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law of conservation of momentum
This is a mind map about the law of conservation of momentum. The law of conservation of momentum, the law of conservation of energy and the law of conservation of angular momentum have become the three basic conservation laws in modern physics.
Edited at 2021-05-03 18:08:18
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- Outline
law of conservation of momentum
Momentum and Momentum Theorem
momentum
Concept: product of mass and velocity of an object
Original formula: p=mv
Unit: kg·m/s
Direction: Same as the direction of velocity [vector]
relationship with kinetic energy
Momentum is a vector quantity and kinetic energy is a scalar quantity. Therefore, when the momentum of an object changes, the kinetic energy does not necessarily change. On the contrary, when the kinetic energy changes, the momentum must change.
Impulse
Unit: N·s
Direction: Same as the force direction [vector]
Original formula: I=Ft
Concept: The product of force and force application time
(3) Momentum theorem
①Content: The change in momentum of an object at the beginning and end of a process is equal to the impulse of the force it experiences during the process.
②Formula: p'-p=I
③Scope of application: single object or system composed of multiple objects
→Newton's second law is an instantaneous expression while the momentum theorem studies the cumulative effect over time
Precautions
vertical gravity
Application of Holistic Approach
Determination of speed relationship (kinematic formula, especially s=0.5v at the end of t)
Model
particle model
law of conservation of momentum
definition
expression
①m1v1 m2v2=m1v1' m2v2'
②△p1= -△p2 (the increments of the momentum of the two interacting objects are equal and opposite)
Applicable conditions
①The system is not subject to external forces or the resultant force of the external forces is zero.
②The internal force acting on each object in the system is much greater than the external force it receives (approximately)
③If the net external force on the system in a certain direction is zero, then momentum is conserved in that direction.
Precautions
Distinguish between what is internal force and what is external force
Pay attention to the conservation of directionality
Pay attention to vectoriality
Pay attention to whether the mechanical energy before and after the collision is conserved
The momentum of each object in the system before and after interaction must be relative to the same inertial frame
p1, p2 or p1', p2' must be the momentum of each object in the system at the same time
Model
Cart and slider
Arc groove
spring critical
Objects moving in opposite directions do not collide
collision
elastic collision
Derivation of the formula for elastic collision
Special case
When m1>>m2, v1'≈v1 remains the same and doubles
When m2>>m1, v1'≈-v1 is reversed and stationary.
Inelastic collision: momentum is conserved and kinetic energy is lost
Precautions
Perfectly inelastic collision: momentum is conserved and kinetic energy loss is maximum
Three sets of relationship constraints
Conservation of momentum
Conservation of energy
perfectly inelastic collision
inelastic collision
elastic collision
movement logic
Momentum is conserved, kinetic energy does not increase, and the motion is reasonable
At the moment of collision, due to the extremely short time, the impulse suffered by the connecting body (rope, spring, etc.) is negligible, that is, the speed remains unchanged.
Pay attention to whether the mechanical energy is conserved after the collision (if it is not conserved, the energy conservation sequence cannot be started from the untouched state, but the energy conservation sequence should be started from the collision state)
Model
Two basic limits of scope problems
perfectly inelastic collision
elastic collision
Inclined plane problem (straight, curved)
bullet hits wood block
recoil motion
definition
Different parts of an object move in opposite directions under the action of internal forces
If the internal force is much greater than the external force, it can be considered that momentum is conserved.
System mechanical energy increases
Rocket
The original mass of the rocket is M. After ejection, m remains. The speed of the gas ejected is u.
The velocity obtained by the rocket v=(M/m-1)u
Precautions
In the man-ship model, the centers of mass of the two objects must move relative to each other, and the original centers of mass will be displaced in different directions.
relativity of speed
The application of holistic approach
Model
man ship model
Variation: fire bullets
Crash and explosion
jet model
*Speed loss