Edexcel IGCSE Physics 复习笔记 1.3.1 Momentum

• A moving object has momentum which is defined by the equation:

p = mv

• Where:
  • p = momentum in kilogram metre per second (kg m/s)
  • m = mass in kilograms (kg)
  • v = velocity in metres per second (m/s)

   

• This means that an object at rest (i.e v = 0) has no momentum
• Momentum keeps an object moving in the same direction, making it difficult to change the direction of an object with a large momentum

• Since velocity is a vector this means that the momentum of an object also depends on its direction of travel
• This means that momentum can be either positive or negative
  • If an object travelling to the right has positive momentum, an object travelling in the opposite direction (to the left) will have negative momentum

   

The tennis ball's momentum is negative when it moves in the opposite direction to which it initially was travelling in

• Therefore, the momentum of an object will change if:
  • The object accelerates (speeds up) or decelerates (slows down)
  • Changes direction
  • Its mass changes

   

• 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

• A closed system means the energy within the system is constant and there is an absence of external forces (e.g. friction)
• In other words:

The total momentum before a collision = The total momentum after a collision

• A system is a certain number of objects under consideration
  • This can be just one object or multiple objects

   

• Since momentum is a vector quantity, a system of objects moving in opposite directions (e.g. towards each other) at the same speed will have an overall momentum of 0 since they will cancel out
  • Momentum is always conserved over time

   

• The diagram below shows two masses m with velocity u and M at rest (ie. zero velocity)

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)

   

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