Core Practical 10: Investigating Collisions using ICT

Two-Dimensional Collisions: Interactions where objects move in a plane rather than along a single straight line, requiring momentum to be treated as a 2D vector quantity.

ICT in Mechanics: The use of Information and Communication Technology, specifically video tracking software, to record and analyze motion that occurs too rapidly for manual measurement.

Conservation of Linear Momentum: The principle stating that the total momentum of a closed system remains constant ($\sum \vec{p}_{initial} = \sum \vec{p}_{final}$) provided no external forces act on it.

System Components: In this practical, the system typically consists of two small spheres (ball bearings) of known masses colliding on a horizontal surface.

Vector Resolution: In 2D collisions, momentum must be resolved into two perpendicular components (usually $x$ and $y$). Conservation applies independently to each: $\sum p_{x, initial} = \sum p_{x, final}$ and $\sum p_{y, initial} = \sum p_{y, final}$.

Impulse-Momentum Relationship: While the total momentum is conserved, individual objects experience an impulse ($I = F\Delta t = \Delta p$) equal to their change in momentum during the collision.

Elasticity and Energy: A collision is elastic if total kinetic energy is conserved ($\sum \frac{1}{2}mv^2_{initial} = \sum \frac{1}{2}mv^2_{final}$). Most macroscopic collisions are inelastic, where some energy is transferred to internal energy (heat/sound).

Frame Rate and Scaling: ICT software calculates velocity by measuring the change in pixel position between frames ($\Delta s$) and dividing by the time interval between frames ($\Delta t = 1/fps$). A physical scale (e.g., a ruler) is required to convert pixels to meters.

Component Check: Always check if the total momentum in the y-direction is zero before the collision. If it is, the sum of the y-momenta of the two objects after the collision must also sum to zero.

Vector Diagrams: When asked to prove conservation, draw a closed vector triangle (or polygon). If the vectors for initial and final momentum form a closed loop, momentum is conserved.

Units and Precision: Ensure masses are converted to kilograms ($kg$) and velocities to meters per second ($m/s$). Use a micrometer to measure sphere diameters for high-precision software scaling.

Sanity Check: If the calculated final momentum is significantly higher than the initial, check for external forces (like a sloped table) or errors in the software's scale calibration.

Ignoring Mass: A common mistake is comparing velocities instead of momenta. Even if spheres look identical, their masses must be measured and multiplied by their respective velocity vectors.

Parallax Error: If the camera is not perfectly vertical, the recorded distances will be foreshortened, leading to incorrect velocity calculations.

Friction Neglect: On a rough surface, external friction acts as an external force, causing a measurable decrease in total momentum over time. The analysis should focus on the frames immediately before and after the impact.

Sign Convention: In 2D, angles matter. A velocity of $1.0 m/s$ at $30^{\circ}$ above the axis has a different momentum component than $1.0 m/s$ at $30^{\circ}$ below the axis.