Key relationship
vCM = (m₁u₁+m₂u₂)/(m₁+m₂); xCM = vCM(t−2).
Physics · Class 11
Follow a collision centre
Internal collision forces change the carts individually, while their centre of mass continues along a straight line at a constant velocity. The sticking collision dissipates kinetic energy but conserves momentum.
Open the interactive experiment →Follow a collision centre
வெளிப்புற விசை இல்லாத மோதலில் நிறை மையம் சீரான வேகத்தில் நகரும். ஒட்டிக்கொள்ளும் மோதலில் இயக்க ஆற்றல் குறையும்.
Key notes, relationships and model limits
Remember
Internal collision forces change the carts individually, while their centre of mass continues along a straight line at a constant velocity. The sticking collision dissipates kinetic energy but conserves momentum.
Common trap
An inelastic collision does not stop the centre of mass unless its initial velocity was zero.
Model limits
Carts start so that they meet at x=0 at t=2 s and stick. No external horizontal force. The curve includes the approach and combined motion.
What you will learn
Separate centre-of-mass motion from internal collision effects.
Try the experiment
Try both scenarios, change one control, and predict the result before checking the graph and readouts.
Think of it this way
Change one input while keeping the others fixed, as you would in a controlled experiment.
Worked example
vCM = 2/6 = 0.333 m/s. The collision loses ½(2×4/6)(3−(−1))² = 10.67 J.
Why this matters
The model connects follow a collision centre with an observable reading. Check the equation and assumptions before applying it.
Before you start
SI units · algebra · graph reading
Check your understanding
For 2 kg at 3 m/s and 4 kg at −1 m/s, what is vCM?
- 1 m/s
- 0.333 m/s
- 2 m/s
Read the explanation
Total momentum is 6−4 = 2 kg·m/s; divide by total mass 6 kg.
Course connection: Class XI Chapter 6. Consult the roadmap for CBSE, NEET, JEE Main and Advanced scope.