Physics 11–12 · Year 11

Impulse from a force-time graph: cart into a spring bumper and bouncing ball

Module 2: Dynamics (Momentum, Energy and Simple Systems)

Practical, model not builtLow risk

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The idea

The area under a force-time graph equals the change in momentum, so a longer collision time means a smaller peak force for the same impulse.

What you need

Dynamics cart with a force sensor mounted on its front, or a force sensor fixed to a wall bumper, sampling at 1 kHz or faster
Spring bumper and a hard bumper, motion sensor or light gate for the approach and rebound speeds
Tennis ball, electronic balance, phone video at 240 frames per second for the bounce version

How to do it

Weigh the cart. Push it at the spring bumper at about 0.5 m/s while logging force and velocity.
Read the approach and rebound velocities and compute the momentum change m (v - u).
Integrate the force-time curve (software area) and compare with the momentum change.
Repeat with the hard bumper: same approach speed, shorter contact time, higher peak force.
Bounce version: film a tennis ball dropped from 1.0 m; read the speeds just before and after the bounce and the contact time to the nearest frame (4.2 ms at 240 frames per second).

What you should see

The learner knows it worked when the area under the force-time curve matches the momentum change within about 10 per cent. A 57 g tennis ball dropped from 1.0 m arrives at 4.43 m/s; if it rebounds to 0.55 m its upward speed after the bounce is 3.28 m/s, a momentum change of 0.440 kg m/s, and if the contact spans two frames (8.3 ms) the average force is 53 N, about 94 times the ball's weight. For the cart the contact time is pi sqrt(m/k) and the peak force v sqrt(k m), so a bumper one quarter as stiff doubles the contact time and halves the peak force while the impulse stays the same.

What changes

What you change: bumper stiffness (contact time)
What you measure: peak force and contact time
What you keep the same: same cart mass
same approach speed

Common misconceptions

Each of these ideas is wrong, and the activity is a chance to test it.

A softer bumper reduces the impulse; it reduces the peak force but the impulse is fixed by the momentum change.
The force during a bounce is about the ball's weight; it is tens of times larger for a short time.

Safety card

Low riskLearners carry it out

Hazards

cart impacts on the sensor

Controls

approach speeds below 1 m/s
sensor rated for the force

Note

Record the activity in RiskAssess (https://www.riskassess.com.au/) and follow the Science ASSIST risk management information sheet (https://asta.edu.au/resource/ais-risk-management-and-risk-assessment/).

Curriculum references

The NSW syllabus outcomes and Australian Curriculum v9 codes this activity supports. They are references, not a verified or complete curriculum alignment.

Physics Stage 6 Syllabus (2017), current: Year 11 until the end of 2026, Year 12 until Term 3 2027PH11-9 PH11/12-4
Physics 11-12 Syllabus (2025), not yet taught: Year 11 from Term 1 2027, Year 12 from Term 4 2027, first HSC examination 2028PY-11-01 PY-11WS-04
Australian Curriculum v9No Australian Curriculum v9 code is listed.

Sources

The pages the author read to write this activity.

All Concept Studio activities