Horizontal 83148

The bend has a radius of r = 100 m and is inclined at an angle of 20° to the horizontal plane (= tilt angle). What is the safe (the "best") speed to go through this curve?
Sketch the picture regarding NIVS, mark the forces, and calculate.

Correct answer:

v =  19.078 m/s

Step-by-step explanation:

$$\begin{gathered} r=100\text{m} \\ \alpha =20{}^{\circ } \\ g=10{\text{m/s}}^2 \\ {F}_o+F_g=F \\ {F}_g=m\cdot g \\ {F}_o=m{v}^2/r \\ \tan \alpha =\frac{F_o}{F_g} \\ \tan \alpha =\frac{m{v}^2/r}{m\cdot g} \\ \tan \alpha =\frac{v^2}{r\cdot g} \\ v=\sqrt{r\cdot g\cdot \tan \alpha }=\sqrt{r\cdot g\cdot \tan 20°}=\sqrt{100\cdot 10\cdot \tan 20°}=\sqrt{100\cdot 10\cdot 0.36397}=19.078=19.078\text{m/s} \end{gathered}$$

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