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A steel wire 2.3 $\mathrm{mm}$ in diameter stretc…
02:22

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Problem 75 Hard Difficulty

Parachutists whose chutes have failed to open have been
known to survive if they land in deep snow. Assume that a
75 -kg parachutist hits the ground with an area of impact of
0.30 $\mathrm{m}^{2}$ at a velocity of $55 \mathrm{m} / \mathrm{s},$ and that the ultimate strength of body tissue is $5 \times 10^{5} \mathrm{N} / \mathrm{m}^{2} .$ Assume that the
person is brought to rest in 1.0 $\mathrm{m}$ of snow. Show that the
person may escape serious injury.

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Related Courses

Physics 101 Mechanics
Physics for Scientists and Engineers with Modern Physics

Chapter 12

Static Equilibrium; Elasticity and Fracture

Related Topics

Equilibrium and Elasticity

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Video Thumbnail

04:12
Elastic Potential Energy - Overview

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.
Video Thumbnail

04:17
Elastic Potential Energy - Example 1

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.
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Video Transcript

So we're gonna be using equation to 12 seed to find the acceleration. The final squared equals the initial squared plus two times the acceleration times Delta X and so the acceleration would be equal to be final squared minus the initial squared divided by two times Delta X. We know that the final zero here, so this would be equaling negative 55 meters per second quantity squared, divided by two times negative 1.0 meters. And the acceleration here is 1513 meters per second squared. Now we can say the force over the area, which would be the stress, would be the mass times acceleration over the area. This would be equal in the mass of the person. 75 kilograms multiplied by 1513 meters per second squared, divided by 0.30 meter squared. So we're gonna be using equation to 12 seed to find the acceleration. The final squared equals the initial squared plus two times the acceleration times Delta X, and so the acceleration would be equal to be final squared minus the initial squared divided by two times doubt the X. We know that the final zero here. So this would be equaling negative 55 meters per second quantities and this is equaling 3.78 times 10 to the fifth Newtons per meter squared. And we know that the tissue strength is equaling five times 10 to the Fifth Newtons per square meter. And this is greater than 3.78 times 10 to the Fifth Newtons per square meter. So essentially we know that the average force on the person where divided by two times negative 1.0 meters and the acceleration here is 1513 meters per second squared. Now we can say the force over the area, which would be the stress, would be the mass times acceleration over the area. This would be equal in the mass of the person. 75 kilograms multiplied by 1513 meters per second squared, divided by 0.30 meter squared and is less than the strength of the body tissue. And so the person can escaped serious injury. We can say that the average force is less than these strength of tissue. This would be our final answer and again this person can escape serious injury. That is the end of the solution. Thank you for watching

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Video Thumbnail

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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.
Video Thumbnail

04:17
Elastic Potential Energy - Example 1

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.
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