1) For most problems I have seen so far, the collisions of 2 objects are on frictionless surfaces and the total momentum of the 2 objects is completely conserved. What would happen if there is friction, will the total momentum of the 2 objects still be completely conserved? 2) On a two-lane highway where the posted speed limit is 80km/h, a car of mass Mc and an SUV of mass Ms have a head-on collision. The collision analyst observes that both vehicles came to a stop at the location of the initial impact. Researching the mass of the vehicles, the analyst found that Ms=2Mc. Both drivers survived the collision and each claimed to be travelling at the legal speed limit when the collision occurred. 2a) It is obvious that the analyst cannot believe both drivers. Use numerical data the explain why. 2b) If both vehicles had been travelling at the legal speed limit before the collision, how would the accident scene have been different? 2a) "both vehicles came to a stop at the location of the initial impact"<---I would like to ask how can this is possible? Shouldn't both cars rebound after the collision. Is it ever possible to have both vehicles to stop immediately after the collision? (i.e. the kinetic energy lost is 100% immediately) "travelling at the legal speed limit" <---does it mean travelling at exactly 80km/h or anywhere equal to or less than 80km/h? Assume the first case, 80km/h=22.222m/s p(total)=p'(total) Mc(22.2222)+Ms(-22.2222)=(Mc+Ms)v' -22.2222Mc=0 Mc=0 Can I prove that one or both drivers may be lying because for both claims to be true, Mc and Ms must both be 0 kg, which is clearly impossible? 2b) Will the 2 vehicles after collision stick together and have the same final velocity? If yes, why? If not, how can I calculate the velocities of both vehicles just after the collision? These are pretty much all my questions for today! I hope someone can explain them to me. Thanks a lot! Please Register or Log in to view the hidden image!
No, its an external force (unless you're also counting the momentum of the surface). Not necessarily. During car crashes, the body of each car is permanently deformed. Does that sound like an elastic collision to you? Is infinite acceleration possible for anything with mass?
Then where did the momentum go? Is it destroyed? Iis the total kinetic energy completely lost during the short period of collision so that both vehicles have zero velocity? Yes. I agree that your way is better. I have shown that vc=2vs so it's impossible for the 2 vehicles to have the same speed before the collision. So the two vehicles will have a common final velocity of -27km/h and this is what the analyst should see at the collision scene. But in general, given that 2 objects collide, how can I tell if they are going to have the same final velocity or not?
No, it just left the system. Momentum is only conserved in systems if no external force is applied. The law of conservation of momentum is a result of Newton's third law (action/reaction). In the case of your object sliding on a table, the reaction of the friction force (the friction force the object exerts on the table) is not a part of your system (unless you're taking the table and everything its in contact with into account - then your system becomes the entire Earth. Momentum is conserved then. The Earth's speed through space changes slightly). Yep. Care to guess what its converted to? You can't, without information about the physical properties of the colliding objects. Typically, hard objects that don't deform significantly and spring back to their original state afterward (the classic example of this is billiard balls), will undergo an elastic collision. Objects that change shape a lot and stay deformed (like pillows) will give an inelastic collision.
