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 $F N = (F_{x} i + F_{y} j)$ N acting on a particle for $t$ seconds the impulse is given by the vector:
- $I = F t = (F_{x} i + F_{y} j) t$
- 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 $i$ or $j$ 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 $(2 i + 3 j) m s^{- 1}$ when it receives an impulse Q N s . Immediately after receiving the impulse, the velocity of the ball is $(5 i - j) m s^{- 1}$ .

(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

Examiner 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.

Impulse in 2D (Edexcel International A Level Maths: Mechanics 2)

Revision Note

Impulse in 2D

How does impulse work in 2D?

How are questions different in 2D?

Worked example

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Author: Dan