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Car's bumper is designed to withstand a 5.76 km/h (1.6-m/s) collision with an immovable object without damage to the body of the car: The bumper cushions the s...

Question

Car's bumper is designed to withstand a 5.76 km/h (1.6-m/s) collision with an immovable object without damage to the body of the car: The bumper cushions the shock by absorbing the force over distance. Calculate the magnitude of the average force on a bumper that collapses 0.150 m while bringing a 940 kg car to rest from an initial speed of 1.6 m/s_

car's bumper is designed to withstand a 5.76 km/h (1.6-m/s) collision with an immovable object without damage to the body of the car: The bumper cushions the shock by absorbing the force over distance. Calculate the magnitude of the average force on a bumper that collapses 0.150 m while bringing a 940 kg car to rest from an initial speed of 1.6 m/s_



Answers

A car’s bumper is designed to withstand a 4.0-km/h (1.1-m/s) collision with an immovable object without damage to the body of the car. The bumper cushions the shock by absorbing the force over a distance. Calculate the magnitude of the average force on a bumper that collapses 0.200 m while bringing a 900-kg car to rest from an initial speed of 1.1 m/s.

All right. So course are design. We have a bumper. They're designed to basically have a collision at a speed of four kilometers an hour or 1.1 meters per second with immovable objects. And there shouldn't be any damage of the vehicle because the bumpers designed to cushion the shop. So when one of these calculates the average force the man to the average force onion, your typical bumper during where it collapses zero point 0.200 meters while bringing it's meters while bringing a vehicle of Mass m equal to 900 kilograms caressed where the initial speed V one is equal to or not, I should say, rather who the not equal to 1.1 year per second. All right, let's see, see what happens here. So remember that work is equal to a couple forms read force that distance. In this case, since his his models one d, it's just halftime. You and of course, panic energies. Well, just 1/2 MV squared. In this case, we're gonna use what we know from the work energy theorem where work is equal to delta. Okay. And because of this, you can model it as Kate final minus K initial equals your work by just expanding the Delta Ko, remember your K Finally, we're gonna be stopped. You gonna be a zero, all right. And that would go ahead and plug in what we know excited this we have. So for the works, I didn't that our force that we don't know that's what we're solving for multiplied by the distance in this case that it is compressed, which is that 0.2 meters. And then we have the chaotic energy as well. It is inside negative 1/2 times m, which is 900 times the square, which is one point once where given the problem. All right, now there's a negative on this side. And because the fact is, what we have to keep in mind here is that this force, it's definitely gonna be next. But remember, they want the magnitude of the anyway. But besides the fact, go ahead to solve this with isolates and divide by 0.2, abide by. 0.2 works for me, all right? And when we do that, so crunchy this map here we get or force people to negative 27 to 2.5. Newton's, however, the question at the beginning and told us that they want us to figure out the magnitude of the average force and what find a magnitude in this case. So we don't need to have a sign. Essentially, we can just go ahead and say This is equal to and I came. But inside the rotation, 2.722 climbs on day three. No, it's and that's your average magnitude of the force in this situation.

For two identical number cars have a linear collision like this. Okay, um, And you in the same direction they were? You okay, So these guys, these guys have this collision with each other, right? And it's perfectly elastic. And also momentum is conserved. Right. Okay, So I'm just gonna use, um, letters here, and we call this velocity A And this would be this one See, in this one D right. So if energy is conserved, we know that 1/2 and a squared plus 1/2 and b squared right is gonna equal 1/2 I m c squared, plus 1/2 m d score Nolan doing saying that the total kinetic energy adds up to the same thing. Right. Okay, well, this boils down to a squared plus B squared, Michael C squared plus B squared. Right. But if we look at momentum, we know that I am a plus. M b equals, um c plus m d. And that boils down to a plus. B equals C plus D. Because we just divide that out. Right? So then the question is, you know what actually obeys this on? And the answer is that recruiters, guests by inspection. OK, that if a is 6.0 plus 5.6, well, guess what, 5.6 plus 6.0 that works, right? And if we put him in a square, that also will work, right? And so the answer is that for this guy is that they just trade velocities, that this one's going 5.6 zero meters per second And there there is no other solution that will work right, 6.0 meters per cent per second, right? There's nothing. There's nothing else we can put in these numbers that will make this work right. And clearly this does work if we just have them trade velocities. So that's that's the trick, right? And of course, you know this If you've ever played pool and you hit a ball dead on, you know, spin and you get it straight like that, right? Um, the way both stops in the other bowl moves in the direction that you had it. Okay, this gets a lot harder. Thes masses are not the same

So this is a conservation of energy problem where you're going to have a car moving with some velocity that we're looking for, actually, and it's got this little bumper here, which is gonna sort of act like a spring. And so when it hits a wall, it's going to take all the kinetic energy that that car had, and it's gonna get converted into the potential energy of this spring, right? So this is assuming there's no energy loss anywhere else. So we are just interested in solving, for with the original Ossetia's right, someone go ahead and cancel the half and say that V looks like X time to the square root of K over in now we should go back to the problem and we can see that in of the cars. 1000 kilograms and Kay was given as five million Newtons per meter and X was given as 3.16 centimeters. But we need to convert that into meters. So is your 0.0 316 leaders and then we just fucking in right? You take 0.316 Hang with the square root of five times 10 to 6 defined by 1000. All right, put that in your trusty calculator and I got 2.23 meters per second.

For this problem. We have a card with the mess off 1300 kilograms. And we're told that he has shock absorbing bumpers that can withstand a fours off 65 kill insurance. We want to convert this killer near instant unions would be 65,000 Newtons and we're told that the maximum speed for a Nun Dominion collision he is off 10 kilometers for our we want to convert kilometers per hour two meters per second. So we would divide 10 right, 3.6 and it 2.78 meters per second. Okay, so now we we want to find the maximum acceleration off the car. So we would said equation force equals to mass times acceleration. Since the four system maximum the car can withstand the acceleration would also be the maximum. So acceleration is equal to force divided by mass. And we have both of these values. So 65 1000 mutants divided right, 1300 kilograms and we would get an acceleration off 50 meters per second squared. Now that we have the acceleration, we want to find the distance the Rupert can move. So we were used. The question. Velocity squared is equal to ah to the time success generation. I thought that eggs So if we divide with the city square, we get that the eggs is equal to velocity squared, divided by two times that acceleration. So now we can substitute the values and find the distance of a power Must be ableto so velocity with we're gonna use the values in meters per second. So it's to a 0.17 eight meters per second and we square that divided by two times 15 meters per second squared and we find that it must seem able to a distance of zero point 077 meters and this is our answer.


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