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Problem 70 Hard Difficulty

Prevention of hip fractures. Falls resulting in hip fractures are a major cause of injury and even death to the elderly. Typically, the hip's speed at impact is about 2.0 $\mathrm{m} / \mathrm{s}$ . If this can be reduced to 1.3 $\mathrm{m} / \mathrm{s}$ or less, the hip will usually not fracture. One way to do this is by wearing elastic hip pads. (a) If a typical pad is 5.0 $\mathrm{cm}$ thick and compresses by 2.0 $\mathrm{cm}$ during the impact of a fall, what acceleration (in $\mathrm{m} / \mathrm{s}^{2}$ and in $g^{\prime}$ s) does the hip undergo to reduce its speed to 1.3 $\mathrm{m} / \mathrm{s} ?$ (b) The acceleration you found in part (a) may seem like a rather large acceleration, but to fully assess its effects on the hip, calculate how long it lasts.

Answer

a) $a=-58 m \cdot s^{-2}, a_{g}=-5.9 g m \cdot s^{-2}$
b) $t=12 \times 10^{-3} \mathrm{s}=12 \mathrm{ms}$

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Physics 101 Mechanics

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Video Transcript

So here B Y initial equals two meters per second. So this is Ahh how fast you come down on your hip. Ve y final equals 1.3 meters per second because if you can reduce this velocity to 1.3 meters per second ah, you can reduce damage to the hip. And there's padding on your hip that compresses by two centimeters so we can save point zero to meters. So party is asking us for the velocity felt by your hip so you can save you. I final squared equals B. Why initial squared plus two times, eh? Some. Why Delta y So a supply would equal v y final squared minus v y initial squared divided by two times delta. Why, this is equaling 1.3 squared, minus two squared, divided by two times 20.2 and a subway. I would be equal to negative 57.75 meters per second squared. If you were to divide this by 9.8, you would get a negative 5.89 geeks. No, excuse me. So this does seem like a very high acceleration sixties would make it would cause a great deal of force Teo be placed on the hip. However, the important time is the time this this is being placed on your hip so we can say that v y final It's v y final equals V Y initial plus a tea. And so we can say that Ah b Y final is going to be equal Teo zero because we're coming to arrest you or rather, ve Y final is going to be 1.3 meters per second. This is still in the cushioning. My my apologies. So t would be v y final minus v y initial divided by eh And this would be to 1.3 minus two divided by negative 57.75 and this would equal 0.121 2nd So you're the the hip is on ly being subject to this acceleration for 0.121 seconds. This is approximately equal to 12 milliseconds. So it is extremely short amount of time even though it is ah, large acceleration. This would be your answer for part A. That is the end of the solution. Thank you for watching

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