The bridge

A vehicle weighing 5,800 kg passes 41 km/h on an arched bridge with a radius of curvature of 62 m. What force is pushing the car onto the bridge as it passes through the center? What is the maximum speed it can cross over the center of the bridge so that it does not fly off the road?

Correct answer:

F =  44764.139 N
v₂ =  24.6621 m/s

Step-by-step explanation:

$$\begin{gathered} m=5800\text{ kg } \\ {v}_1=41\text{ km/h}\to \text{ m/s}=41\mathrm{/}3.6\text{ m/s}=11.38889\text{ m/s } \\ r=62\text{ m } \\ g=9.81{\text{m/s}}^2 \\ F=F_g-F_o \\ F=m\cdot g-m\cdot v_1^2\mathrm{/}r=5800\cdot 9.81-5800\cdot 11.3889^2\mathrm{/}62\text{ N}=44764.139\text{ N}=4.476\cdot 10^4\text{ N} \end{gathered}$$

$$\begin{gathered} F_g=F_o \\ m\cdot g=m\cdot v_2^2\mathrm{/}r \\ g=v_2^2\mathrm{/}r \\ {v}_2=\sqrt{r\cdot g}=\sqrt{62\cdot 9.81}=24.6621\text{ m/s} \end{gathered}$$

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