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Problem 22 Medium Difficulty

$\cdot$ On a highly polished, essentially frictionless lunch counter, a 0.500 kg submarine sandwich moving 3.00 $\mathrm{m} / \mathrm{s}$ to the left collides with a 0.250 $\mathrm{kg}$ grilled cheese sandwich moving 1.20 $\mathrm{m} / \mathrm{s}$ to the right. (a) If the two sandwiches stick together, what is their final velocity? (b) How much mechanical energy, dissipates in the collision? Where did this energy go?

Answer

a) 1.6 $\mathrm{m} / \mathrm{s}$
b) $-1.47 \mathrm{J}$

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Video Transcript

in this problem. We have two sandwiches, one ofthe wait 0.250 kilograms on one ofthe wait 0.5 Ciro Ciro kilograms. Now they're both moving on a frictionless surface on the heavier one. It's moving with velocity three meters per second on the lighter. One is going with the velocity 1.20 meters per second. This is 3.0 meters per second. By the way. Now we want to find out the final velocity off the system if both of them stick together. So for part A, let's say after the collision, the stick together, then they would have a mass of 0.750 kilograms, adding the two masses on, Let's say it has a velocity, we in the right direction as usual, which was exacts in the horizontal direction and why access in the political direction So initially the momentum is the sums off the moon does Momenta ofthe body the sums off, then went off with sandwiches, which would be let's call this A and B sandwich. Answer would be for sandwich. A demon want that? Would we mass, which is the 1 to 5 times were lastly, which is one point. And for you sandwich be the one that would be mass, which is 0.5 times velocity, which would be minus three meters a second. No, that decoration is in the negative X direction and hence I put a minus sign before its velocity on the final moment. It would simply be the momentum off this joint large sandwich. And that would be the mask which is 0.75 times velocity. We Now we know that because there is no other horizontal force, the initial moment will be the final moment. And excuse us, Wasik will do. 0125 I'm sorry. 1.2 minus three times 0.5 divided by 0.75 This turns out to be minus 1.60 meters per second. Know that this minus means the velocity is actually in the static shin. Now that we know this velocity, we want to find out the amount of energy dissipated during this process. So the initial kind of guarantee is simply the kind of vanities off the project which would be half m v squared. And for the object it would be half time smiles. They want to fight. And so three squared, which is fun. 30.2 squared. Let's for the second object, half times mass 015 times velocity squared, three square. This turns out to be 2.43 jewels on the final kind of energy with school simply with the kind of unity off this large sandwich, which would be simply half times mass. 0.75 times velocity squared, which is 1.6 squared. As they found out here. This turns out to be 0.96 Jules, and the kind of guarantee lost would be initial minus. K final would be 1.47 jewels. This energy is converted from K kind of mechanical kinetic energy into others. Other forms of energy, like heat, usually are elastic energy. This is usually when non elastic collisions happen. This lost energy usually caused in tow, changing the shapes of objects on DH. Stuff like that

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