Physics · Class 11

Impulse and contact time

Momentum is mv. Newton’s second law links force to its rate of change; integrating force over time gives impulse. Both the short and long triangular force pulses remove the same incoming momentum. The broader pulse needs a lower peak but produces a longer stopping distance.

Open the interactive experiment →

The area stops the object.

விசை–நேர வரைபடத்தின் பரப்பளவு உந்தம் மாற்றத்திற்குச் சமம். நிறுத்தும் நேரம் அதிகரித்தால் அதே உந்தம் மாற்றத்திற்கான உச்ச விசை குறையும்.

Key notes, relationships and model limits

Key relationship

J = ∫F dt = Δp = −mu; triangular pulse: |Fpeak| = 2mu/τ.

Remember

Common trap

A smaller peak force can still produce the same impulse if it acts for longer.

Model limits

A prescribed triangular stopping force brings the object to rest without rebound. Force opposes incoming motion. Animation stops at the contact end.

What you will learn

Relate force-time area, impulse, momentum change and peak force.

Try the experiment

Compare hard and soft presets with unchanged mass and speed. Scrub across the triangular pulse.

Think of it this way

A catcher moves the hands backward to extend the stopping time of a ball.

Worked example

A 2 kg object at 5 m/s has 10 kg·m/s momentum. A 1 s triangular stop needs a 20 N peak and impulse −10 N·s.

Why this matters

Impulse explains cushioning; a force value alone does not specify the change in momentum.

Before you start

Vector components · velocity · SI units

Check your understanding

If stopping time doubles with the same triangular shape and momentum change, peak force is…

Doubled
Halved
Unchanged

Read the explanation

The triangle area is ½Fpeakτ. A doubled base requires half the height to retain the area.

Course connection: CBSE XI Chapter 4; NEET/Main Unit 3; JEE Advanced Mechanics. Apply each exam’s stated assumptions.