Question

A car of mass $m=1000$kg is moving with constant speed $v=100$m/s on a parabolic shaped bridge AFOE of span $r-40$, and height h$=20$m as shown in the figure. Then the net force applied by the bridge on the car when the car is at point F, is?

• A. $5000\sqrt{\frac{5}{2}}$N
• B. $\frac{5000}{\sqrt{2}}$N
• C. $\frac{10000}{\sqrt{2}}$N
• D. $5000\sqrt{\frac{2}{5}}$N

Answer 1

The correct option is A $5000\sqrt{\frac{5}{2}}$N

$\text{Taking origin at}0\&0C\text{as}y\text{-axis equation of}$

$\text{bridge is}y=\frac{x^2}{20}=\frac{dy}{dx}=\frac{2x}{20}=\frac{2\times 10}{20}=1$

$\text{So, slope at}F=\frac{d{y}^2}{2}$

$\text{At point}F,\mathrm{mg}\frac{1}{\sqrt{2}}-N=\frac{m{v}^2}{R}$

$N=\frac{mg}{\sqrt{2}}-\frac{m{v}^2}{R}\&f_s=\frac{mg}{\sqrt{2}}$

$$\begin{array}{cc}AtF,R=\frac{(1+1{)}^{3/2}}{1/10}=20\sqrt{2}\text{(metre)}& \\ \therefore N=\frac{10m}{\sqrt{2}}-\frac{100m}{\sqrt{2}}=\frac{5m}{\sqrt{2}}\&f_s=\frac{10m}{\sqrt{2}}& \\ \therefore \text{Net force}=m\sqrt{\frac{25}{2}+\frac{100}{2}}& =5m\sqrt{\frac{5}{2}}N=5\times 1000\sqrt{\frac{5}{2}}N\\ & =5000\sqrt{\frac{5}{2}}N\end{array}$$