Edexcel International A Level Maths: Mechanics 2

Revision Notes

International A LevelMaths: Mechanics 2EdexcelRevision Notes4. Collisions4.1 Collisions4.1.1 Impulse in 2D

4.1.1 Impulse in 2D

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Impulse in 2D

How does impulse work in 2D?

  • Impulse and momentum can be used in 2D as they are vector quantities
    • Impulse in 2D essentially works the same way as impulse in 1D
  • For a constant force given by the vector bold F space N space equals space left parenthesis F subscript x bold i bold space plus space F subscript y bold j right parenthesis N acting on a particle for t seconds the impulse is given by the vector:
    • bold I space equals space bold F t space equals space left parenthesis F subscript x bold i space plus space F subscript y space bold j right parenthesis t 
    • The units are still N s  (equivalent to kg m s-1 )
  • For a particle of mass the impulse is still equal to the change in momentum
    •  bold I space equals space m left parenthesis bold v bold minus bold u right parenthesis
    • where u m s-1 is the initial velocity vector and v m s-1 is the final velocity vector

How are questions different in 2D?

  • You could be asked to work out the magnitude of the impulse
    • You would need to find the two components of the impulse vector and then use Pythagoras
  • You could be asked to work out the direction of the impulse
    • You would need to find the two components of the impulse vector and then use SOHCAHTOA (right-angled trigonometry)
    • You might need to find the angle between the impulse and the vector text i end text or text j end text so always draw a sketch
  • If two particles collide in 2D then for this specification they will always be direct collisions
    • This means that they will be travelling along the same line so the velocity vectors will be scalar multiples of each other
    • These problems are rare and would be solved using conservation of momentum in exactly the same way as in 1D
  • If you know the magnitude and direction of the impulse or a velocity then you might have to resolve it into horizontal and vertical components

Worked example

A ball of mass 0.8 kg is moving with velocity left parenthesis 2 straight i plus 3 straight j right parenthesis space straight m space straight s to the power of negative 1 end exponent when it receives an impulse Q N s . Immediately after receiving the impulse, the velocity of the ball is left parenthesis 5 straight i minus straight j right parenthesis space straight m space straight s to the power of negative 1 end exponent. 

(a)
Find the magnitude of the impulse Q N .

(b)
Find the angle between the direction of the impulse and the vector j.

4-1-1-impulse-in-2d-example-solution

Exam Tip

  • Be careful with negatives, especially when adding and subtracting vectors.
  • When finding angles and directions always sketch a diagram. Read the question carefully to help you decide where the angle should be measured from.

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    Dan

    Author: Dan

    Dan graduated from the University of Oxford with a First class degree in mathematics. As well as teaching maths for over 8 years, Dan has marked a range of exams for Edexcel, tutored students and taught A Level Accounting. Dan has a keen interest in statistics and probability and their real-life applications.