Work is the area under F–x
"Work is the area under F–x" is a free, interactive Class 11 Physics simulation for NEET and JEE, built on the NCERT section "Work done by a variable force" in Work, Energy and Power. Drag points of an F-x graph; the signed area is the work, which (by the work-energy theorem) sets the block's final speed. NEET has asked about this idea 4 times in 10 years of papers. JEE Main asked 44 questions from this chapter across the 42 shifts Lumi has analysed (2017–2026).
From the lesson Work done by a variable force in Work, Energy and Power. Change the values and watch what happens.
What it shows
NCERT § Work by a Variable Force
Drag points of an F-x graph; the signed area is the work, which (by the work-energy theorem) sets the block's final speed.
Controls
4 to try
- Drag4–6 F-x points (−20…20 N over 0–10 m)
- Sliderblock mass 0.5–5 kg
- Sliderinitial speed 0–5 m/s
- Togglefriction μ(x) variable
Try this
Shape a force graph that takes a 2 kg block from rest to exactly 5 m/s at x = 10 m (net area 25 J).
Common mistake
Using W = Fd with an average or end-point force; ignoring negative area.
In NEET
10 years of papers
Asked 4 times in 10 years of NEET.
See the past questions: Work-Energy Theorem, Friction Forces, Work, Energy and Power (chapter)
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 § "Work Done by a Variable Force"
- When a force varies with position, split the displacement into small steps and add F(x)Δx; in the limit, W = ∫F(x) dx between the initial and final positions.
- Graphically, the work done is the area under the force-displacement graph, taken with sign.
- The work-energy theorem holds for variable forces as well; it is proved by integrating the second law over the displacement.
- Work by a spring from x_i to x_f is −½k(x_f² − x_i²), which follows from integrating F = −kx.
- Area below the displacement axis on an F-x graph represents negative work.
Questions
5 answers
- What does the "Work is the area under F–x" simulation show?
- Drag points of an F-x graph; the signed area is the work, which (by the work-energy theorem) sets the block's final speed.
- What mistake does the "Work is the area under F–x" simulation fix?
- A common mistake it clears up: using W = Fd with an average or end-point force; ignoring negative area.
- Has NEET asked about this idea?
- Yes. NEET has asked about this idea 4 times in 10 years of papers.
- 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 "Work done by a variable force" 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.