Interactive practical

Two-dimensional collision analysis using ICT

Calibrate a video scale, track sphere centres and investigate momentum and kinetic energy in two-dimensional collisions.

Open interactive simulation

A-Level Physics

Analysing collisions with video or data logging

CCEA 1210 — matched to your course.

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Practical focuses1

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Practical focus

Use ICT to measure two-dimensional velocities before and after collisions and test momentum conservation.

Practical method

Aim

Use video analysis or a data logger to test conservation of momentum in collisions and compare kinetic energy before and after.

Variables

Independent variable: type of collision (elastic or sticking) and masses
Dependent variable: velocities before and after
Control variables: level, friction-compensated track; the same camera position and scale.

Apparatus

Two trolleys with magnetic buffers or Velcro pads
Level track
Video camera or phone at 120 frames per second, or light gates with data logger
Metre rule in view for scale
Balance

Method

Measure each trolley's mass. Place a metre rule in the plane of motion for scale.
Push trolley A towards stationary trolley B and film the collision from the side.
Step through the video frame by frame. Measure the distance moved over a known number of frames before and after the collision to find each velocity.
Calculate total momentum before and after, and total kinetic energy before and after.
Repeat with Velcro pads so the trolleys stick together, and with different masses.

Sample results

Both trolleys 0.50 kg; B initially at rest; video at 120 frames per second.

Collision	\(u_{A}\) / m s⁻¹	\(v_{A}\) / m s⁻¹	\(v_{B}\) / m s⁻¹	p before / kg m s⁻¹	p after / kg m s⁻¹
Sticking (Velcro)	0.80	0.40	0.40	0.40	0.40
Magnetic buffers	0.80	0.02	0.77	0.40	0.40

Analysis

Momentum is conserved in both collisions within measurement uncertainty. In the sticking collision kinetic energy falls from 0.16 J to 0.08 J (inelastic). With magnetic buffers kinetic energy is almost unchanged (0.16 J to 0.15 J), so the collision is nearly elastic.

Uncertainty

Positions are read to about ±1 mm over a distance of about 50 mm, so each velocity has about 2–4% uncertainty. Measuring over more frames reduces this.

Errors and improvements

Problem	Effect	Improvement
Camera not side-on	Distances distorted by perspective	Place the camera level and far away, with the scale in the plane of motion
Too few frames analysed	Large velocity uncertainty	Measure over 10 or more frames
Friction	Velocities fall before and after	Friction-compensate the track and measure close to the collision

Risk assessment

Hazard	Risk	Control measure
Trolleys leaving the track	Injury	Use end stops
Electrical equipment near the track	Trip hazard	Keep cables tidy

Common mistakes

Assuming kinetic energy is always conserved.
Forgetting the scale factor between the video and real distances.
Using velocities measured far from the collision.

Worked analysis

Trolley A (0.50 kg) at 0.80 m s⁻¹ sticks to stationary B (0.50 kg). Momentum before = 0.40 kg m s⁻¹, so common velocity = \(\dfrac{0.40}{1.00}\) = 0.40 m s⁻¹. KE before = ½ × 0.50 × 0.80² = 0.16 J; after = ½ × 1.00 × 0.40² = 0.08 J.

Common misconception

Momentum is conserved in every collision of a closed system, but kinetic energy is conserved only in elastic collisions.

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