Edexcel A Level Physics:复习笔记2.14 Conservation of Linear Momentum

The Principle of Conservation of Linear Momentum

  • The principle of conservation of momentum states that in a closed system, the total momentum before an event is equal to the total momentum after the event
  • Momentum is always conserved in collisions where no external forces act
  • This is usually written as:

Total momentum before a collision = Total momentum after a collision

  • Since momentum is a vector quantity, a system of objects moving in opposite directions can have an overall momentum of 0
    • This applies to objects moving towards each other or away from each other
  • The diagram below shows two masses m with velocity u and M at rest (M has zero velocity)

conservation-of-momentum-1

The momentum of a system before and after a collision

 

  • Before the collision:
    • The momentum is only of mass m which is moving
    • If the right is taken as the positive direction, the total momentum of the system is m × u

     

  • After the collision:
    • Mass M also now has momentum
    • The velocity of m is now -v (since it is now travelling to the left) and the velocity of M is V
    • The total momentum is now the momentum of M + momentum of m
    • This is (M × V) + (m × -v) or (M × V) – (m × v)

     

Worked Example

Trolley A of mass 0.80 kg collides head-on with stationary trolley B whilst travelling at

3.0 m s–1. Trolley B has twice the mass of trolley A. On impact, the trolleys stick together.

Using the conversation of momentum, calculate the common velocity of both trolleys after the collision.

Worked-example-1D-momentum-quesions-solution

Conservation of Linear Momentum & Newton's Third Law

  • Newton’s third law of motion states:

Whenever two bodies interact, the forces they exert on each other are equal and opposite

  • This means:
    • When one object exerts a force on another object, the second object will exert an equal force on the first object in the opposite direction
    • When two objects collide, both objects will react, generally causing one object to speed up (gain momentum) and the other object to slow down (lose momentum)

     

Newton%E2%80%99s-Third-Law-of-Motion

Newton's third law can be applied to collisions

 

  • Consider the collision between two trolleys, A and B:
    • When trolley A exerts a force on trolley B, trolley B will exert an equal force on trolley A in the opposite direction

     

  • In this case:

FB–A = –FA–B

  • While the forces are equal in magnitude and opposite in direction, the accelerations of the objects are not necessarily equal in magnitude
  • From Newton's second law, acceleration depends upon both force and mass, this means:
    • For objects of equal mass, they will have equal accelerations
    • For objects of unequal mass, they will have unequal accelerations

     

Exam Tip

Momentum questions are often very long and wordy. Even if you are given a diagram, make a quick sketch representing all the bodies as point masses. Mark the velocities with arrows and include positive and negative signs.

2-14-exam-tip-drawn-solutions_edexcel-al-physics-rn

The Maths of momentum is straightforward, so as long as you have your vector directions clear in your mind, nothing can go wrong!

 

转载自savemyexams

更多Alevel课程
翰林国际教育资讯二维码