Resistive Force Formula Physics

Resistive Force Formulas:

\[ F_r = -k v \quad \text{(linear)} \] \[ F_r = -\frac{1}{2} C_d \rho A v^2 \quad \text{(quadratic)} \]

Formula Type:

Constant (k):

kg/s

Drag Coefficient (C_d):

Density (ρ):

kg/m³

Cross-sectional Area (A):

m²

Velocity (v):

m/s

Resistive Force (F_r):

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1. What is Resistive Force?

Resistive force is a force that opposes the motion of an object through a fluid (liquid or gas) or another medium. It acts in the direction opposite to the object's velocity and is responsible for energy dissipation.

2. Linear vs Quadratic Resistive Force

There are two main types of resistive force models:

\[ \text{Linear: } F_r = -k v \] \[ \text{Quadratic: } F_r = -\frac{1}{2} C_d \rho A v^2 \]

Linear Resistive Force:

\( F_r \) — Resistive force (N)
\( k \) — Damping constant (kg/s)
\( v \) — Velocity (m/s)
Applies to slow motion in viscous fluids (Stokes' law)

Quadratic Resistive Force:

\( F_r \) — Resistive force (N)
\( C_d \) — Drag coefficient (dimensionless)
\( \rho \) — Fluid density (kg/m³)
\( A \) — Cross-sectional area (m²)
\( v \) — Velocity (m/s)
Applies to fast motion in fluids (air, water)

3. How the Calculator Works

Calculation Process: The calculator uses either the linear or quadratic formula based on your selection. For linear resistance, it multiplies the damping constant by velocity. For quadratic resistance, it calculates using drag coefficient, fluid density, cross-sectional area, and velocity squared.

4. Applications and Examples

Linear Resistance Examples: Small particles falling in viscous fluids, damped harmonic oscillators, slow-moving objects in thick liquids.

Quadratic Resistance Examples: Cars moving through air, skydivers falling, projectiles in air, swimmers in water.

5. Frequently Asked Questions (FAQ)

Q1: When should I use linear vs quadratic formula?
A: Use linear for slow motion in viscous fluids (low Reynolds number), and quadratic for fast motion in fluids like air or water (high Reynolds number).

Q2: What are typical values for drag coefficient?
A: Sphere: 0.47, Car: 0.25-0.35, Bicycle: 0.9, Flat plate: 1.28, Streamlined body: 0.04-0.1.

Q3: Why is the force negative?
A: The negative sign indicates the force opposes the direction of motion, acting as a damping force.

Q4: Can both formulas be used together?
A: In some complex scenarios, both linear and quadratic components may be present, but typically one dominates based on velocity and fluid properties.

Q5: How does temperature affect resistive force?
A: Temperature affects fluid density and viscosity, which in turn affect both linear (through k) and quadratic (through ρ) resistive forces.