What does two dimensions (2D) mean in mechanics?

• In?two?dimensions, a particle may be considered as existing and being able to move around two-dimensional space rather than in a single straight line (1D)
  • This 2D space is called a?plane?– so you may see the?0xy?plane?mentioned

• The directions of the two dimensions are chosen so that they are perpendicular to each other
• The two directions are usually
  • horizontal?and?vertical, or
  • parallel?and?perpendicular?to an inclined plane

What is the resultant force in 2D and an unbalanced force in 2D?

• The?resultant?force?in 2D is the?sum?of?forces?acting on a particle but this will now need to be considered in two parts – one for each direction
• An?unbalanced?force?is a force acting on a particle that whereby one or both parts are?not?cancelled by another force acting in the opposite direction
• So a?non-zero?resultant force will be non-zero in at?least?one?of the two dimensions, is therefore?unbalanced?and the particle will?accelerate

What does equilibrium in 2D mean?

• In two dimensions a?particle?is in?equilibrium?if the?resultant?force?acting on it is?zero
  • For example, if the two dimensions involved are the?horizontal?and?vertical?directions, a particle will be in equilibrium if any forces acting?left?are?balanced?by any forces acting?right?and?any forces acting?up?are?balanced?by any forces acting?down
• When a particle has?several?forces (at least 3 – have a think as to why!) acting on it – and it is in?equilibrium?– the forces can be drawn “nose-to-tail” such that they form a polygon

(a)? Write down the resultant forces acting on the particle in both the horizontal and vertical directions.

(b)? Find the value of?F.