Car on a level road and on a banked roadसमतल सड़क और ढालू (बंकित) सड़क पर कार

NCERT Fig 4.14 · interactive diagram

Parts and their functions

• Car on a level road (समतल सड़क पर कार) — Only friction can push it towards the centre.
• Friction gives the centripetal force (घर्षण अभिकेंद्र बल देता है) — mv²/R ≤ μₛmg ⇒ v ≤ √(μₛRg), independent of mass.
• Banked road (ढालू (बंकित) सड़क) — The outer edge is raised so the road tilts by θ towards the centre.
• Banking angle θ (ढाल कोण θ) — Optimum speed (no friction needed): v₀ = √(Rg tan θ).
• Car on the bank (ढाल पर कार) — No vertical acceleration; horizontal net force = mv²/R towards the centre.
• Normal force N (अभिलंब बल N) — Perpendicular to the road surface, so it tilts towards the centre.
• N cos θ (vertical) (N cos θ (ऊर्ध्वाधर)) — N cos θ = mg + f sin θ.
• N sin θ (towards centre) (N sin θ (केंद्र की ओर)) — N sin θ + f cos θ = mv²/R.
• Friction f (down the slope) (घर्षण f (ढाल पर नीचे)) — At the maximum speed the car tends to slide outwards, so friction acts down the slope: v_max = √[Rg(μₛ + tan θ)/(1 − μₛ tan θ)].
• Weight mg (भार mg) — Vertical; has no part towards the centre.
• Direction of the centre (केंद्र की दिशा) — The net force must point here: F = mv²/R.

Original diagram drawn by Simple Learning Hub, based on NCERT Fig 4.14. Report a mistake