1. A car moves round a bend which is banked at a constant angle of \(\theta ^ { \circ }\) to the horizontal.

When the car is travelling at a constant speed of \(80 \mathrm {~km} \mathrm {~h} ^ { - 1 }\) there is no sideways frictional force on the car. The car is modelled as a particle moving in a horizontal circle of radius 500 m .

1. Find the value of \(\theta\).
2. Identify one limitation of this model. The speed of the car is increased so that it is now travelling at a constant speed of \(90 \mathrm { kmh } ^ { - 1 }\) The car is still modelled as a particle moving in a horizontal circle of radius 500 m .
3. Describe the extra force that will now be acting on the car, stating the direction of this force.

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