The radius of the curved road at the given condition is 54.1 m.
The given parameters:
- mass of the car, m = 1000 kg
- speed of the car, v = 50 km/h = 13.89 m/s
- banking angle, θ = 20⁰
The normal force on the car due to banking curve is calculated as follows;
[tex]Fcos(\theta) = mg[/tex]
The horizontal force on the car due to the banking curve is calculated as follows;
[tex]Fsin(\theta) = \frac{mv^2}{r}[/tex]
Divide the second equation by the first;
[tex]\frac{Fsin(\theta)}{Fcos(\theta) } = \frac{mv^2}{rmg} \\\\tan(\theta) = \frac{v^2}{rg} \\\\r = \frac{v^2}{g \times tan(\theta)} \\\\r = \frac{13.89^2}{9.8 \times tan(20)} \\\\r = 54.1 \ m[/tex]
Thus, the radius of the curved road at the given condition is 54.1 m.
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