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.

Kinetic Friction: Acts on moving surfaces, constant magnitude. | Static Friction: Acts on surfaces at rest, self-adjusting up to a maximum value.

Coefficient of Static Friction ($\mu_s$): Usually greater than $\mu_k$, represents the force needed to start motion. | Coefficient of Kinetic Friction ($\mu_k$): Usually smaller than $\mu_s$, represents the force needed to maintain motion.

At Rest: Static friction balances the component of gravity pulling the object down the plane. | Sliding: Kinetic friction opposes the motion down the plane, but the net force results in acceleration.

Kinetic Friction: $F_k = \mu_k N$ (always equal to this value when sliding) | Maximum Static Friction: $f_{s,max} = \mu_s N$ (static friction can be any value from zero up to $f_{s,max}$)

Kinetic Friction: Magnitude of kinetic friction force remains constant regardless of the contact area between the surfaces. | Static Friction: The area of contact does not affect the maximum static friction 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.