ii-a-person-has-a-reasonable-chance-of-surviving-an-automobile-crash-if-the-deceleration-is-no-more-

Name: ii a person has a reasonable chance of surviving an automobile crash if the deceleration is no more
Uploaded: 2021-08-26
Channel: Numerade
Description: (II) A person has a reasonable chance of surviving an automobile crash if the deceleration is no more than 30 $g$'s. Calculate the force on a 65-kg person accelerating at this rate.What distance is traveled if brought to rest at this rate from 95 km/h?

Question

(II) A person has a reasonable chance of surviving an automobile crash if the deceleration is no more than 30 $g$'s. Calculate the force on a 65-kg person accelerating at this rate.What distance is traveled if brought to rest at this rate from 95 km/h?

Lydia Guertin · Accepted Answer

All right. So in this problem we&#x27;re told that a human can survive a car crash, that&#x27;s less than or equal to 30 Gs of force. So if it&#x27;s maintaining under 30 Gs um of force deceleration of acceleration. I&#x27;m so sorry, I was gonna say um and we want to know first off, so one, what is the force on a 65 kg person that is decelerating at 30 Gs? So we know that force equals mass times acceleration obviously. And we have the mass. We want to know the force and we actually have the acceleration and that&#x27;s 30 Gs. And that is literally 30 Times the acceleration due to gravity, which is 9.8 m/s. So if we just multiply our 65 Times 30 times 9.8 We&#x27;ll get our force, which is 19,110 Newtons. And that&#x27;s the standard unit for force. And then second we want to know what distance are you going to move if you are decelerating at 30GS um from 95 km/h all the way down to rest. So for this we want to find out what cinematics equation we want to use. So what do we have? We have our initial velocity, our final velocity and a distance that we want to know. We don&#x27;t have any time. So that actually rules out three out of the four cinematics equations automatically. So we&#x27;re left with V squared equals V, not squared plus two times the acceleration times the distance which is delta X. So we know that our V squared is equal to zero. So now we have zero equals V not squared plus to R A. Is 30 Gs. So 30 times 9.8 times delta X. And we know that our Vienna Is 95 km/h. But what is that? In meters per second? Because that&#x27;s the standard for velocity. So we&#x27;ve got one hour equals 60 minutes times one minute, 60 seconds. Okay, we&#x27;re getting somewhere within seconds And we also know that one km Is 1000 m. So if you multiply all of that out, you&#x27;re going to get the speed in m per second that you&#x27;re moving at is about 26 .389 meters per second. So now we can solve this. And if you just move these terms around, you&#x27;ll get the delta X equals or the distance that you&#x27;re going to decelerate, or the distance you&#x27;re going to go before you hit rest Is equal to 1.184 meters. Mhm. Pretty simple. If you use your cinematics equations

Averell Hause · Answer

velocity and a formula for the displacement and the extraction. We know that the force is going to be equal to mass tended celebration. And they&#x27;re telling us that this is equal to some constant C Teach the cue TC squared other. At this point, we can say that the acceleration would be equal to C T squared, divided by M and according to the definition of acceleration, this is gonna equal the change in velocity. With respect to time, we can say that the change in velocity would be equal to C T squared, divided by, um with respect to time so times d t and so we can finally take the integral. So it be zero to V of TV and this would equal, uh, in this case, it would be C over m. So factor of those constants and then from zero to t of t square D t. And, uh, we have that V is going to be equal to C T cubed over three m. So this would be our expression for philosophy? No, for ah, the ex displacement. You know that this is equaling d X. Rather, the change of displacement with respect to time according to the definition of velocity. So we simply have to integrate again. So now it would be integrating from zero to X uh, d X. And this will be, uh, integrated from rather this one equal See over three m times the integral from zero to t of T cubed D t. And, uh, we have the X is gonna be equal to see t to the fourth, divided by 12 them. And this would be our formula for the displacement in the ex direction. That is the end of the solution. Thank you for watching.

Averell Hause · Answer

that&#x27;s e trope must support 1/6 of the weight of, more specifically, Tom&#x27;s. Wait So we can say that T vert tension vertical will be equal to 1/6 mg. So at this point, we can say T&#x27;s of one would be equal to 1/6 mg and we could solve. So this would be 1/6 time, 74 kilograms times 9.8 meters per second squared, giving US 120 0.9. Newton&#x27;s now tensions up to why would be equal to tensions of two co sign of 30 degrees. And this would equal again 1/6 mg. So to find tensions of to tensions of two would simply be equal to M G, divided by six co sign of 30 degrees. And so we can solve. This would be equal to 120.9 Nunes that would simply represent mg over six, and then this would be divided by coastline of 30 degrees. So we find that tensions of two is gonna be equal to 139 0.6 Newton&#x27;s. So we have our first answer for T someone. Do you have tea set too? And then for teeth of three. Why, ah t&#x27;s of three. Why would be equal to T&#x27;s of three co sign of 60 degrees and we know coast out of 60 degrees is gonna be 1/2. So essentially, um, tease of three would be to one over time 74 kilograms times 9.8 meters per second squared. And we find that T&#x27;s of three is gonna be equal to 60 0.45 Nunes. So this would be our final answer. That is the end of the solution. Thank you for watching.

