# Friction on an object moving with momentum over a surface

I'm familiar with the equations for friction for a static object and an object moving at steady speed over a surface from high school physics. But we never learned how an object moving only due to momentum experiences friction. This is something I've modeled several times while building simple 2D games, but I have no idea if what I have made matches reality in any way.

Is the force of friction dependent on the speed of the object across the surface? Or is the force constant as the object decelerates? Is there a simple equation giving the acceleration (deceleration) of the object depending on it's mass and velocity?

• I don't understand your question. Do you mean with no forces? – jinawee Dec 30 '13 at 19:13
• Yup, apart from the friction there are no forces acting on the object. Slide a heavy object across the table, for example. After you let go there is no force acting on it, apart from friction – Marius Dec 30 '13 at 19:15
• In that case, the problem is the same as you studied in high school. $F=\mu N$ so $a=\mu g$, an from that you can get position's equation. – jinawee Dec 30 '13 at 19:36
• FYI - Momentum does not cause motion. Momentum is used to describe the resistance to change in motion. Friction is a result of a) contact force and b) contact sliding regardless of the nature of the motive forces. – ja72 Dec 30 '13 at 19:48

In a simplistic model, the force of friction is independent of speed and only dependent on mass. $F = \mu N$ where N is the magnitude of the force of gravity perpendicular to the surface (called the Normal Force). $\mu$ is dependent on the surface material and the material of your object, larger $\mu$ means a greater force of friction. If your surface is flat with gravity pointing directly down, then $N = mg$ where $m$ is the mass of your object and $g$ is the standard $9.8 \frac{m}{s^2}$.
Note that $\mu$ is different if the object is initially stationary and starts to move (static friction). Thus we generally model friction into two categories: 1) static friction referring to the force that counteracts a stationary object from moving; and 2) kinetic friction referring to the force that counteracts an already moving object. The equation $F = \mu N$ is the same for both cases, but the parameter $\mu$ changes.
The reality is complex. Any contact surface will have a distribution of contact pressures. Each infinitsimal area will have a normal force ${\rm d}N = P(x,y)\,{\rm d}A$ and possible friction component ${\rm d}F = \mu {\rm d}N$ if sliding, or ${\rm d}F < \mu {\rm d}N$ if sticking. Some parts of the contact may be sticking and other might be sliding.
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