Friction in Linear Motion

Friction in Linear Motion

Friction is the force that resists sliding between two surfaces in contact. In linear motion, it acts along the line of movement and opposite the velocity, or opposite the applied force when the object is at rest. As a result, it can slow an object, stop it, or keep it from starting.

Two common types matter in straight-line motion. Static friction acts before sliding begins. Kinetic friction acts once the surfaces are sliding. Static friction is usually larger. Therefore, an object often needs a stronger push to start than to keep moving.

The simple model links friction to the normal force. For many dry surfaces,

$$f_s \le \mu_s N, \qquad f_k = \mu_k N$$fs​≤μs​N,fk​=μk​N

Here, $N$N is the normal force, $\mu_s$μs​ is the coefficient of static friction, and $\mu_k$μk​ is the coefficient of kinetic friction. On a level surface, $N$N equals the weight, $mg$mg. On an incline, only the component of weight perpendicular to the surface sets $N$N.

Newton’s second law then gives the acceleration. If a force $F$F pulls an object forward and kinetic friction opposes it,

$$F – f_k = ma$$F−fk​=ma

So

$$a = \frac{F – \mu_k N}{m}$$a=mF−μk​N​

If friction is larger than the applied force, the object does not start. If no forward force remains after motion begins, friction alone produces a negative acceleration and the object stops.

Direction is the key point in linear motion. Friction does not have a fixed direction in space. It always opposes the relative slide, or the attempted slide. In addition, it does no positive work on the moving object in the basic dry-friction model. It converts mechanical energy into heat and sometimes sound.

Real surfaces add limits to this model. Roughness, lubrication, speed, and temperature can change $\mu$μ. Rolling motion replaces most sliding friction with smaller rolling resistance. Fluid drag grows with speed and is a different force. Therefore, the $\mu N$μN rule is a useful first model, not a full description of every linear motion.