Impulse in 2D (Edexcel IAL Maths)

Spec point — 4.1

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 $FN=(F_{x}i+F_{y}j)$ N acting on a particle for $t$ seconds the impulse is given by the vector:

  • $I=Ft=(F_{x}i+F_{y}j)t$
  • 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

  • $I=m(v-u)$
  • 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 $\text{i}$ or $\text{j}$ 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 $(2i+3j)ms^{-1}$ when it receives an impulse Q N s . Immediately after receiving the impulse, the velocity of the ball is $(5i-j)ms^{-1}$.

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

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

Answer:

Exam Hint

• 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.