How to find the total momentum before and after a collision?

Consider two blocks of equal mass m sliding across a surface along an x-axis. (momentum problem)?

• Consider two blocks of equal mass m sliding across a surface along an x-axis. When they meet in a one-dimensional collision, block A has a velocity of uA, and block B has a velocity of uB. After the blocks collide, they have velocities vA and vB. 1)What is the total momentum of the system before the collision? 2)Total momentum of a system is always conserved if no outside forces act on it. For an "isolated" collision such as this one, the total momentum of both objects is always conserved. Why is this not enough information to find vA and vB? 3)In a perfectly inelastic collision, the two objects stick together. If the collision between block A and block B is perfectly inelastic, find vA and vB. 4)In a perfectly elastic collision, the two objects bounce off of each other, and kinetic energy is conserved (in addition to momentum, which is always conserved.) If you know that the collision between block A and block B is perfectly elastic could you find vA and vB? (Don't actually do it unless you really want to.)

• Answer:

  1) Ptot1 = m*(uA+uB) 2) The energy lost to heat is unknown. 3) P1 = P2 → m(uA+uB) = 2m*V → V = vA = vB = (uA+uB)/2 4) Yes