Lecture 15: Momentum - Conservation of Momentum - Center of Mass
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1. Conservation of Momentum:
The momentum vector, internal forces, external forces and the conservation of momentum are discussed.
2. Kinetic Energy and Momentum for a 1D Collision:
Conservation of momentum is used to calculate the final velocity of a pair of masses that collide and stick together (this is called a completely inelastic collision). It is shown that kinetic energy is then always lost, but momentum is conserved.
3. Energy and Momentum for a 2D Car Collision:
The impact time is so short that the work done by the frictional force from the road exerted on the cars during the impact can be ignored. Internal frictional forces between the cars will merge the wrecks into one mass. A momentum diagram is sketched. This is a completely inelastic collision. If we compare the moment just before and just after the collision, kinetic energy is lost, but momentum is conserved.
4. Scenarios that Increase the Kinetic Energy:
When there is a bomb explosion, the momentum and kinetic energy are zero before the explosion. Thus the total momentum must remain zero, but the kinetic energy clearly increases after the explosion. Professor Lewin does some air track experiments where the released energy is from a compressed spring; kinetic energy increases but momentum is conserved.
5. Center of Mass of a System:
The definition of the center of mass is described. The center of mass behaves as if all the matter were together at that point. The center of mass of a system of objects moves with constant speed along a straight line in the absence of external forces on the system (internal forces between the objects are allowed - e.g. the objects can collide). An example is worked calculating the position vector for the center of mass for a system of three masses. An air track demonstration shows the center of mass of an oscillating system (2 objects) is moving at constant velocity. The center of mass of a tennis racket follows a parabolic trajectory while it tumbles through the air.
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