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Chapter 5. Momentum

Recommended article : 【Physics】 Physics Table of Contents


1. Momentum

2. Coefficient of Restitution

3. Collisions in a Plane



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.

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.

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.

Type 1: Perfectly inelastic collision : e = 0. Momentum is conserved. Kinetic energy is not conserved ( converted into heat).

Type 2: Inelastic collision : 0 < e < 1. Momentum is conserved. Kinetic energy is not conserved ( converted into heat).

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

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