Collisions — OCR A-Level Physics
Test yourself on Collisions with OCR A-Level practice questions.
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Collisions explained
The principle of conservation of momentum states that, for a system with no resultant external force, total momentum before an interaction equals total momentum after it.
Read the full explanation
Momentum is a vector, p = mv, so assign a positive direction and give opposing velocities negative signs. For two bodies A and B: m_A u_A + m_B u_B = m_A v_A + m_B v_B. This applies to collisions, explosions and recoil, provided external forces such as friction or a driving force are negligible during the interaction. For example, a 2.0 kg trolley at 3.0 m s⁻¹ colliding with a stationary 1.0 kg trolley and sticking gives total momentum 6.0 kg m s⁻¹ before and after, so the combined 3.0 kg moves at 2.0 m s⁻¹.
(b) collisions and interaction of bodies in one dimension and in two dimensions
Momentum conservation applies along each perpendicular direction independently. In one dimension, choose a positive axis and solve m_A u_A + m_B u_B = m_A v_A + m_B v_B. In two dimensions, resolve all velocities into x and y components, then conserve momentum separately in each direction: total p_x before equals total p_x after, and total p_y before equals total p_y after. For example, a ball moving east at 4.0 m s⁻¹ striking a stationary ball and deflecting at 30° requires x and y equations to find both final velocities. Draw a vector diagram, resolve with sine and cosine, and solve the simultaneous equations.
(c) perfectly elastic collision and inelastic collision.
In a perfectly elastic collision, both momentum and kinetic energy are conserved. In an inelastic collision, momentum is conserved but kinetic energy is not; some is transferred to thermal energy, sound or deformation. A special case is a perfectly inelastic collision, where bodies stick together and move with a common velocity, giving maximum kinetic energy loss. For example, two identical trolleys approaching at equal speeds and sticking together have zero total momentum and stop, converting all kinetic energy. To test elasticity, calculate total ½mv² before and after; equal values indicate a perfectly elastic collision, while a decrease indicates an inelastic one.
Your focus
- State the principle of conservation of momentum and its condition of applicability.
- Apply conservation of momentum to one-dimensional interactions.
- Use sign conventions correctly when solving momentum problems.
Show all 9 objectives
- Apply conservation of momentum to one-dimensional collisions.
- Resolve velocities into components and conserve momentum along two perpendicular axes.
- Solve two-dimensional collision problems using vector diagrams and simultaneous equations.
- Distinguish between perfectly elastic and inelastic collisions using conservation of kinetic energy.
- Apply conservation of momentum to perfectly inelastic collisions where bodies coalesce.
- Calculate kinetic energy before and after a collision to classify it.
Collisions exam tips
Marking Points
- Total momentum of a system remains constant when no resultant external force acts on it.
- Momentum is a vector quantity, so direction must be represented by positive and negative signs.
- The conservation equation equates the vector sum of momenta before and after an interaction.
- The principle applies to collisions, explosions and recoil where external forces are negligible during the interaction.
- Momentum is conserved independently in each perpendicular direction for a system with no resultant external force.
- In one dimension, velocities are given signs along a single chosen axis.
- In two dimensions, resolve velocities into components and write separate conservation equations for x and y.
- Vector diagrams or component tables help track before and after momenta in two dimensions.
- A perfectly elastic collision conserves both momentum and kinetic energy.
- An inelastic collision conserves momentum but not kinetic energy.
- In a perfectly inelastic collision the bodies coalesce and share a common final velocity.
- Kinetic energy may be transferred to thermal energy, sound or deformation in an inelastic collision.
Examiner Tips
- 💡Draw a before-and-after diagram and mark the positive direction on it.
- 💡Write the full conservation equation before substituting numbers, so no term is omitted.
- 💡Check that the final velocity's sign is physically sensible for the direction chosen.
- 💡Draw a clear before-and-after diagram with axes labelled and angles marked.
- 💡Make a component table for x and y momenta before and after the collision.
- 💡Solve the simpler axis equation first, then substitute into the other to find the remaining unknown.
- 💡Calculate total kinetic energy before and after to classify a collision as elastic or inelastic.
- 💡Use conservation of momentum first to find unknown velocities, then test kinetic energy.
- 💡State clearly which quantity is conserved and which is not when explaining a collision.
Common Mistakes
- Treating momentum as a scalar and adding speeds regardless of direction: the correct approach is to assign signs to velocities along a chosen axis.
- Assuming momentum is conserved when a significant external force acts, such as friction during a long slide: the correct condition is that the resultant external force is zero or negligible.
- Forgetting to include a stationary body's zero momentum in the before total: the correct equation includes every body in the system.
- Conserving momentum only along the original direction of motion in a two-dimensional collision: the correct method conserves momentum along both perpendicular axes.
- Mixing up sine and cosine when resolving a velocity at an angle: the correct component adjacent to the angle uses cosine and the perpendicular component uses sine.
- Adding component magnitudes without signs: the correct approach assigns positive and negative directions on each axis.
- Assuming kinetic energy is always conserved in collisions: the correct test is to compare total kinetic energy before and after, since only perfectly elastic collisions conserve it.
- Believing momentum is lost in an inelastic collision: the correct principle is that momentum is conserved whenever no resultant external force acts.
- Treating a collision as perfectly elastic because the bodies bounce apart: the correct criterion is numerical conservation of kinetic energy, not the appearance of bouncing.