1D Collisions

Collisions in one dimension are an application of two major physics concepts – the idea of isolated systems and the Law of Conservation of Momentum. In an isolated system, no matter, energy, or other information is allowed to enter or leave the system; in other words, the total energy and mass stay the same. (There is no true example of an isolated system other than the universe, but to simplify calculations, all collisions are considered to occur in isolated systems unless specifically stated, such as a fender flying off a car.) The Law of Conservation of Momentum is very similar to the Laws of Conservation of Energy or Mass. It states the sum of momentum before an event is equal to the sum of momentum afterwards. This is written mathematically as Σpi = Σpf (Include vector arrows over the p’s!).

2 Types of collisions:
1. Elastic Collision – the objects collide and bounce back with no loss of energy and without deformation; both energy and momentum are conserved (i.e. two marbles bouncing off of one another)
2. Inelastic collision – the objects collide and deform in some way, losing energy, but conserving momentum (i.e. a fender bender)

Categories of 1D Collision Problems:
Before you begin the calculations for any conservation of momentum problem, it’s important to draw a vector diagram and write a conservation of momentum statement. Also, it’s necessary to label vectors as positive and negative, depending on their direction (up/right = positive; down/left = negative)
  • Hit and Rebound – two objects collide and bounce back in their initial directions

Ex. (Pg. 478 Q 1) A 0.25 kg volleyball is flying west at 2.0 m/s when it strikes a stationary 0.58 kg basketball dead centre. The volleyball rebounds east at 0.79 m/s. What will be the velocity of the basketball immediately after impact?

  • Hit and Stick – two objects “hit and stick” together; mfinal = m1 + m2; pf = p1 + p2
  • Explosion – the objects are initially at rest, then two or more pieces move in opposing directions; pi – 0 Ns

An important application of 1D collisions is the ballistics pendulum. Check your notes or page 423 in the textbook for an explanation.

For more fun, check out these applets! 1-D Collisions Applet Another 1D Collisions Applet

Wiki by Emily Holden