IB DP Physics: SL复习笔记2.4.1 Force & Momentum

• Linear momentum, p, is defined as the product of mass and velocity

• Momentum is a vector quantity - it has both a magnitude and a direction
• This means it can have a negative or a positive value
  • If an object travelling to the right has positive momentum, an object travelling to the left (in the opposite direction) has a negative momentum
  • The negative or positive directions are defined by the observer on a case-by-case basis
• The SI unit for momentum is kg m s−1

Direction of Momentum

• If a ball of mass 60 g travels at 2 m s−1, it will have a momentum of 0.12 kg m s−1
• If it then hits a wall and rebounds in the exact opposite direction, it will have a momentum of −0.12 kg m s−1

When the ball is travelling in the opposite direction, its velocity is negative. Since momentum = mass × velocity, its momentum is also negative

• Both the tennis ball and the brick have the same momentum
• Even though the brick is much heavier than the ball, the ball is travelling much faster than the brick
• This means that on impact, they would both exert a similar force (depending on the time it takes for each to come to rest)

Force & Momentum

• Force is defined as the rate of change of momentum on a body
• The change in momentum is defined as the final momentum minus the initial momentum
• These can be expressed as follows:

• It should be noted that the force in this situation is equivalent to Newton's second law:

F = m × a

• Only when mass is constant
  • In situations where mass is not constant, Newton's second law can only be considered to assist descriptions and not for calculations

• The force and momentum equation can be derived from Newton's Second law and the definition of acceleration

Direction of Forces

• Force and momentum are vectors so they can take either positive or negative values
• The force that is equal to the rate of change of momentum is still the resultant force
• A force on an object will be negative if it is directed in the opposite motion to its initial velocity
  • This means that the force is produced by the object it has collided with

The wall produces a force of -300N on the car and (due to Newton’s Third Law) the car also produces a force of 300 N back onto the wall