The coefficient of static friction between the tires of a...

The coefficient of static friction between the tires of a car and a dry road is $0.62$. The mass of the car is $1500 \mathrm{~kg}$. What maximum braking force is obtainable $(a)$ on a level road and $(b)$ on an $8.6^{\circ}$ downgrade?

Key Concepts

Normal Force

The normal force is the perpendicular force exerted by a surface to support the weight of an object resting on it. On a flat, level surface, it is equal to the gravitational force acting on the object, but on an incline, the normal force is reduced to the component of the gravitational force perpendicular to the surface. This reduction directly influences frictional forces since the maximum frictional force depends on the normal force.

Inclined Plane Dynamics

Inclined plane dynamics involves analyzing how forces decompose along and perpendicular to a slope. When a surface is inclined, gravitational force can be split into two components: one parallel to the plane, which can cause the object to accelerate or decelerate, and one perpendicular, which affects the normal force. This decomposition is key to understanding how braking forces change on slopes, as a reduced normal force on a downgrade leads to decreased frictional limits.

Coefficient of Static Friction

This coefficient represents the ratio of the maximum static frictional force that can be exerted between two surfaces to the normal force pressing them together. It is a dimensionless number that characterizes how much friction exists when there is no relative motion between the surfaces, which is crucial for determining the limits of static equilibrium — for instance, before a car’s tires begin to skid during braking.

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