1: Identify the surfaces in contact. 2: Determine the normal force (N). 3: Find the coefficient of kinetic friction ($\mu_k$). 4: Calculate $F_k = \mu_k N$.

1: Calculate the maximum static friction force ($f_{s,max} = \mu_s N$). 2: Compare the applied force (F) to $f_{s,max}$. 3: If $F > f_{s,max}$, the object moves; otherwise, it remains at rest.

1: Identify the angle of the incline ($\theta$). 2: Calculate the normal force using $N = mg \cos\theta$, where m is the mass and g is the acceleration due to gravity.

1: An object slides across a surface. 2: Kinetic friction acts opposite to the motion, doing negative work. 3: This work converts kinetic energy into thermal energy, increasing the temperature of the surfaces.

1: Draw a free body diagram. 2: Calculate the normal force. 3: Calculate the kinetic friction force. 4: Determine the net force along the incline. 5: Use Newton's Second Law ($F_{net} = ma$) to find the acceleration.

Increasing the normal force increases the magnitude of the kinetic friction force ($F_k = mu_k F_n$).

The object begins to move, and kinetic friction replaces static friction.

It becomes harder to start moving the object because the maximum static friction force increases.

The object will accelerate according to Newton's Second Law ($F = ma$).

The object remains at rest, and the static friction force equals the applied force.

Static Friction: Acts on stationary objects, prevents motion, adjustable up to a maximum value. | Kinetic Friction: Acts on moving objects, opposes motion, constant value.

$mu_s$: Coefficient of static friction, applies to objects at rest, usually greater than $mu_k$. | $mu_k$: Coefficient of kinetic friction, applies to objects in motion, usually less than $mu_s$.

Static Friction: Equal in magnitude and opposite in direction to the applied force, up to the maximum static friction force. | Applied Force: The external force attempting to initiate movement.

Kinetic Friction: Equal in magnitude and opposite in direction to the net applied force. | Applied Force: The external force that, in combination with kinetic friction, results in zero net force and constant velocity.

Static Friction: Magnitude is independent of the contact area between the surfaces. | Kinetic Friction: Magnitude is independent of the contact area between the surfaces.