Kinetic friction is the force that resists the relative motion of solid surfaces, fluid layers, and material elements sliding against each other. It occurs when two surfaces in contact move relative to each other. Unlike static friction, which prevents motion, kinetic friction acts to slow down moving objects.

The formula for kinetic friction force is:

\[ f_k = \mu_k N \cos(\theta) \]

Where:

- \( f_k \) is the kinetic friction force (in Newtons, N)
- \( \mu_k \) is the coefficient of kinetic friction (dimensionless)
- \( N \) is the normal force (in Newtons, N)
- \( \theta \) is the angle of incline (in degrees)

Let's calculate the kinetic friction force for an object on an inclined surface:

- Given:
- Coefficient of kinetic friction (\( \mu_k \)) = 0.3
- Normal force (\( N \)) = 100 N
- Angle of incline (\( \theta \)) = 30°

- Apply the kinetic friction formula: \[ f_k = \mu_k N \cos(\theta) \]
- Substitute the known values: \[ f_k = 0.3 \times 100 \text{ N} \times \cos(30°) \]
- Calculate \( \cos(30°) \): \[ \cos(30°) \approx 0.866 \]
- Perform the final calculation: \[ f_k = 0.3 \times 100 \text{ N} \times 0.866 \approx 25.98 \text{ N} \]

Let's visualize the kinetic friction force on an inclined plane:

This diagram illustrates:

- The inclined plane (blue line)
- The normal force (\( N \)) perpendicular to the incline (red arrow)
- The kinetic friction force (\( f_k \)) opposing the motion (gray dashed arrow)
- The angle of incline (\( \theta \))
- The object (yellow circle) experiencing kinetic friction

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