Key relationship
Wg = mg(hi − hf) = −ΔUg; Wresistance = −fL; slow external work = ΔUg + fL.
Physics · Class 11
Two routes, different losses
Gravity is conservative: its work depends only on the initial and final heights. The two routes have identical gravity work even when one climbs higher. A resisting force does negative work along every part of the journey, so its energy loss depends on total length. External work for slow transport supplies both the potential-energy increase and the dissipated energy.
Open the interactive experiment →Ask whether the route matters.
ஈர்ப்பு விசையின் வேலை ஆரம்ப மற்றும் இறுதி உயரங்களை மட்டும் சார்ந்தது. உராய்வு போன்ற எதிர்ப்பு விசையின் வேலை பாதையின் நீளத்தைச் சார்ந்தது.
Key notes, relationships and model limits
Remember
Gravity is conservative: its work depends only on the initial and final heights. The two routes have identical gravity work even when one climbs higher. A resisting force does negative work along every part of the journey, so its energy loss depends on total length. External work for slow transport supplies both the potential-energy increase and the dissipated energy.
Common trap
A conservative force can do nonzero work on an open path; its closed-path work is zero.
Model limits
Two prescribed straight/segmented routes in uniform gravity. Constant tangential resistance f opposes travel, independent of normal force. External transport is quasistatic; corners are idealized.
What you will learn
Compare endpoint-dependent work with length-dependent dissipative work.
Try the experiment
Set resistance to zero and change detour height. Then add resistance and compare route losses.
Think of it this way
Climbing between the same floors changes the same gravity energy; a longer rough route consumes more effort.
Worked example
For m = 2 kg, hi = 1 m and hf = 3 m, gravity work is −39.24 J on either route. A 1 N resistance adds loss equal in joules to each route’s length in metres.
Why this matters
Path independence lets potential energy replace a complicated force-work integral.
Before you start
Vector components · velocity · SI units
Check your understanding
Two paths join the same endpoints in uniform gravity. Gravity’s work is…
- Greater on the longer path
- The same on both paths
- Always zero
Read the explanation
Wg = mg(hi − hf), so equal endpoints give equal gravity work.
Course connection: CBSE XI Chapter 5; NEET/Main Unit 4; JEE Advanced Mechanics. Apply each exam’s stated assumptions.