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 pushes the car onto the bridge as it passes through the center? What maximum speed can it cross over the bridge's center so it does not fly off the road?

Correct answer:

F =  44764.139 N
v₂ =  24.6621 m/s

Step-by-step explanation:

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

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

Try another example