98, 100; CP9, CP10Further MechanicsCore

Core Practicals 9–10: Impulse and Collision Analysis

A force sensor and motion analysis provide two independent descriptions of an interaction. Compare impulse with momentum change, then test vector momentum conservation in a collision.

40 min 6.1 Momentum and Circular Motion

What you'll be able to do

Integrate a force–time trace graphically
Extract velocities from calibrated video
Distinguish momentum conservation from kinetic-energy conservation

CP9: compare impulse and change of momentum

Use a suitable trolley, force sensor and motion detector or light gates in a controlled collision arrangement. Measure mass and signed velocities immediately before and after the interaction. The momentum change is m(v−u), with one consistent positive direction.

Zero the force sensor, record at a sufficiently high sampling rate, and find the area under its force–time trace over the whole interaction. Subtract any baseline offset. Compare this impulse with momentum change within their uncertainties rather than comparing peak force alone with a velocity.

J=\int F\,dt=\Delta p

CP10: use ICT to analyse small-sphere collisions

Record suitable small spheres moving and colliding on a level surface, with a length calibration in the plane of motion and a known frame rate. Keep the camera perpendicular to that plane to reduce perspective distortion. Track centres over several frames close to the collision, avoiding frames during contact.

Convert displacement components to velocity components using frame intervals. For two-dimensional collisions, compare total x momentum before and after and separately compare total y momentum. A scalar sum of speeds cannot test vector conservation. Account for mass differences and include every moving object in the chosen system.

Evaluate the model and energy evidence

A short collision interval makes external frictional impulse relatively small, but it is not automatically zero. Motion far before or after contact can be altered by friction. Finite pixel size, uncertain centre positions and limited frame rate affect inferred velocities; a longer tracking interval helps only while velocity stays suitably constant.

Calculate total kinetic energy separately using each object’s speed squared. Momentum can be conserved while kinetic energy falls in an inelastic collision. Use scatter and measurement uncertainties to decide whether a difference is significant, rather than declaring a perfectly elastic collision from two rounded equal totals.

Work through the reasoning

Try each problem before opening the worked solution. State the physical model, show substitutions with consistent units, and explain what your answer means.

Example 1A 0.50 kg trolley changes velocity from +0.60 to −0.20 m s⁻¹. Find signed impulse and average force over 0.10 s.

\Delta p=0.50(-0.20-0.60)=-0.40

kg m s⁻¹.

F_{average}=-0.40/0.10=-4.0

Answer−0.40 N s and −4.0 N in the chosen direction convention.

Example 2At 100 frames/s a sphere moves 24 mm horizontally over four frame intervals. Find its x velocity and the momentum component for mass 0.020 kg.

1Elapsed time

=4/100=0.040

v_x=0.024/0.040=0.60

m s⁻¹ and

p_x=0.020(0.60)=0.012

kg m s⁻¹.

Answer0.60 m s⁻¹ and 0.012 kg m s⁻¹ in the positive x direction.

Equation recap

J=\int F\,dt=\Delta p

Equation recap

Common mistakes to avoid

Using speed changes without velocity signs.

Direction matters in Δp.

Counting five frames as five intervals between their centres.

Five successive frame positions span four intervals.

Key takeaways

Force–time area predicts momentum change.
Video requires length and time calibration.
Momentum and kinetic-energy tests answer different questions.

Test yourself

Answer a few questions, then review anything you missed.

Next step

Keep practising

Start with the quiz above to check the key ideas. You can also choose another topic from the practice library.

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