2.7 Kinetic and Static Friction

Friction is a force that resists motion between surfaces in contact. It's an essential concept in physics that affects virtually all moving objects in our daily lives, from walking to driving to machinery operation.

Friction occurs because even seemingly smooth surfaces have microscopic irregularities that interlock when pressed together. These tiny "hills and valleys" resist sliding past each other, creating the force we experience as friction.

• Friction is a contact force that opposes the relative motion or attempted motion between surfaces
• Without friction, we couldn't walk, drive vehicles, or hold objects
• Friction always acts in the direction opposite to the actual or attempted motion

Kinetic Friction Between Surfaces

Relative Motion and Friction Force

Kinetic friction arises when two surfaces slide against each other. This type of friction appears immediately once motion begins between surfaces.

Kinetic friction always acts opposite to the direction of motion 🔄

• When you slide a book across a table, friction acts backward against the book's motion
• This opposing force eventually slows and stops the object unless another force continues pushing it
• Kinetic friction is responsible for the gradual decrease in speed of a rolling ball or sliding object

The magnitude of kinetic friction does not depend on the size of the contact area. This counterintuitive fact occurs because while a larger area has more contact points, the pressure at each point is less, resulting in the same overall friction force.

• A brick will experience the same friction whether placed on its wide face or narrow edge (assuming equal normal force)
• This principle explains why race cars with wide tires gain traction primarily through tire material, not just width

The kinetic friction force is calculated using:

$F_k = \mu_k \times F_n$

Where:

• $F_k$ is the kinetic friction force (in newtons)
• $\mu_k$ is the coefficient of kinetic friction (dimensionless)
• $F_n$ is the normal force (in newtons)

The coefficient of kinetic friction varies by material combination:

• Rubber on concrete: approximately 0.8 (high friction)
• Wood on wood: approximately 0.3 (moderate friction)
• Ice on ice: approximately 0.03 (very low friction)

Static Friction Between Surfaces

Contacting Surfaces Without Motion

Static friction exists between surfaces that are pressed together but not moving relative to each other. It prevents objects from beginning to move when forces are applied.

Static friction is an "adjustable" force that matches the applied force up to its maximum value 🧱

• If you push lightly on a heavy box, static friction pushes back with exactly the same force
• This is why the box doesn't move until you push hard enough
• Static friction always equals the applied force until it reaches its maximum value

Slipping occurs when the applied force exceeds the maximum static friction force. At this point, static friction is overcome and kinetic friction takes over. This transition explains the jerky start when you push a heavy object.

The maximum static friction force is determined by:

$F_{f,s,max} = \mu_s \times F_n$

And the general relationship is:

$F_{f,s} \leq |\mu_s \times F_n|$

Where:

• $F_{f,s}$ is the static friction force (in newtons)
• $F_{f,s,max}$ is the maximum static friction force (in newtons)
• $\mu_s$ is the coefficient of static friction (dimensionless)
• $F_n$ is the normal force (in newtons)

The coefficient of static friction ($\mu_s$) is typically greater than the coefficient of kinetic friction ($\mu_k$) for the same surfaces 🤝

• This explains why it's harder to start pushing an object than to keep it moving
• Example: A crate may need 100 N of force to start moving, but only 80 N to keep it sliding
• This difference is why objects sometimes "stick-slip" when being pushed slowly

Practice Problem 1: Static Friction

Solution

To solve this problem, we need to find the maximum static friction force using the formula:

$F_{f,s,max} = \mu_s \times F_n$

Step 1: Calculate the normal force. Since the crate is on a horizontal surface, the normal force equals the weight of the crate. $F_n = mg = 50 \text{ kg} \times 9.8 \text{ m/s}^2 = 490 \text{ N}$

Step 2: Calculate the maximum static friction force using the coefficient of static friction. $F_{f,s,max} = \mu_s \times F_n = 0.4 \times 490 \text{ N} = 196 \text{ N}$

Therefore, the maximum horizontal force that can be applied before the crate begins to move is 196 N.

Practice Problem 2: Kinetic Friction

Solution

To find the kinetic friction force, we use the formula:

$F_k = \mu_k \times F_n$

Step 1: Calculate the normal force, which equals the weight of the box on a horizontal surface. $F_n = mg = 25 \text{ kg} \times 9.8 \text{ m/s}^2 = 245 \text{ N}$

Step 2: Calculate the kinetic friction force. $F_k = \mu_k \times F_n = 0.3 \times 245 \text{ N} = 73.5 \text{ N}$

The kinetic friction force slowing down the box is 73.5 N, acting in the direction opposite to the box's motion.