Same ends, different paths
"Same ends, different paths" is a free, interactive Class 11 Physics simulation for NEET and JEE, built on the NCERT section "Potential energy and conservative forces" in Work, Energy and Power. Drag a crate between two points along different paths: gravity's work stays the same, friction's work grows with path length. JEE Main asked 44 questions from this chapter across the 42 shifts Lumi has analysed (2017–2026).
From the lesson Potential energy and conservative forces in Work, Energy and Power. Change the values and watch what happens.
What it shows
NCERT § Concept of Potential Energy
Drag a crate between two points along different paths: gravity's work stays the same, friction's work grows with path length.
Controls
3 to try
- Dragwaypoints of the path
- Togglecount gravity / friction
- Sliderμ 0–0.5
Try this
Find two different paths with equal gravity work but friction work differing by a factor of 2.
Common mistake
Assigning a potential energy to friction.
In JEE Main
42 shifts analysed
44 questions from Work, Energy and Power across the 42 JEE Main shifts Lumi has analysed (2017–2026).
The idea behind it
NCERT § "The Concept of Potential Energy"
- Potential energy is energy stored by virtue of a body's position or configuration. It is defined only for conservative forces.
- A force is conservative if the work it does depends only on the start and end points, not on the path; equivalently, the work it does over any closed path is zero.
- Gravity near the earth's surface and the spring force are conservative. Friction and air drag are not, since the work they do depends on the path.
- For a conservative force in one dimension, F(x) = −dV/dx: the force points towards decreasing potential energy.
- Near the earth's surface the gravitational potential energy of a mass m at height h is V(h) = mgh, measured from a chosen zero level.
- Only changes in potential energy have physical meaning; the zero level can be chosen wherever convenient.
- Potential energy has the same unit as work and kinetic energy, the joule.
Questions
4 answers
- What does the "Same ends, different paths" simulation show?
- Drag a crate between two points along different paths: gravity's work stays the same, friction's work grows with path length.
- What mistake does the "Same ends, different paths" simulation fix?
- A common mistake it clears up: assigning a potential energy to friction.
- Does JEE Main ask questions from Work, Energy and Power?
- Yes. JEE Main asked 44 questions from this chapter across the 42 shifts Lumi has analysed (2017–2026).
- Is this simulation free?
- Yes. It is free and runs in the browser on a phone or a laptop. It belongs to the lesson "Potential energy and conservative forces" in Work, Energy and Power (Class 11 Physics).
Embed this simulation
Free, with a link back
Teaching this idea? Put the simulation on your own page or LMS with this code.