Eric Mockensturm · Answer

Now we have says a person has a reasonable chance of surviving an automobile crash. Of the deceleration is no more than 30GS. We want to calculate the force on the 70 kg person undergoing this acceleration And then what distances travelled to the person who brought the rest at this rate from 100 km/h. So let&#x27;s see here, we have 30GS. And it&#x27;s a deceleration. So I&#x27;m gonna say is -30GS. Um, so the A is in the opposite direction as the velocity Mass 70 kg. So the forest is simply force is mass times acceleration. And that winds up being minus or 2100 G. And we can plug in um, G here And again, to two significant digits G is close to 10 and we wind up with -21000 newtons. So again, it&#x27;s roughly minus 21 20. The magnitude is roughly 21,000 newtons, 20 killer newtons of force that the person would experience. Now they ask us, how long would it take to go from 100 km/h to arrest with that? With this acceleration or deceleration. So 100 km/h is 27.8 m/s. And then our final velocity is zero. So we wind up with V. One squared equals V not squared plus two A. D. This is zero. Um, and then we can solve for D. Which is the value we want, which is um, minus B, not squared all over to a. You can use a hey here, And that gives us a distance of 13 m. So if you can, If you can stop in less than 1.3 m, then you have a decent chance or greater than if it takes you longer than this to stop. Um, and that&#x27;s, that&#x27;s why head on collisions are hitting something. That&#x27;s, you know, like a brick wall is bad because, you know, there&#x27;s this um this is a pretty long distance for something to, you know, for your friend, for the front of your car to crumple, you know? Um So again, you&#x27;re gonna be, if you hit a brick wall, you&#x27;re gonna be stopping at a a shorter distance than this, which would mean that your accelerations are going to be greater, which means the force that your experience is also going to be greater.

Averell Hause · Answer

So in order for the G&#x27;s to be less than thirty g&#x27;s by how many? But by what distance? Which should the car crumple in order to save the passenger inside in the event of a car crash? So we have an initial velocity equaling ninety five kilometers per hour and then this is a thousand meters per kilometer times Ah, one hour for every thirty six hundred seconds and this is going to be equal to twenty six point three eight nine meters per second. Now we have an acceleration of negative thirty g&#x27;s. So this is as this is nay. If they&#x27;d even negative thirty g&#x27;s that will be really close to death on ly because it&#x27;s thirty times the acceleration due to gravity that we feel normally. So even with this, it&#x27;s ah pretty low chance of survival. However we any anything above thirty g&#x27;s is a zero percent chance of survival, So we need to we need the acceleration to be at least negative two hundred and forty two hundred ninety four meters per second squared or more so it could take an XL. It it can decelerate at a slower pace, so a less negative acceleration, however, any greater than this, and the car is going to stop too quickly, and the person will experience some of the force in the car crash and ultimately die. So we have to say Ah has to be less than thirty. Has to be basically greater than negative. Thirty g&#x27;s. However, we&#x27;re trying to find how how much the car needs to crumple so we can say that velocity final squared equals velocity. Initial squared plus two eh times Delta acts. We know that the finals final velocity zero because this car is coming to arrest So we can say that Delta acts is going to be equal to negative velocity. Initial divided by two. And this is going to equal negative twenty six point three eight nine squared divided by two times negative to ninety four, and we have a Delta X equaling one point one eight meters. So it will be beneficial if the hood of the car ah extends past extends it a bit. Ah extends a bit past the ah required length because if you make the hood of the car longer, it will be able to absorb more impact. And again it&#x27;LL come closer to this one point one eight meter mark that it needs Teo crumple in order for the AA passenger to survive and experience an acceleration that won&#x27;t cause them to pass out or die. So the car must crumple at least one point one eight meters. And that&#x27;s the end of the solution. Thank you for watching.

Mayukh Banik · Answer

So for the first part, the force due to the crash is given by mass of the car times its acceleration. So we have got 800 kg for the card and the acceleration is 300 m per second squared. So the force becomes 2.4 times 10 to the Five Newton way. Know that? Uh huh. If we calculate the reaction time, then the the reaction distance is given by the not times the reaction time which comes out to be 20 times 0.6. It was 12. I made dinner. Now, using the form of the the finance squared equals we initiate square minus two acceleration times displacement. The final velocity being zero. We have just X equals V initiates were over to a equals 20 square over two times 300 acres, 0.67 committed. So the total distance record will be given by the distance that you travel while before you are able to react us. Tell the X on that will come out to be who else? Foreign 67 m now, right? The assumption here is negligible here resistance and we&#x27;re working with one B most

