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Potenua enelg) [0bcs stunt person jumps from the roof of tall building; but injury occurs because large. air-filled bag: Which one of the following best describe...

Question

Potenua enelg) [0bcs stunt person jumps from the roof of tall building; but injury occurs because large. air-filled bag: Which one of the following best describes the person lands why no injury occurs? Kun Aranceo force [o Stop thc Derson_

potenua enelg) [0bcs stunt person jumps from the roof of tall building; but injury occurs because large. air-filled bag: Which one of the following best describes the person lands why no injury occurs? Kun Aranceo force [o Stop thc Derson_



Answers

A $78.0-\mathrm{kg}$ person falls straight down from a $1.60-\mathrm{m}$ height (meas ured from his feet) and lands with weight distributed equally on both feet. To soften the blow, he bends his knees so that it takes $0.750 \mathrm{~s}$ for him to stop once his feet touch the ground. (a) What constant force does the floor exert on each foot while he's stopping? (b) Suppose instead that he lands stiff-legged and stops in only $0.100 \mathrm{~s}$. What force does the floor now exert on each foot? (c) In which case is he more likely to sustain injury? Why?

In this problem, we have to kill Clear the energy absorbed by the pillow and the force exerted bite. So the energy is routinized e on the force is represented by So in order to kill, clear this irregular supply The law of conservation, of energy The scenario will vehicles to absorb in that issue vehicles to Michelle potential energy that is don't e initial so it could be written as equals two m g h where they say I'm musicals to the wet so we can Why disquieting as w on edge Because of this musicals to m g. No way and setting. Where is into this? Quiet and we can write It is equals to We have the value for this w as a 480 you turn on the it is 22 meters. So this will give us a value for this W S W recalls to 11 point six. Katie, this is it cools down his power tree. No skill cleared this force. According to Newton's Law of Motion, we can white f vehicles to, um it and this can be written as, um equals toe WD wanted by G. So this question can be written as f equals two W. Eddy Wanted by Jewel Digital The gravitation explanation Why inciting well is into this question. You can white. It is f equals two. We are ready for W as it 100. And Eddie, you done on de escalation is 3.0 Mr Portman Square you wanted by G s value off 9.80 meter per second squared. So from here, we can get divided for this Fs f equals two, 147. You did. So this is the answer. Thank you.

This problem. We have an 80 telegram person jumping off 800.6 meter ledge and the first probably want to calculate the magnitude of the stopping force of the knee joint compresses by 1.5 Senate leaders at the bottom of this path when he hits the floor. Okay, so to do this, we want to look at the non conservative version of Conservation of Energy, which tells us that the initial energy plus the work done by this in the it's gonna be equal to our final energy here. The initial energy there is no kinetic. He's just starting from rest at the top of this 0.6 meter ledge. So it's just gonna be purely gravitational potential energy MGH. But recall here that the age is the distance above our zero reference here. It's gonna be a little bit different because usually reset our reference to be at the surface of birth. But with this compression, it's gonna be easier to set the reference at this person's knee at the bottom of their trajectory. So this dotted line I was going to be zero reference. That's our zero reference for the gravitational potential energy, and here we can see why that's useful, because our MGH at H is not only in the 0.6 meters of this ledge, and you could think about that. If this person didn't land with a compression that would be the same as this distance between their knees. It's not only that 0.6, but there's an additional 1.5 centimeter compression. And if that doesn't make sense, just just take a couple of seconds to convince yourself of how any point on the body J the neck have been neck. That's also gonna be the same as your 0.6. And so setting your reference, it's gonna be most convenient to be at that bottom point of the knee because it takes into consideration the additional 1.5 centimeters. So now that we have that out of the way of what is the work done by the me that's gonna be full to the force of this knee call that F K was pardoned by the distance over which it acts, and then the co sign the angle between those two hear that stopping force is gonna be opposing. The downward motion will be up, whereas the displacement is down there are greater D. C, which is that the angle between those two is 1 80 so co center born 80 is minus one and this is minus F k g. And how about our final energy final energy? This person is going to be at rest, so there's no kinetic energy and we've set our zero reference to be the location of this bottom configuration. So there's also no potential so that final energy is zero. Now we can put the pieces together. We want to know what the magnitude of stopping forces. So we see that that it's going to be equal to you. God are minus f k d plus the initial energy, which is our M G h being equal to zero. The stopping force is N g H over d. Here are h is gonna be this year 0.6 plus the compression distance of D that this is equal to one plus and he 26 over g here we've got an 80 kilogram person and that compression distances 1.5 centimeters. Put that into meters and that's if we plug this in three significant figures gives us 32,100 Newtons pretty significant. You could see why. This is why you do not want to jump stiff legged than just have all of the the impact be absorbed by the compression of your knee. So the next part is kind of the more realistic situation Saying that usually you you have a significant bend in your knee when you land. And here is asking us to calculate the same stopping force if the the distance over which of acts is 0.3 meters so we can utilize the same equation that were calculated here. But now our D is going to be 0.3 meters. So we do that. We have our f k. You call Thio one plus here we got aeighty 9.8 r h is still 0.6, but now are D is 0.3 and this get us to three significant figures. 2350 news showing us why it ISS is much better of an idea toe bend your knees when you land, which is also just a natural thing for sea. It wants us to compare these forces with the weight of the person. So here if we were to look at the ratio of the weight and what would we want to put on? Let's put the stopping course on the numerator just cause it's gonna be larger than the weight on the bottom. So this we have is being mg your 0.6 plus the D over the This is divided by energy. So we see that that ratio ratio is just equal to this one plus 0.6 divided by whatever our compression distances. Whatever the force, distance the distance over which that stopping forces acting so and part, eh? Chris is equal to one plus 0.6 divided by 1.5 centimeters, and this ratio comes out Thio 41 in Part B. We had that acting over going three meters. So we see that being three. And this is also a good representation of how significant that force in part is. That's stopping force is gonna be 41 times your your weight, whereas of you if you if you bend your knee to absorb your impact, it's only gonna be three times your weight

