6-1 LAB 6: Conservation of Linear Momentum Intuitively, which of the following has more “motion,” a mosquito or a semi-truck travelling at the same velocity? Which is more difficult to slow down? Which would win in a collision and which is more destructive? In asking which object contains more “motion,” we seem to know the answer even though both are travelling with the same velocity, and this means the velocity alone appears not to be enough to answer the question. Whatever this quality of “motion” is, itappears also to depend upon the object’s mass. You may be tempted to say that the kinetic energy of the objects can serve as a “gauge” of the object’s contained “motion,” butconsider an exploding ball. Before the explosion, there is no motion. After the explosion, fragments may fly off in many directions. A system’s center of mass can only be moved when acted upon by an outside force, and because the explosion is considered an “internal” force,the fragments’combined center of mass is unmoved. Using kinetic energy (a scalar quantity) is inappropriate for describing the “motion” an object possesses because there’s no way to add up contributions from the fragments in a way that gives us zero for the combined center of mass. We need something else that is a vector. The quality of “motion” we have described is called momentum, specifically linear momentum. It is given the symbol ⃗ , it is a vector quantity, and it is a conserved quantity in physics. If we allow to represent an object’s mass and ⃗ to represent its velocity, then the object’s momentum is⃗ ⃗ Eqn. 6-1: Linear Momentum The momentum vector’sdirection is the same as the velocity vector’s. The momentum’s magnitude is the product of (mass · velocity), which gives us the unit of momentum, kg · m/s. Unlike Newtons (kg · m/s2) for force or Joules (N · m or kg · m2/s2) for energy, the unit for momentum has no special name. In the case of the mosquito and semi-truck mentioned above, if we were to slow them both to a halt in the same amount of time, the semi-truck would require much greater force due to its greater momentum. Similarly, it would have a more dominant effect than the mosquito in a head-on collision. The faster-moving or more-massive object is not always the dominant one! A speeding low-mass car that didn’t see the red light will do much more damage than a high-mass semi-truck slowly inching forward at an intersection. A light high-velocity spitwad will do much less damage than the heavy slowly-lumbering bully who shot it. One must always consider the product of mass and velocity over either one of them alone.
6-2 The momentum of an object can only be changed by an external force. This is in fact Newton’s famous Second Law of Motion; more specifically, the net rate of change of momentum is proportional to the net force applied.