• In both collisions and explosions,?momentum is always conserved
  • However,?kinetic energy?might not always be
• A collision (or explosion) is either:
  • Elastic?– if the kinetic energy?is?conserved
  • Inelastic?– if the kinetic energy is?not?conserved
• Collisions are when objects strike against each other
  • Elastic?collisions are commonly those where objects colliding do not stick together and then?move in opposite directions
  • Inelastic?collisions are commonly those where objects collide and?stick together?after the collision

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

• An explosion is commonly to do with?recoil
  • For example, a gun recoiling after shooting a bullet or an unstable nucleus emitting an alpha particle and a daughter nucleus
• 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:

• The principle of conservation of momentum can be used to solve various types of problems for isolated systems such as problems involving:
  • Collisions
  • Fluid jets
  • Conveyor belts
  • Explosions & many more

• Kinetic energy can also be used to check if a collision is elastic or inelastic
  • In elastic collisions, momentum and kinetic energy are conserved
  • In inelastic collisions, momentum is conserved, but kinetic energy is not
  • Inelastic includes explosions

Step 1: List the known quantities

• • Mass of the crossbow: 2 kg
  • Mass of the arrow: 100 g = 0.1 kg
  • Speed of arrow during release: 40 m s^?1

Step 2: Determine the momentum before release

• • Since before release neither the arrow nor the crossbow was moving, their momentum together is?0 kg m s^?1

Step 3: Determine the momentum of the arrow

• • The momentum of the arrow can be found from the equation:

p = m × v

parrow?=?0.1?×?40 = 4 kg m s^?1

Step 4: Determine the recoil velocity of the crossbow

• • The arrow has a momentum of 4 kg m s^?1?and the system had a total momentum of 0 kg m s^?1?before the collision
  • Therefore, the crossbow must have a momentum of 4 kg m s^?1?in the opposite direction to the arrow
  • Therefore:

pcrossbow?= m × v

pcrossbow?÷ m = v

v?= 4?÷?2?=?2 m/s in opposite direction to arrow

Step 5: State the final answer

• • The magnitude of the recoil velocity of the crossbow is?2 m s^?1.