symmetrical situation, with no preference between right and left, so we assume that they stand still. We shall also suppose that any two objects of equal mass even if the objects are made of dIfferent materials, which collide and stick together when moving with the same velocity in opposite directions will come to rest after 10-3 Momentum is conserved! We can verify the above assumptions experimentally: first, that if two station ary objects of equal mass are separated by an explosion they will move apart with the same speed, and second, if two objects of equal mass, coming together with the Fig. 10-1. End view of linear air same speed, collide and stick together they will stop. This we can do by means of trough marvelous invention called an air trough, *which gets rid of friction, the thing which continually bothered Galileo(Fig. 10-1). He could not do experiments by sliding things because they do not slide freely, but, by adding a magic touch, we can today get rid of friction. Our objects will slide without difficulty, on and on at a constant velocity, as advertised by Galileo. This is done by supporting the objects BUMPER SPRING OY PISot CA on air. Because air has very low friction, an object glides along with practically s constant velocity when there is no applied force. First, we use two glide blocks CNND was measured really, but we know that this weight is proportional to the mass), YLIND PISTON BUMPER SPRING and we place a small explosive cap in a closed cylinder between the two blocks (Fig. 10-2). We shall start the blocks from rest at the center point of the track and Fig. 10-2. Sectional view of gliders force them apart by exploding the cap with an electric spark. What should happen? with explosive interaction cylinder attach If the speeds are equal when they fly apart, they should arrive at the ends of the ment trough at the same time. On reaching the ends they will both bounce back with ractically opposite velocity, and will come together and stop at the center where they started. It is a good test; when it is actually done the result is just as we have described(Fig. 10-3) Now the next thing we would like to figure out is what happens in a less simple D situation. Suppose we have two equal masses, one moving with velocity v and the Mm3htme白9与m that if we ride along in a car, physics will look the same as if we are standing still. We start with the knowledge that two equal masses, moving in opposite directions with equal speeds v, will stop dead when they collide. Now suppose that while g.103. of action. this happens, we are riding by in an automobile, at a velocity -. Then what does reaction experiment with equal masses. it look like? Since we are riding along with one of the two masses which are coming together, that one appears to us to have zero velocity. the other mass, however, going the other way with velocity v, will appear to be coming toward us at a velocity 2v(Fig. 10-4). Finally, the combined masses after collision will seem to be passing by with velocity We therefore conclude that an object with velocity 2u, hitting ELocITY. -v) an equal one at rest, will end up with velocity v, or what is mathematically exactly he same, an object with velocity w hitting and sticking to one at rest will produce an object moving with velocity v/2. Note that if we multiply the mass and the locity beforehand and add them together, mo+o, we get the same answer as mm AFTER COLLISION [ mIm hen we multiply the mass and the velocity of everything afterwards, 2m times v/2. So that tells us what happens when a mass of velocity v hits one standing still Fig. 10-4. Two views of an inelastic In exactly the same manner we can deduce what happens when equal objects collision between equal masses. having any two velocities hit each other. Suppose we have two equal bodies with velocities vI and U2, respectively, hich collide and stick together. What is their velocity v after the collision Again we ride by in an automobile, say at velocity u2, so that one body appears to be at rest. The other then appears to have a velocity v1-v2, and we have the same case that we had before. When it is all finished they will be moving at vr-2)with respect to the car. What then is the actual speed on the ground? H. V. Neher and R. B. Leighton, Amer. Jour. of Phys. 31, 255(1963)