1.2.8 · D5 · HinglishNewton's Laws & Dynamics
Question bank — Angle of friction, angle of repose — derivation
1.2.8 · D5· Physics › Newton's Laws & Dynamics › Angle of friction, angle of repose — derivation
True or false — justify
A heavier block ka angle of repose bada hota hai
False. Down-slope pull aur friction limit dono mein same hai, isliye wo cancel ho jaata hai; ko mass ke baare mein kuch nahi pata.
Bada contact area angle of repose ko kam karta hai
False. Na mein, na mein area aata hai, isliye area-independent hai — yeh Coulomb friction model mein baked in hai.
Angle of friction surface se measure hota hai, normal se nahi
False. Definition ke anusaar , ka normal se tilt hai; surface se jo angle banta hai woh hai.
aur equal hain, isliye dono same reference line se measure hote hain
False. Dono sirf value mein equal hain: normal se measure hota hai, plane ka horizontal se tilt hai. Same number, alag geometry.
Horizontal floor par koi push nahi hai toh reaction seedha normal ke saath upar point karta hai
True. Koi horizontal force apply nahi hai toh , isliye aur — reaction bilkul normal par hi baithta hai.
Angle of repose par block equilibrium mein hota hai
True. "Verge par hona" matlab abhi bhi nahi hila: forces balance hain ( per Newton's First Law (Equilibrium)), friction apne maximum par hai lekin abhi exceed nahi hua.
Ramp ko se zyada tilt karne par block accelerate karta hai kyunki static friction khatam ho jaati hai
False. Static friction ki jagah kinetic friction aata hai; kyunki , down-slope pull ab friction se zyada ho jaata hai aur net force block ko accelerate karta hai.
Agar (frictionless) hai, toh angle of repose hai
True. : thodi si bhi tilt par block slip kar jaata hai, kyunki koi friction hai hi nahi usse rokne ke liye.
Angle of friction kabhi se zyada nahi ho sakta
True. aur , hone par bhi ke paas jaata hai lekin kabhi reach nahi karta, isliye hamesha.
double karne par angle of repose double ho jaata hai
False. Relation hai , jo nonlinear hai; double karne par double se kam badhta hai (jaise lekin , na ki ).
Spot the error
"Repose par, ."
Galat coefficient. Block move karne ke kaagaar par hai lekin abhi hila nahi, isliye yeh static hai — use karo, jisse milta hai.
"Incline par , kyunki block ka weight surface par push karta hai."
Galat. Sirf perpendicular component surface par press karta hai: . Poora sirf horizontal ground par hota hai jahan .
"Kyunki , hamesha weight se bada hota hai."
Ye general nahi hai. Horizontal ground par verge par hota hai, lekin incline par apne axes ke saath sirf gravity ka ek hissa balance karta hai, isliye yeh blanket claim galat hai.
", aur kyunki bina limit ke badh sakta hai, bhi tak pahunch sakta hai."
Galat. Static friction par cap hai, isliye maximum tak jaata hai aur maximum tak, jo strictly se neeche hai.
"Kyunki hai, steeper repose angle matlab slipperier surface."
Ulta hai. Bada matlab bada — ek grippier surface block ko steeper slope par rokta hai. Slippery = chhota = chhota .
"Slipping ke verge par, block ki slope ke neeche thodi si velocity hoti hai."
Galat. "Verge" matlab velocity exactly zero hai; yeh motion se pehle ka boundary instant hai, abhi bhi static friction aur equilibrium se governed hai.
"Reaction angle nikalne ke liye humein block ka mass chahiye."
Galat. — mass cancel ho jaata hai. Reaction ki direction () ke liye sirf chahiye; sirf uski magnitude ke liye actual forces chahiye.
Why questions
Normal forces cancel kyun ho jaate hain jab compute karte hain?
Kyunki verge par hai, isliye — same upar aur neeche dono mein aata hai aur divide out ho jaata hai, sirf ek pure coefficient bachta hai.
Hum weight ko horizontal/vertical ke bajaye incline ke along aur perpendicular resolve kyun karte hain?
Kyunki slipping incline ke along hoti hai; woh axes choose karne par driving force aur normal force clean, alag directions par aa jaate hain, isliye kisi bhi single force ko dobara split nahi karna padta (dekho Resolving Vectors into Components).
Angle of friction, angle of repose ke equal kyun hota hai?
Dono derivations independently par khatam hoti hain. Geometrically, repose par gravity normal se exactly utna tilt hoti hai jitna reaction normal se tilt hota hai, aur equilibrium dono tilts ko match karne par force karta hai.
Hum aur dono ke liye static (kinetic nahi) friction kyun use karte hain?
Dono motion se just pehle maximum grip describe karte hain, jo static limit hai. Kinetic friction tabhi apply hota hai jab sliding already shuru ho chuki ho.
Wahi idea Banking of Roads mein dobara kyun aata hai?
Kyunki banking mirror question poochta hai — kis tilt par gravity aur contact forces ek given friction ke liye balance hote hain — isliye critical/safe angle phir se ek friction-related ratio ka banta hai.
Do perpendicular forces aur ko Pythagoras se kyun combine kar sakte hain?
Kyunki perpendicular vectors ek right triangle ki do legs banate hain, aur uska hypotenuse hai, isliye — force triangle par Pythagorean theorem ka direct application.
Edge cases
Jab surface perfectly smooth ho () toh kya hoga?
: koi bhi nonzero tilt slide karaata hai, kyunki down-slope pull ko resist karne ke liye koi friction hai hi nahi.
Jab (extremely grippy surface) toh ka kya hoga?
jaata hai lekin kabhi reach nahi karta. Infinitely grippy surface bhi gravity ke against friction se block ko perfectly vertical wall par nahi rok sakti.
Flat horizontal surface par koi horizontal push nahi hai toh , , aur kya hain?
, isliye aur seedha upar point karta hai — reaction normal ke saath coincide karta hai kyunki koi cheez block ko slide nahi kar rahi.
Agar flat ground par ke saath horizontal push exactly verge tak pahunche, toh kya hoga?
; reaction vertical se lean karta hai kyunki tab friction aur normal size mein equal hote hain.
Exactly par, kya friction apne maximum par hai ya exceed ho gaya?
Exactly apne maximum par, , aur exceed nahi hua — wahi equality hi repose angle ki definition hai.
Ek block incline par ke saath baitha hai; friction force kitni badi hai?
Sirf utni badi jitni balance ke liye zaroori hai, , jo se kam hai. Friction "hamesha max par" nahi hoti — repose se neeche yeh self-adjust karti hai jo bhi equilibrium maintain kare.
Recall Lock karne ke liye ek-line summary
Is page ki har cheez ek single equation se nikalti hai: . Mass aur area vanish ho jaate hain, static friction verge par rule karti hai, aur normal se reaction ka tilt, horizontal se ramp ke tilt ke equal hota hai.