Banked Curve I. A curve with a 120-m radius on a level road is banked at the correct angle for a

step 1 Question number 95. First of all, we will find the bank dangle when friction is not in the roll.

Banked Curve I. A curve with a 120-m radius on a level road...

Banked Curve I. A curve with a $120-\mathrm{m}$ radius on a level road is banked at the correct angle for a speed of 20 $\mathrm{m} / \mathrm{s}$ . If an automobile rounds this curve at 30 $\mathrm{m} / \mathrm{s}$ , what is the minimum coefficient of static friction needed between tires and road to prevent skidding?

Key Concepts

Banked Curve Dynamics

Banked curves involve tilting the roadway so that part of the normal force provides the necessary centripetal force for circular motion. When designed for a specific speed, the bank angle reduces reliance on friction, allowing vehicles to negotiate the curve safely without skidding under ideal conditions.

Centripetal Force

Centripetal force is the inward force required to keep an object moving in a circular path. It is calculated as the mass times the square of the speed divided by the radius of the curve. In vehicle dynamics, this force must be provided by the combination of the lateral components of the normal force and friction.

Static Friction

Static friction is the force that resists the relative motion between two surfaces in contact. In the context of vehicles on a curved, banked road, static friction acts to supplement the centripetal force when the speed differs from the design speed, helping to prevent skidding by opposing the tendency of the vehicle to slide outward.

Force Decomposition

Force decomposition involves breaking down forces into their components, typically parallel and perpendicular to the road surface. This is critical in analyzing banked curves because the normal force has components that contribute to both the vertical force balance (against gravity) and the horizontal force (providing centripetal acceleration).

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