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in Physics by (50 points)
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Explain why a cyclist bends while negotiating a curve road? Arrived at the expression for angle of bending for a given velocity.

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2 Answers

+1 vote
by (33.2k points)

The forces acting on the system

* gravitational force(mg)

* Normal force(v)

* Frictional force (f)

* Centrifugal force \((\frac{mv^2}r)\)

A system is in equilibrium is the rotational from of reference,

the net external force = net external torque = 0

(i) Torque = Due to gravitational force = ng AB

(ii) Torque - Due to centripetal force

\(\frac{mv^2}r BC\)

Vc(T)net = 0 → Rotational equilibrium

-mg AB + \(\frac{mv^2}r BC\) = 0

mg AB = \(\frac{mv^2}r BC\) 

From ABC,

AB = AC sin θ and BC = AC cos θ

mg AC sin θ = \(\frac{mv^2}r\)AC cos θ

tan θ = \(\frac{r}g\)

θ = tan-1\((\frac{v^2}{rg})\)

A cyclist has to bend by an angle θ from vertical θ = tan-1\((\frac{v^2}{rg})\) to stay in equilibrium and Hence to avoid falling.

0 votes
by (50 points)
        * we have to apply centrifugal force on the system which will be mv2/r.
         * The force will act through the centre of gravity.
         * The force is acting on a system is.                              1)gravitational force=(mg) 
                    2)normal force=(N) 
                    3)frictional force=(F) 
                    4)certrifugal force=[mv2/r]
         * The net external force and net external torque be zero. 
         * Let us consider all torques about the point A.image
For rotation equilibrium 
          τnet=0
           * The torque due to gravitational force about point A is(mg AB) is rotation will anti-clockwise that taken negative.
          * The torque due to the centrifugal force is [mv2/r BC] is rotation that taken as positive.
           -mg AB +mv2/rBC=0
            mg AB =mv2/r BC
From ΔABC
   AB=AC sinΦ and BC=AC cosΦ
   mg AC sinΦ=mv2/r AC cosΦ
   tanΦ=v2/rg
   Φ=tan-1 [v2/rg]
               *While negotiating a circular level road of radius r at velocity v, a cyclist has to bend by the angle Φ from vertical given by the above expression to stay in equilibrium.

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