Collisions & Explosions in One-Dimension (DP IB Physics): Revision Note

Collisions & Explosions in One-Dimension

• Collisions are when two or more moving objects come together and exert a force on one another for a relatively short time

• Explosions are when two or more objects that are initially at rest are propelled apart from one another

• In both collisions and explosions, momentum is always conserved

  • However, kinetic energy might not always be

Collisions in one dimension

• Collisions in one dimension (1D) usually involve two objects interacting on a single straight line

  • This means the velocity vectors before and after the collision are directed along the same axis and can be either positive or negative

During a collision in one dimension between two objects, A and B, they move along the same line before and after the collision

Explosions in one dimension

• Explosions in one dimension (1D) usually involve one stationary object becoming two objects that move away from each other along the same line

  • Before the explosion, the velocity and, therefore, momentum, are zero

  • After the collision, the velocity vectors are directed along the same axis and can be either positive or negative

During an explosion in one dimension, a single object AB explodes and becomes two objects, A and B, which move along the same line in opposite directions

Elastic and inelastic collisions

• Collisions can be either:

  • elastic – if the kinetic energy is conserved

  • inelastic – if the kinetic energy is not conserved

• A perfectly elastic collision is an idealised situation that does not actually occur in everyday life

• Perfectly elastic collisions do occur commonly between particles 

  • All collisions occurring on a macroscopic level are inelastic collisions

  • However, exam questions can use the theoretical idea of an elastic collision on a macroscopic level

• A totally inelastic collision is a special case of an inelastic collision where the colliding bodies stick together and move as one body

• In a totally inelastic collision, the maximum amount of kinetic energy is transferred away from the moving bodies and is dissipated to the surroundings

Elastic collisions are where two objects move in opposite directions. Inelastic collisions are where two objects stick together

• An explosion is commonly associated with recoil

  • For example, a gun recoiling after shooting a bullet or an unstable nucleus emitting an alpha particle and a daughter nucleus

  • Kinetic energy is never conserved in an explosion, as the objects are always at rest initially

• To find out whether a collision is elastic or inelastic, compare the kinetic energy before and after the collision

• The equation for kinetic energy is:

• Where:

  • E_k = kinetic energy (J)

  • m = mass (kg)

  • v = velocity (m s^–1)