Question number 75 Mars off person is m equals Do 75. Yeah, G area is a quality 0.3. Media is swell. The initially lost is you go to 60. Me that. But it's again that they made. This trend is saying Michael do five into can do the power five Newton but military squad, the distance office stopping is one meter. So now using that are the question off motion weakened I lost equals zero. This is a quote to initial velocity squared, which is 60. It's what, minus two A into stopping this tense one meter. Solving this, we will get them there. Tex elation off the person is it? Did you know that meter parts again? This choir now the average force on the person but me that is quite is f upon a which is a quarto, um a mass into x elation upon area, substituting the values 75 into 18 undead divided by zero point. Hey, solving this we will get the average force per unit area as 4.5 into 10 to the power five Newton permitted is square. We can conclude there. This force per unit area is less than the ultimate strength off the body, so that person will not get injured

Question Number 22. The mosque is the dignity and the initial height. Yeah, a. Let is a 2000 meters. In the first case, the parachute is opened at an altitude off at equal to no wonder made that the force, when the parachute disclosed, is equal to 50. You're done, and when the parachute is open, open the frictional force. It's 3600 new gun. So now, for the first part of the question, we can that the initial additional potential energy mg let minus the work done by the frictional force. When the parachute disclosed its FC, you have the ledge. Minuses. Moral edge minus have open. In the the height that was a parachute is open, it's more. Let's is equal to Oh, I m. And finally, last year, the wrong, substituting the values it be in the 9.8 in the house and minus FC. It's Rippey in tow. Hyundai in tow, 800 minus that the 600 in tow 200. They should be equal to half times it be into velocity and the ground. He is far solving this. We will get the velocity equal to 24.5 me that, but its second. Now For the second part of the question, this is we lost a 24.5 m pass again is very large to learned on the ground. So the pilot will be in your Yes, sir. My leg will be injured in Parsi. It is given if the velocity of the around this 5 m per second then we have to find the height that was a parachute is open so again using the expression in by bay and yet which is a key into 9.8 into initial high top 1000 m minus. We've been your guns into initial hide 1000 minus the height at which the parachute is open X minus like the 600 eggs. And they should be quick half times must a big aggie into below Ceasefire, which is five is what? So solving this We will get that value off x or the altitude at which the parachute should be open X equal to to one bird six wine five made that in the body. We know that the frictional force by the air is directly proportional to the velocity squared. So as the velocity off the person increases on moving towards the are the frictional force also in prison. So they're Jepsen's made in question about the frictional forces are not realistic, so we can say that exemption Cinda question are not realistic.


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