Problem

Starting with equations $m_{1} v_{1}=m_{1} v_{1}^…

04:57

Problem 50 Hard Difficulty

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Two cars collide at an icy intersection and stick together afterward. The first car has a mass of 1200 $\mathrm{kg}$ and is approaching at 8.00 $\mathrm{m} / \mathrm{s}$ due south. The second car has a
mass of 850 $\mathrm{kg}$ and is approaching at 17.0 $\mathrm{m} / \mathrm{s}$ due west. (a) Calculate the final velocity (magnitude and direction) of the cars. (b) How much kinetic energy is lost in the collision? (This energy goes into deformation of the cars.) Note that because both cars have an initial velocity, you cannot use the equations for conservation of momentum along the $x$ -axis and $y$ -axis; instead, you must look for other simplifying aspects.

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Physics 101 Mechanics

College Physics for AP® Courses

Chapter 8

Linear Momentum and Collisions

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Video Transcript

in this problem. You have one car traveling south with a 1200 kilogram mess and a speed of eight meters per second and another car traveling west at 17 meters per second with a massive 850 kilograms. And it tells us that these two cars collide and then travel off at an angle. So this is going to be a perfectly in the last two collision. But remember that moment, um, are vectors, so we can actually treat this as vectors before anything else so we can solve for our mo mentum in the UAE direction, we can assault for our momentum in the ex direction and then we can use that to determine our initial mo mentum. It's at an angle, and that momentum at the beginning at an angle would have to be equal to this moment at the end when they have collided so we can say our moment in the ex direction squared, plus our moment of the Y direction squared Square rooted will give us this moment. We're gonna kind of do this someone big Chuck. So our momentum of the ex direction is just 17 times 8 50 mass times velocity I swear. Plus that 1200 times eight squared gives us a momentum of 17,348 kilograms meters per second. Again, this is our moment before and after. And since it tells us they stick together than this, momentum is equal going to be equal to mass times velocity. So are mass is the total mess. So that's that 17,348 divided by my total mouse of 1200 plus 8 50 gives me velocity in this direction of about 8.46 meters per second. Now it also wants us this offer the direction of this velocity. So our direction of this velocity will be in the same direction as its moment. Um so we can actually go back and use moment for this. So the inverse tangent of my why component of momentum divided by my ex component of momentum. So again, inverse tensions opposite over adjacent gives me an angle of 33.6 degrees. Now this angle's measured from 180 so that's 33.6 degrees downward. If this is 180 degrees. So if we were to measure from zero that would be 1 80 plus 3 36 3 33.6 And the next part asks us to determine how much kinetic energy is lost. So for that, we simply need to calculate my kinetic energy at the beginning, my kinetic energy at the end, and then compare those two values. So my kinetic energy at the beginning, because kinetic energy is a scaler we don't need to include direction doesn't matter. That one is traveling South and one's traveling list. We can just calculate its total kinetic energy. And I get a kinetic energy of 161,000 225 jewels and then at the end there, both traveling together so I can add their masses together and then use the velocity that I found that 800 that 8.46 and this gives me a kinetic energy of 73,360. And then the difference between these two kinetic energies my final minus initial will give me in negative 87,000 800 and 64.1. Jules

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