Part or riding a bicycle involves leaning at the correct angle when making a tur

Question

Part or riding a bicycle involves leaning at the correct angle when making a turn, as seen in the figure. To be stable, the force exerted by the ground must be on a line going through the center of gravity. The force on the bicycle wheel can be resolved into two perpendicular components friction parallel to the road (this supplies the centripetal force), and the vertical normal force (which must equal the system's weight). Randomized Variables v = 10.5 m/s r = 25.5 m/s Calculate theta for a 10.5 m/s turn of radius 25.5 m (as in a race) in degrees. A numeric value is expected and not an expression. theta =

Explanation / Answer

Given that

Velocity (v) =10.5m/s

Angle(theta) =?

Radius (r) =25.5m

Acceleration (g) =9.81m/s2

Now equating the forces in vertical and horizontal directions we get

mv2/r =Fsintheta

mg =Fcostheta

m =Fcostheta/g

Now using the above equations we get

theta =tan-1(v2/rg) =tan-1( (10.5)2/25.5*9.81) =tan-1(0.4407)=23.784degrees

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