Applying Conservation of Linear Momentum (Edexcel A Level Physics)

• The principle of conservation of linear momentum states:

The total momentum before a collision = the total momentum after a collision provided no external force acts

• Linear momentum is the momentum of an object that only moves in a straight line
• Momentum is a vector quantity
  • This means oppositely-directed vectors can cancel each other out resulting in a net momentum of zero
  • If after a collision an object starts to move in the opposite direction to which it was initially travelling, its velocity will now be negative

• Momentum, just like energy, is always conserved

Conservation of Linear Momentum in 1D

The conservation of momentum in 1D, for two objects A and B colliding then moving apart

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Conservation of Linear Momentum in 2D

• For objects moving in 2D, there are components of momentum to consider
  • This is similar to projectile motion in 2D, in which we consider horizontal and vertical components of motion

Vector R split into its vertical, R cos (30) and horizontal, R sin (30), components

• Each component of momentum is conserved separately 
  
  • Since momentum is a vector, it can be resolved into horizontal and vertical components
  • The sum of horizontal components will be equal before and after a collision
  • The sum of vertical components will be equal before and after a collision

Step 1: Write the conservation of linear momentum for horizontal components

• • The question is worded in terms of the horizontal direction, so write: 

Horizontal momentum before = horizontal momentum after

Step 2: Resolve the velocity of each ball to find the horizontal component: 

• • Since momentum p = mv, then the horizontal component of momentum p_horiz = mv_horiz
  • Therefore, the horizontal component of the red ball is 1.8 cos 28°
  • The horizontal component of the green ball is v cos 55°

Step 3: Substitute quantities into the conservation of momentum

Horizontal momentum before = horizontal momentum after

mu_red + mu_green = mv_horiz(red) + mv_horiz(green)

m (2.5) + 0 = m (1.8 cos 28°) + m (v cos 55°)

Step 4: Simplify and rearrange to calculate v

2.5 = 1.8 cos 28° +  v cos 55°

2.5 = 1.6 + v cos 55°

0.9 = v cos 55°

v = 1.6 m s^–1