Lydia Guertin · Answer

Allah. So this&#x27;s problem. Eight. Check before gang Coley. Our start problem. Six. A person has a reasonable chance of surviving an automobile crash if they&#x27;d deceleration is no more than thirty g&#x27;s. Calculate the force on a sixty five kilogram person, accelerating at this rate what distances traveled if brought to rest at this rate from ninety five kilometers per hour. So first just write down the panties that were given, which is and sixty five kilograms. And we&#x27;re told that the deceleration they really just exhilaration a, um, his thirty g&#x27;s. And remember, this isn&#x27;t a simple for grams. This is the symbol for exploration to the gravity nine point eight meters per second and this is decelerating so you can put a negative sign they&#x27;re free wanting. Those really dependent the direction we picking our diagrams. And we&#x27;re also told for the second part of the problem. When I asked about the distance traveled that it starts out at with a velocity of ninety five kilometers per hour and we&#x27;re told that it&#x27;s also throughout to rest, like were asked, the distance traveled when it&#x27;s brought to rest. So that means that the final velocity is zero and where we want to find force f and the distance traveled. Well, level Delta X And we also want to convert the colossi into meters per second just so we can reporter answering you make sure all of our units are consistent. So we can, um we can do some dimensional analysis to convert this. So one hour, sixty minutes trying get seconds on bottom and in one minute you have sixty seconds and in one kilometer what meters on top From meters per second. We have a thousand meters one times ten to the three meters. So you can now plug this into a calculator ninety five, time two thousand and and divided by sixty I&#x27;m sixty the denominator. You should get twenty six point three nine years per second approximately so you can start with the first part of the problem which is asking for the force. So we are no from in second law vehicles mass times acceleration. And we&#x27;re told both of us want t so really septum multiply them together. Sixty five kilograms and the thirty g&#x27;s two sister Pretty Lina Sybil, make them vector quantities. And what do you listen to? A calculator she get nineteen thousand enduring ten millions, which we can approximate as one point nine times ten to the four seasons. Thank you. And this will be in the negative direction. Um, it sounds like when they&#x27;re asking the force required for this deceleration is already implied that we know that it&#x27;s decelerating and me are really given enough details at that point. Call it a loan, positive or negative. So you can just report the mines, shoot a few on the force and then the distance traveled. We are given suspects about the initial in final velocity. We also know the exploration and then it for this part of the problem we&#x27;re not gonna be using. Newton&#x27;s laws were really just sing out. Kanna Matics. Now so you want to find the kinnah Mac equation that it contains all the variables that you are given and want to find. So we want Delta X. We know the zero, the final, which is zero. We also know a exploration, so you don&#x27;t remember you can flip back to your book and find we have the combat equation be final squared minus V zero square, be initial over to Delta X and we just put this equation around that we have equated for Delta X. Is that everything we know? Everything. Um this plug in the values and, you know, from we&#x27;re told final ballsy zero is decelerating to rest. So then we could just plug in what we&#x27;re given and we want to use the meters per second quantity that calculated for that initial Swede. Oh, and this should to minus signs will cancel each other outlets. And you get one point one eight meters. I wish. Well, perks me as one point two meters for financing.

Lydia Guertin · Answer

for this problem. On the topic of dynamics, we are told to calculate the force on a 65 65 kg person that is decelerating at a rate of 30 Gs. And we want to know the distance through which they will travel if they are brought to rest at this rate from 95 km an hour. Now we can find the acceleration of a person having a 30 D. D 30 G. Deceleration to be A and E. Is equal to 30 Gs, knowing that each G Is 9.8 m per square second. So this gives us a deceleration of 294 m per square second. Now, the average force causing that acceleration is F. And from Newton&#x27;s second law, it&#x27;s the mass of the person, m times this acceleration. A And so if the person has a mass of 65 kgs, Decelerating at a rate of 294 meters per square second, The average false they will feel in this impact is 1.9 Times 10 to the four newton&#x27;s. Now, since the person is undergoing a deceleration, acceleration and force would be directed in opposite to the direction of motion. To find the distance traveled during the deceleration, we&#x27;ll take the initial velocity to be in the positive direction so that the acceleration will have a negative value and the final loss to be zero. So the initial speed we not is 95 kilometers per hour and we&#x27;ll convert this two m per second. And if we do do so, we get this to be 26 point 39 m/s. Using the kinda magic equation, re squared minus V North squared is able to to a into x minus X. Not, we can rearrange and find the distance over which the person would come to rest, which is x minus X. Not this is V squared minus Vinod squared over to a Which is zero 26.39 m/s squared, Divided by two times The Deceleration -294 meters per square second, which gives us the distance over which this person would come to rest To be 1.2 m.

Problem

(II) What average force is required to stop a 950…

Problem 6 Medium Difficulty

(II) A person has a reasonable chance of surviving an automobile crash if the deceleration is no more than 30 $g$'s. Calculate the force on a 65-kg person accelerating at this rate.What distance is traveled if brought to rest at this rate from 95 km/h?

Answer

$1.9 \times 10^{4} \mathrm{N}$
$1.2 \mathrm{m}$

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$1.9 \times 10^{4} \mathrm{N}$$1.2 \mathrm{m}$

Physics

Elyse G.

Farnaz M.

Aspen F.

Jared E.

Math Review - Intro

Algebra - Example 1

Douglas C. GiancoliPhysics

Elyse G.

Farnaz M.

Aspen F.

Jared E.

$1.9 \times 10^{4} \mathrm{N}$
$1.2 \mathrm{m}$

Douglas C. Giancoli

Physics