Collisions in two dimensions (HL)
Momentum is a vector: conserve it separately along two perpendicular axes, then use the kinetic energy to tell elastic from inelastic.
Two snooker balls meet off-centre and fly off at an angle. One equation cannot cope with two directions at once. How do you keep track of the momentum?
A 2.0 kg body moves at 3.0 m s⁻¹ east and a 1.0 kg body moves at 4.0 m s⁻¹ north. The total momentum has size…
Before a collision the total y-momentum is zero. After the collision, one body has a y-momentum of +2.4 kg m s⁻¹. The other body has a y-momentum of…
Two equal masses collide elastically, one initially at rest, and neither reverses. The angle between their paths afterwards is…
In a collision the kinetic energy after is less than before. The collision is…
A stationary 6.0 kg object explodes into two pieces: 2.0 kg moves at 6.0 m s⁻¹ east, and the other piece moves…
Explain why, in a two-dimensional collision, you must apply conservation of momentum along each axis separately.
The total momentum of an isolated system is…
In an explosion the kinetic energy…
Key points
- • Resolve momentum into components and conserve each axis separately.
- • Compare the kinetic energy before and after to classify the collision.
- • In an explosion of a stationary body the momentum arrows form a closed triangle.
Formulas
- Σpx (before) = Σpx (after)
- Σpy (before) = Σpy (after)
Key terms
- Glancing collision :
- an off-centre collision after which the bodies move in new directions
Common errors
- • Adding magnitudes instead of components
- • Using only one equation
- • Taking cos for the y-component