Q$6).$ A loaded van has a total mass of $2\mathrm{.}5$ tonne and a wheel$-$base width of $1\mathrm{.}9$ m $,$ and its centre of mass is $1\mathrm{.}65$ m above the ground. Assuming a coefficient of static friction between the tyres and the road is $0\mathrm{.}65,$ calculate the maximum limit of safe speed on a level road that has a horizontal radius of curvature of $125$ m $.$ What is likely to occur if the vehicle enters the curve at $\backslash (100\backslash$mathrm$\{$~km$\}/\backslash$mathrm$\{$h$\}\backslash )?$

Q$7).$ A circular plate rotates on a vertical spindle through its centre, making $10$ revolutions per second. It supports two masses of $7$ kg and $14$ kg at a radii of $0\mathrm{.}9$ m and $0\mathrm{.}7$ m respectively. The angle between the masses is $90$ degrees. Determine the resultant out$-$of$-$balance centrifugal force acting on the spindle due to the revolving masses.

Q$8).$ If a car takes a banked curve at less than the ideal speed, friction is needed to keep it from sliding toward the inside of the curve $($a real problem on icy mountain roads$).$

$($a$)$ Calculate the ideal speed to take a $120$ m radius curve banked at $\backslash (12\mathrm{.}0^\{\backslash$circ$\}\backslash )$

$($b$)$ What is the minimum coefficient of friction needed for a frightened driver to take the same curve at $\backslash (22\mathrm{.}0\backslash$mathrm$\{$~km$\}/\backslash$mathrm$\{$h$\}\backslash )?$

Note: In an "ideally banked curve," the angle $\backslash (\backslash$theta $\backslash )$ is such that you can negotiate the curve at a certain speed without the aid of friction between the tires and the road