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Last exams 2024

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Force & Momentum (DP IB Physics: SL)

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Katie M

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Katie M

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Force & 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 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

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

Determine 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 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:

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 s1 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

Examiner 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 questionIn 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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Katie M

Author: Katie M

Expertise: Physics

Katie has always been passionate about the sciences, and completed a degree in Astrophysics at Sheffield University. She decided that she wanted to inspire other young people, so moved to Bristol to complete a PGCE in Secondary Science. She particularly loves creating fun and absorbing materials to help students achieve their exam potential.