(Solved): The force exerted by an F1 tyre crash barrier Fig Q12 can be expressed by F=x3 where x is the dis ...

The force exerted by an F1 tyre crash barrier Fig Q12 can be expressed by $F=\beta x^3$ where $x$ is the distance deformed as the car makes impact and $\beta \left(\mathrm{N}/{\mathrm{m}}^3\right)$ is a constatnt. An F1 car with mass $637\mathrm{kg}$ including the driver travelling at a speed of $222\mathrm{km}/\mathrm{h}$ runs into the barrier and stops after $1.92\mathrm{m}$ displacement. Assuming that $15\%$ of the KE was lost during damage to the car, calculate the value of the barrier constant $\mathrm{C}\beta =\beta \times 10^{-5}$. [Answer to 2 d.p.] rig $4\perp$