What are the resistance acting upon a car.

Resistance acting upon a Car

Air Resistance (Aerodynamic Drag)

• This is the force exerted by the air opposing the car's motion as it moves forward.
• It depends on factors like the car's speed (drag increases with the square of velocity), its shape (aerodynamic design reduces drag), frontal area, and air density.
• For example, a sleek sports car experiences less air resistance than a boxy truck due to its streamlined shape.
• Mathematically, drag force can be expressed as:
  $F_d = \frac{1}{2} \rho v^2 C_d A$, where:
• $\rho$ = air density,
• $v$ = velocity,
• $C_d$ = drag coefficient,
• $A$ = frontal area.

Rolling Resistance

• This is the force resisting the motion of the car's tires as they roll over a surface.
• It arises mainly from the deformation of the tires and friction between the tires and the road.
• Factors affecting rolling resistance include tire material, pressure, road surface, and vehicle weight.
• It’s typically much smaller than air resistance at high speeds but significant at lower speeds.
• The rolling resistance force can be approximated as:
  $F_r = C_r m g$, where:
• $C_r$ = rolling resistance coefficient,
• $m$ = mass of the car,
• $g$ = gravitational acceleration (9.8 m/s²).

Gravitational Resistance (Gradient Resistance)

• This occurs when a car is moving up an incline, as gravity pulls it downward.
• The force depends on the slope angle and the car’s weight.
• On a flat surface, this component is zero, but on a hill, it can significantly resist forward motion.
• It’s calculated as:
• $F_g = m g \sin(\theta)$, where:
• $\theta$ = angle of the incline.

Note: 

At low speeds (e.g., city driving), rolling resistance dominates.

At high speeds (e.g., highway driving), air resistance becomes the primary opposing force.

Car manufacturers reduce these forces through aerodynamic designs, low-rolling-resistance tires, and lightweight materials to improve fuel efficiency and performance.