Key relationship
a = g(sinθ − μ cosθ); K + U + Q = K₀ + U₀; Q = μmg cosθ · s.
Physics · Class 11
Track energy balance
Without friction, gravitational potential turns into kinetic energy and their sum stays constant. With friction, mechanical energy decreases but the energy balance includes dissipated thermal energy. A large enough resistance can prevent starting or stop an initially moving slider before the bottom.
Open the interactive experiment →Energy can change form without disappearing.
உராய்வு இல்லாமல் நிலை மற்றும் இயக்க ஆற்றல்களின் கூட்டுத்தொகை மாறாது. உராய்வுடன் இயந்திர ஆற்றல் வெப்ப ஆற்றலாக மாறும்; மொத்த ஆற்றல் கணக்கு நிலைத்திருக்கும்.
Key notes, relationships and model limits
Remember
Without friction, gravitational potential turns into kinetic energy and their sum stays constant. With friction, mechanical energy decreases but the energy balance includes dissipated thermal energy. A large enough resistance can prevent starting or stop an initially moving slider before the bottom.
Common trap
Mechanical energy is conserved only when non-conservative work is absent, while total accounted energy remains conserved.
Model limits
Point-mass slider on a straight ramp, no rotational energy. One equal static/kinetic coefficient; a resting slider remains at rest when tanθ ≤ μ. Motion ends at rest or the ramp end; final arrival speed is held.
What you will learn
Track conservation across kinetic, potential and dissipated energy; identify stopping limits.
Try the experiment
Play the frictionless and dissipative presets. Finally choose a strong-friction stop and observe the height at rest.
Think of it this way
An energy ledger moves value between accounts; friction moves some into a thermal account.
Worked example
A 2 kg slider at 3 m starts with 58.86 J potential energy. With no friction its bottom speed is √(2gh) = 7.67 m/s, independent of mass.
Why this matters
An explicit loss account prevents confusion between mechanical-energy conservation and total-energy conservation.
Before you start
Vector components · velocity · SI units
Check your understanding
On a rough ramp, why is K + U smaller at the bottom?
- Energy has ceased to exist
- Some mechanical energy became thermal energy
- Gravity stopped acting
Read the explanation
Friction converts mechanical energy into thermal energy. Including that loss restores the energy balance.
Course connection: CBSE XI Chapter 5; NEET/Main Unit 4; JEE Advanced Mechanics. Apply each exam’s stated assumptions.