When cars are equipped with flexible bumpers, they will bounce off each other during low-speed collisions, thus causing less damage. In one such accident, a 1750-kg car traveling to the right at 1.50 m/s collides with a 1450-kg car going to the left at 1.10 m/s. Measurements show that the heavier car's speed just after the collision was 0.250 m/s in its original direction. Ignore any road friction during the collision. (a) What was the speed of the lighter car just after the collision? (b) Calculate the change in the combined kinetic energy of the two-car system during this collision.

Video transcript

Hey everyone, Welcome back in today's video, We have a problem where we have two cars driving towards each other, they're gonna collide and after the collision, we're going to try to determine the speed of one of those cars. So what we want to do with a problem like this is draw a little sketch of what's going on before and after the collision and try to fill in the details that were told. So before the collision, we have two cars that make up our system. So we have car A here, this will pretend this little box is a car and red and we have car B over here in blue. Okay, now we're told that the first car, car a is 850 kg and we're told that it's moving east at 1.3 m per second. Okay, so we're gonna take the right direction to be the positive X direction, and that's gonna be the east direction. Okay, so this car is moving to the east, so it's going to be moving right with a velocity Of 1.3 m/s. Okay, now, Karbi, Karbi, we're told as 400 kg. Alright, and it's headed west at one m per second, so it's going to be going to the left. So, we've chosen east to be to the right, so west is going to be to the left, we're told that its speed is going to be one m per second. We have to remember here, we're writing a velocity, the velocity, the direction matters. So if the positive direction is to the right or to the east, then this car going west is going to be going in the negative direction. Okay, so the velocity will be negative. And then after the collision, the same thing our system contains the two cars, Car A That is going to have the same mass as before kg. And Carby again, it's gonna have the same mass as before kg. Now, we're told that the first car after the collision will be traveling .435m/s in its earlier direction. In its early direction means it's going to be going to the right still with the speed mm with a velocity a final of 0.435 m per second. Okay, We're not given any information about V B F. The speed of car be after the collision. Thats what we want to try to find out determine the speed of the 400 kg car after the collision. Okay, Alright. So what we want to do for this problem is we want to deal with the conservation of momentum. We know that momentum is conserved. So we know that the momentum in the system initially is going to be equal to the momentum in the system at the end. After the collision. Now, when we look at our diagram, we already know that our system consists of car A and car be. So our total system, momentum is going to be the sum of the momentum in car A plus the momentum in Kirby. Okay. And same thing on the right, we have car at the end and we have Car B at the end that make up our system. Now recall that momentum is given by the mass times the velocity. So for each of these momentum's we can write out the corresponding equation that's going to be mass times velocity. Okay. And same thing on the right, mass times the corresponding velocity on the right hand side. We have the final velocities. Alright, and again, this is V B F. That's what we're looking for. The speed of that second car. Alright, now, let's plug in the information we know. So the massive car a is going to be 850 kg and its velocity is going to be 1.3 m/s. The massive car B is going to be 400 kg. The velocity is going to be -1 m/s. OK, recall that momentum is a vector. The direction matters, just like with velocity. So, when we're putting in the velocity into the momentum equation, we need to include that minus sign to indicate the direction and on the right hand side doing the same thing with the values we have been given final velocity N V B f again, that quantity that we're trying to find. All right. So now the hard part's done, we've figured out what's going on in the system, We've written down our equations Now, we just need to go ahead, do some addition subtraction and solve for V B F. All right. So on the left hand side we're going to get kg meters per second. Okay? So we have a kilogram and then we're multiplying by meters per second. So we're gonna get kilogram meters per second as our unit on the left hand side. We're gonna have there on the right hand side. Sorry, 369.75 kg meters per second. Same thing plus 400 kg times V B F. Alright, we're gonna go ahead and move this over to the left by subtracting the units are the same. So when we're subtracting, we can go ahead and do that. 3 35.25 kg meters per second. On the left, on the right hand side, 400 kg BBF. Alright. The last step to solve is going to be dividing by 400. Here, we have kg. So when we divide the unit of kilogram is gonna cancel and we're gonna be left with 0.838 with a unit just of meters per second, which is exactly what we want for velocity. Alright, And we notice that this velocity is positive and that tells us that the directions to the right, we've chosen right to be the positive direction. So this car is actually gonna be going to the right to the east with a speed or velocity of 0. meters per second. Okay, and that makes sense. So, the car red car initially has a higher mass and is traveling faster, so when they collide it makes sense that it's gonna push car B to the right now. Last thing the question was asking for the speed, not the velocity. So we're just going to remember that the speed Is the absolute value of velocity, and in this case it's going to be the same thing .83, m/s. Okay, that's gonna be our speed. So the answer is gonna be c Alright, thanks for watching. See you in the next video.