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MindMap Gallery law of conservation of momentum

law of conservation of momentum

The law of conservation of moment of momentum, also known as the law of conservation of angular momentum. It refers to the inference based on the Moment of Moment Theorem that when the total external moment is 0, its momentum moment remains unchanged.

Edited at 2022-09-10 20:57:25

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Outline

law of conservation of momentum

momentum

Invariants in collisions

One-dimensional collision

The product of mass and velocity remains unchanged

momentum

p=mv

Momentum change amount (final amount-initial amount)

Momentum and kinetic energy

Definition

p=mv E=1/2mv²

Targetedness

vector scalar

Conversion relationship

p=√2ME E=½MV²

Momentum and speed

When V changes, ΔP will definitely change

momentum theorem

Impulse

I=Ft

N·S

Vector

The direction of the force is constant

The I direction is the same as the force direction

change in direction of force

The direction of I is the same as the change direction of the object's momentum at the corresponding time.

Impulse and work

In a certain process, the impulse of a variable force is zero, and the work is not necessarily zero.

In a certain process, the impulses of the action force and reaction force are equal, and the total work is not necessarily zero.

momentum theorem

FΔT=MΔV

application

Momentum changes by a certain amount

The shorter the action time, the greater the force

step

Clarify the research object

Force analysis

To find the resultant impulse

Find the initial and final states

column momentum theorem equation

The principle of selection of kinetic energy theorem and Newton's second law

The sum of external forces is constant force

Priority kinetic energy theorem

multi-process problem

The kinetic energy theorem can solve the whole process

Niu Erdecomposable Process

fluid problems

ΔM=ΡSΔL=ΡSVΔt

The law of conservation of momentum stipulates the positive direction

System, internal force, external force

System: a whole composed of two (or more) interacting objects

Internal force: the force between objects in the system

External force: the force exerted by objects outside the system on objects within the system

law of conservation of momentum

condition

Not subject to external force

The net external force is zero

Internal force is much greater than external force

established in a certain direction

expression

ΔP=0

Universality

vectoriality

application

m₁v₁ m₂v₂=m₁v₁′ m₂v₂′

step

Clarify system components

Force analysis

Specify the positive direction and determine whether it is conserved

Specify the positive direction and determine the initial and final momentum.

Plug in the data and get the result

critical case

spring

closest to each other

equal speed

Elastic potential energy is maximum

The largest loss of kinetic energy

Slider-cart

equal speed

Maximum relative displacement

Generates maximum heat energy

The largest loss of kinetic energy

Slider-Bevel

The slider has the smallest speed in the vertical direction

equal speed

Maximum gravitational potential energy

The largest loss of kinetic energy

Three basic viewpoints and five rules for solving mechanical problems

dynamic perspective

Kinesiology

v=v₁ at

x=v₁ ½at²

Niu Er

F=ma

energy perspective

Kinetic energy theorem

law of conservation of mechanical energy

momentum view

momentum theorem

law of conservation of momentum

Selection principles

subject to constant force

dynamic perspective

Movement changes due to sustained force

Momentum Theorem (Time)

Kinetic Energy Theorem (Displacement)

system

conservation of mechanical energy

Conservation of momentum

recoil phenomenon rocket

Features

Movement in the opposite direction under the action of internal force

The system is not subject to external forces or the internal forces are much greater than the external forces

Kinetic energy increases

Follow the law of conservation of momentum

man ship model

Conservation of momentum

People walk and the boat goes, people stop and the boat stops, people go fast and the boat goes fast, people go left and the boat goes right

mx₁-Mx₂=0

x₁ x₂=L

Solve the problem together

bullet hits wood block

bullet lodged in block of wood

Conservation of momentum

Mechanical energy loss (friction heat generation)

Fd=½mv₁²-½ (m M)v₂² d is the depth of the bullet injected into the wood block

The bullet penetrated the block of wood

Conservation of momentum

Mechanical energy loss (friction heat generation)

FL=½mv₁²-½ (m M)v₂² L is the length of the wood block

When two objects have the same velocity, it is a completely inelastic collision.

Elastic and inelastic collisions

elastic collision

Conservation of momentum

Conservation of kinetic energy

m₁v₁=m₁v₁′ m₂v₂′

½m₁v₁²=½m₁v₁′² ½m₂v₂²

From the above, we can get: v₁′=（m₁-m₂）÷（m₁ m₂）v₁ v₂′=2m₁÷（m₁ m₂）v₁

inelastic collision

Conservation of momentum

Kinetic energy is not conserved

perfectly inelastic collision

Conservation of momentum

Kinetic energy is not conserved

in conclusion

Small hit, big hit, bounced back

The big one hits the small one and runs towards

Equal masses, elastic collision, v exchange

possibility judgment

step

Conservation of momentum

Does kinetic energy increase?

Realistic

Movement in the same direction before collision v after v > v before

Reciprocal motion before collision v front′ ≥ v back′

Spring-ball model

Spring shortest/longest: similar to perfectly elastic collision

Spring returns to original length: similar to elastic collision

Small ball-slope model

Highest point: Similar to perfectly inelastic collision

Separation: Similar to elastic collision

Experiment: Verify the law of conservation of momentum

Study the conservation of momentum when the slider on the air cushion guide rail collides

Study the momentum of the ball at the end of the chute when it collides