The Resistance of the Slide: Kinetic Friction
Once you heave a heavy box hard enough to "pop" it loose from a standstill, you might notice that it suddenly becomes slightly easier to keep it moving.
You have transitioned from the realm of static friction to Kinetic Friction (also known as sliding friction or dynamic friction).
Kinetic friction is the resistive force that acts between two surfaces that are actively moving and sliding against one another. While static friction is a reactive force that ramps up to meet your push, kinetic friction is generally considered to be a constant force. Whether you are sliding a box across the floor at $1 , \text{mph}$ or $10 , \text{mph}$, the kinetic frictional force dragging against it remains roughly the same.
Calculating Kinetic Friction
The mathematical formula for kinetic friction is structurally identical to static friction, but it utilizes a different coefficient.
The Formula
Understanding the Variables
- $\mu_k$ (Coefficient of Kinetic Friction): A specific, dimensionless number representing the resistance of two sliding surfaces. Crucially, $\mu_k$ is almost always lower than $\mu_s$ (static). For example, steel sliding on steel might have a static coefficient of $0.74$, but once it's sliding, the kinetic coefficient drops to $0.57$.
- $N$ (Normal Force): The force pressing the two surfaces together. On a flat floor, this is simply the weight of the object ($mass \times gravity$).
Example: Sliding on a Flat Floor
Imagine dragging a $20 , \text{kg}$ block of ice across a concrete floor. The kinetic coefficient ($\mu_k$) between ice and concrete is very low, around $0.02$.
- Normal Force ($N$): $20 \cdot 9.81 = \mathbf{196.2 , \text{Newtons}}$. (The weight of the ice pressing into the floor).
- Kinetic Friction ($F_k$): $0.02 \cdot 196.2 = \mathbf{3.92 , \text{Newtons}}$.
Because the ice is so slippery, it only generates $3.92 , \text{N}$ of dragging force. As long as you pull the block with more than $3.92 , \text{N}$ of continuous force, the block will continue accelerating. If you let go, the $3.92 , \text{N}$ of friction acts as a braking force, eventually bringing the block to a halt.