3. A car of mass \(m \mathrm {~kg}\) moves round a curve of radius \(r \mathrm {~m}\) on a road which is banked at an angle \(\theta\) to the horizontal. When the speed of the car is \(u \mathrm {~ms} ^ { - 1 }\), the car experiences no sideways frictional force. Given that \(\tan \theta = \frac { u ^ { 2 } } { g r }\), show that the sideways frictional force on the car when its speed is \(\frac { u } { 2 } \mathrm {~ms} ^ { - 1 }\) has magnitude \(\frac { 3 } { 4 } m g \sin \theta \mathrm {~N}\).