Question

Discuss the motion of a car on a circular level road.

Answer 1

Explanation:

When a vehicle goes round a level curved path, it should be acted upon by a centripetal force. While negotiating the curved path, the wheels of the car have a tendency to leave the curved path and regain the straight-line path. As this force is provided only by the force of friction.

Answer 2

Answer:

Explanation:

Answer

N is normal force,

f is frictional force

Ncosθ=mg+fsinθ⟶(1)

and

fcosθ+Nsinθ=rmv2​⟶(2)f=μN⟶(3)∴Ncosθ=μNsinθ+mgN(cosθ−μsinθ)=mg⇒N=cosθ−μsinθmg​⟶(4)

Putting (3) and (4) in (2):

cosθ−μsinθμmgcosθ​+cosθ−μsinθmgsinθ​=rmv2​⇒μmgrcosθ+mgrsinθ=mv2cosθ−μmv2sinθ⇒μmgr+mgrtanθ=mv2−μmv2tanθ⇒mgr(μ+tanθ)=mv2(1−μtanθ)⇒(1−μtanθ)rg(μ+tanθ)​=v2⇒v=(1−μtanθ)rg(μ+tanθ)​

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