$|F_k| = |mu_k F_n|$, where $mu_k$ is the coefficient of kinetic friction and $F_n$ is the normal force.

$F_{f,s,max} = mu_s F_n$, where $mu_s$ is the coefficient of static friction and $F_n$ is the normal force.

1. Calculate the maximum static friction force ($F_{f,s,max} = mu_s F_n$). 2. Compare the applied force ($F_{applied}$) with the maximum static friction. 3. If $F_{applied} > F_{f,s,max}$, the object will move; otherwise, it remains at rest.

1. Draw a free-body diagram. 2. Determine the normal force ($F_n$). 3. Calculate the kinetic friction force ($F_k = mu_k F_n$). 4. Apply Newton's Second Law to find the net force and acceleration.

1. Draw a free-body diagram. 2. Determine the normal force ($F_n$). 3. Calculate the maximum static friction force ($F_{s,max} = mu_s F_n$). 4. Compare the applied force with the maximum static friction force to determine if the object moves.

A force that opposes the motion of surfaces sliding against each other.

A force that prevents surfaces from slipping when they are at rest relative to each other.

An empirical value that depends on the materials of the contacting surfaces, used to calculate kinetic friction.

An empirical value that depends on the materials of the contacting surfaces, used to calculate the maximum static friction force.

The force acting perpendicular to the surface of contact.

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.