Chapter 5. Momentum
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1. Momentum
1. Momentum
⑴ A physical quantity represented by the product of mass and velocity (P)
⑵ The rate of change of momentum of a single particle is proportional to the net force acting on that particle and is in the same direction as the force.
① F = ΔP/Δt = d(mv) / dt = ma, which can be summarized as Newton’s second law of motion, F = ma.
⑶ Impulse : The change in momentum ΔP = F·Δt
① A measure of the intensity of impact on an object when objects collide.
② I = F ·Δt
③ Area under the force-time graph represents impulse.
⑷ Law of Conservation of Momentum
① Definition : When no external forces act and two objects collide, the sum of the initial momenta is equal to the sum of the final momenta, and this sum remains constant.
② Reason 1: Newton’s Third Law : Law of action and reaction.
○ (Note) Newton’s Third Law is also a reason for the conservation of momentum.
○ (Note) In fact, the conservation of momentum and Newton’s Third Law are necessary and sufficient conditions.
③ Reason 2: Noether’s Theorem
○ Content : For every symmetry in nature, there is a corresponding conserved quantity.
○ The universe has linear symmetry in space.
○ Momentum is considered the corresponding conserved quantity.
④ Application : The velocity of the center of mass of an object remains unchanged before and after a collision.
2. Coefficient of Restitution
⑴ The ratio of the relative velocities of objects before and after a collision.
⑵ Type 1: Perfectly inelastic collision : e = 0. Momentum is conserved. Kinetic energy is not conserved ( ∵ converted into heat).
⑶ Type 2: Inelastic collision : 0 < e < 1. Momentum is conserved. Kinetic energy is not conserved ( ∵ converted into heat).
⑷ Type 3: Elastic collision or perfectly elastic collision : e = 1. Momentum is conserved. Kinetic energy is conserved.
3. Collisions in a Plane
⑴ Principle : Momentum along the x-axis and y-axis is conserved before and after the collision.
⑵ Example
Input : 2016.06.26 23:26