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

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 $\mathbf{F}N=(F_x\mathbf{i}+F_y\mathbf{j})$ N acting on a particle for $t$ seconds the impulse is given by the vector:

  • $\mathbf{I}=\mathbf{F}t=(F_x\mathbf{i}+F_y\mathbf{j})t$ 

  • 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

  •  $\mathbf{I}=m(\mathbf{v}\mathbf{-}\mathbf{u})$

  • 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