IB Physics SL

Revision Notes

2.4.1 Force & Momentum

Force & Momentum

Linear Momentum

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

Linear momentum equation, downloadable AS & A Level Physics revision notes

Momentum is 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 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

 

Negative momentum, downloadable AS & A Level Physics revision notes

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

Worked Example

Which object has the most momentum?

WE - Momentum comparison question image, downloadable AS & A Level Physics revision notes

WE - Momentum comparison answer image, downloadable AS & A Level Physics revision notes

  • Both the tennis ball and the brick have the same momentum
  • Even though the brick is much heavier than the ball, the ball is traveling 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 and 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:

Force and momentum equation, downloadable AS & A Level Physics revision notes

  • 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

Direction of forces, downloadable AS & A Level Physics revision notes

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

Worked Example

A car of mass 1500 kg hits a wall at an initial velocity of 15 m s-1.
It then rebounds off the wall at 5 m s-1 and comes to rest after 3.0 s.

Calculate the average force experienced by the car.

WE - Force on a car answer image (1), downloadable AS & A Level Physics revision notesWorked example-force on a car (2), downloadable AS & A Level Physics revision notes

Exam Tip

  • The direction you consider positive is your choice, as long the signs of the numbers (positive or negative) are consistent with this throughout the question
  • In an exam question, carefully consider what produces the force(s) acting. Look out for words such as ‘from’ or ‘acting on’ to determine this and don’t be afraid to draw a force diagram to figure out what is going on.
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