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$\bullet$ $\bullet$ Stress on the shinbone. The compressive strength of our bones is important in everyday life. Young's modulus for bone is approximately 14 GPa. Bone can take only about a 1.0$\%$ change in its length before fracturing. If Hooke's law were to hold up to fracture: (a) What is the maximum force that can be applied to a bone whose minimum cross-sectional area is 3.0 $\mathrm{cm}^{2} .$ . This is approximately the cross-sectional area of a tibia, or shinbone, at its narrowest point.) (b) Estimate the maximum height from which a 70 $\mathrm{kg}$ man can jump and not fracture the tibia. Take the time between when he first touches the floor and when he has stopped to be $0.030 \mathrm{s},$ and assume that the stress is distributed equally between his legs.

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a. 4.2x10^4 Nb. 64 m

Physics 101 Mechanics

Chapter 11

Elasticity and Periodic Motion

Equilibrium and Elasticity

Periodic Motion

Rutgers, The State University of New Jersey

University of Michigan - Ann Arbor

Hope College

McMaster University

Lectures

04:12

In physics, potential energy is the energy possessed by a body by virtue of its position relative to others, stresses within itself, electric charge, and other factors. The unit for energy in the International System of Units is the joule (J). One joule can be defined as the work required to produce one newton of force, or one newton times one metre. Potential energy is the energy of an object. It is the energy by virtue of an object's position relative to other objects. Potential energy is associated with restoring forces such as a spring or the force of gravity. The action of stretching the spring or lifting the mass is performed by a force which works against the force field of the potential. The potential energy of an object is the energy it possesses due to its position relative to other objects. It is said to be stored in the field. For example, a book lying on a table has a large amount of potential energy (it is said to be at a high potential energy) relative to the ground, which has a much lower potential energy. The book will gain potential energy if it is lifted off the table and held above the ground. The same book has less potential energy when on the ground than it did while on the table. If the book is dropped from a height, it gains kinetic energy, but loses a larger amount of potential energy, as it is now at a lower potential energy than before it was dropped.

02:18

In physics, an oscillation is the repetitive variation, typically in time, of some measure about a central value or between two or more different states. The oscillation may be periodic or aperiodic.

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All right. So for the first question, was asking us What is the force? The maximum force that can be apply. Okay, we know that the force constant is he going to the forced You ever changing in displacement, which is you go to the young's modules times the cross sectional area over the land off the shin bone. And we know that the force can be go to dance modules times. The area tends to be changing displacement over the lands off the sheep. Oh, and in question, it was saying that only 1% change Ace land people factoring. Okay, So delta l O L is equal to 1% which is your 10.1 And we know they asked Modules equals 0 14 Giga Pascoe, which is 14 times tens of pope nine pascal cross sectional areas is given is 3.1 centimeter square, which is three point times tension that however negative four meters were and ivory plug in value will get force people to 14 times 10 to oppose nine pascal times three point no as 10 to the power off negative four meters square times 0.1 We got the maximum force that can be applied to the bone is 4.2 its hands. Chance to apo off four Utah. Okay, well, question be he was asking us what is his heights? Um, the maximum height that a person with a 70 kilo grand can jump and all fracture the tibia. Okay, so we know that the total imposed J here is the total impulse is equal to the maximum force, minus the gravity off the person and times toe imposed high. Okay. And the imposed time with us 0.3 seconds. And we know the mass is given a 70 kilograms and the force we just calculated, which is 4.2 times potential power for us. Home. Okay, If we plugging, we'll get the total imposed JSA go to times 4.2 Would have potential power for you, Tom. Minus 70 kilogram times. A gravitational constant with just 9.8 meter per second square. That's the time, which is 0.3 seconds. And this will give us the total. Impose is about 2000 and 478 point a four kilograms. Ties meter per second. Okay. And we know that due to the energy conservation law, looking at energy is equal to the potential energy. Okay. And the kinetic energy is equal to the square off told the post until the impulse you are by two times old mass. Okay, And this will give us J square over to him is equal to MGH. So age is equal to J square over to M squared G. And if we plug in the values we got 2000 and 478 pointing a four Children times meter per second. Jose Square. Do you have I to times 70 kilograms square? That's the gravitational constant, which is 9.8 meter per second square. This will give us the highs as well. Uh, I'm sorry. Here, 64 meter. Okay. And that's the answer for this question. Thank you.

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