See, I'm going to get picky with my vectors here. I'm gonna call this a negative, Um, 5880 Newton force its downward. So let's call the acceleration grabbed you downward. Why am I doing that? What? We're looking at that the compression of this cartilage material. So I would rather get a situation where the delta L we get is a negative member. Either way, we're just asked for the percentage of how much the cartilage is compressed during these activities. So that's exactly park A. When this 75 kilogram person is jogging, how much in terms of percentage is the knee cartilage compress? Well, that's simply just asking us for this ratio. What is the change in length of the cartilage as a ratio up, its are off its original ng L Okay, we're just doing some quick out, bro. We're just swapping here where we can express that strain as f over a divided by Young's module is Hopefully you contract with the algebra from our given equation there. And then we have what we need again. I'm gonna put this in as a negative. 5880 Newtons divided by Pardon me there. That should be We're So this is the 5000 Hey, Internet dating Newton's divided by the cross sectional area here, which is one times 10 to the negative third meter square. That's on top. Okay, that's Newtons per meter squared on top. That's Pascal's. So the units are gonna cancel out because we have Our Youngs module is 2.4 times 10 to the positive seventh on the bottom. And when we calculate that out, this ratio of change and link over over not over. A change in length, just over length gives us a nice clean negative zero point 245 So what is that telling us? It's compressing it by about 24.5%. Again, I like that negative there because the shape of this thing is becoming smaller. Delta album would be a negative, but either way the compression we can say is right at 24.5%. And then Part B were asked. All right, what's the compression rate if you will, Or compression percentage if we're jogging And in that situation rather than eight times the body weight were said, it's about four. Well, what are we looking at? Here we go back to our relationship. Cross sectional area stays the same, The materials the same. So the Youngs module is is the same. Essentially, we're looking at half the amount of force when we're power walking as opposed to jogging. So F is just going to go down by a factor of two. So all that's gonna do is that's just gonna change our amount of compression. It's gonna cut that in half. So I think we're safe to say, Just take this figure and divided by two to get the hears of the compression percentage when we're power walking would pay right at about 12.25 percent interesting application of the length eat elasticity of cartilage in our knees when power walking and jogging

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