Two cars, one a compact with mass 1200kg and the other a large gas-guzzler with mass 3000 kg, collide head-on at typical freeway speeds. (a) Which car has a greater magnitude of momentum change? Which car has a greater velocity change? (b) if the target car changes its velocity by ?v,? alculate the change in the velocity of the small car in terms of ?v.? (c) Which car’s occupants would you expect to sustain greater injuries? Explain.
Solution 39E Step 1 of 5: The momentum of the system of the two cars is conserved. (If we neglect the external forces during collision) mass of the small car,m = S200 kg mass of the large car,m = L000 kg velocity of the small car,v S velocity of the large car,v L Step 2 of 5: (a) The total momentum of the system is conserved, so the momentum lost by one car equals the momentum gained by the other car. They have the same magnitude of change in momentum. Since p = mv and p is the same, the car with the smaller mass has a greater change in velocity. Step 3 of 5: b) m sv =sm v L L v = mLvL s mS = 3000 kv L 1200 kg = 2.50 v L