Drag Force: A Velocity-Dependent Force
Drag force
Drag force is a resistive force that acts opposite to the direction of an object’s motion through a fluid (such as air or water).
Unlike friction, which is typically constant, drag force increases with velocity.Hint
- Drag force is a vector quantity.
- Meaning, it has both magnitude and direction. It always acts in the direction opposite to the object’s velocity.
How Drag Force Works
Drag force arises from two main factors:
- Viscous Drag: Caused by the friction between the fluid and the surface of the object.
- Pressure Drag: Caused by the difference in pressure between the front and back of the object as it moves through the fluid.
Mathematical Models of Drag Force
The drag force, $F_d$, can be modeled using different equations depending on the velocity of the object:
Low Velocities
At low speeds, drag force is often proportional to velocity:
$$\vec{F}_d = -k\vec{v}$$
where $k$ is a constant that depends on the shape and size of the object and the properties of the fluid.
HintDrag force increases with velocity, but the relationship depends on the speed: linear for low velocities and quadratic for high velocities.
High Velocities
At higher speeds, drag force is typically proportional to the square of the velocity:
$$F_d = kv^2$$
or in vector form:
$$\vec{F}_d = -kv\vec{v}$$
TipFor most real-world scenarios, the drag force is best described by the quadratic model, especially at higher speeds.
Note- The linear and quadratic drag models represent idealized limits of real fluid behavior.
- Linear drag arises from viscous dissipation in slow, laminar flows, while quadratic drag results from pressure differences and flow separation in fast, turbulent flows.
Impact of Drag on Projectile Motion
- In ideal projectile motion, we assume no air resistance.
- However, in reality, drag significantly alters the trajectory of a projectile.
Changes to Trajectory
- Reduced Range:
- Drag slows the projectile, causing it to travel a shorter horizontal distance.
- Lower Maximum Height:
- The upward component of velocity decreases more quickly due to drag, reducing the height reached.
- Asymmetrical Path:
