Conservation of Momentum: In an isolated system where no external resultant forces act, the total momentum before a collision equals the total momentum after the collision: .
Impulse-Momentum Theorem: The change in momentum of an object is equal to the impulse applied to it, defined as the product of the average force and the time interval: .
Kinetic Energy Analysis: While momentum is always conserved in isolated collisions, kinetic energy () is only conserved in elastic collisions. In inelastic collisions, some is transformed into thermal energy or sound.
Ticker Timers: A device that marks dots on a paper tape at a constant frequency (usually 50 Hz). The spacing between dots represents the distance moved in seconds; increasing spacing indicates acceleration, while constant spacing indicates uniform velocity.
Video Analysis: High-speed cameras record motion against a calibrated scale. By knowing the frame rate (frames per second), the time between positions can be determined, allowing for precise tracking of projectiles or complex collisions.
Friction Compensation: To simulate an isolated system on a ramp, the incline is adjusted until the trolley moves at a constant velocity when given a small push, meaning the component of weight down the slope exactly balances the frictional forces.
Vector Signs: Always define a positive direction (e.g., right is positive). If an object bounces back, its final velocity must be entered as a negative value in the conservation equation.
Unit Consistency: Ensure all masses are in kilograms (kg) and velocities in meters per second (m/s) before calculating momentum ().
System Boundaries: Clearly identify which objects are part of the 'system' to ensure you are only accounting for internal forces during the collision analysis.
Sanity Check: If a collision is inelastic, the total kinetic energy after the event MUST be less than the total kinetic energy before. If it is higher, a calculation error has occurred.
Scalar vs. Vector: A common mistake is treating momentum as a scalar. Because and is a vector, momentum has direction. Adding magnitudes without considering direction leads to incorrect results.
Energy 'Loss': Students often say energy is 'lost' in inelastic collisions. It is more accurate to say kinetic energy is transformed into other forms (heat, sound, deformation), as total energy is always conserved.
Reaction Time: When comparing methods, always note that manual stopwatches introduce human reaction time (approx. s), making them unsuitable for high-speed collision events compared to light gates.
