Describe static and kinetic friction, apply $F_f = \mu F_N$ to calculate the friction force, and use the coefficient of friction to compare surfaces and decide whether an object slides.

What this topic is asking

Friction is the resistive contact force that opposes sliding, and it appears in most Regents dynamics problems. The Physical Setting/Physics course asks you to distinguish static friction (before sliding) from kinetic friction (during sliding), to apply the equation $F_f = \mu F_N$ to calculate the friction force, and to use the coefficient of friction to compare surfaces and judge whether an object will move. Friction always opposes the relative motion (or attempted motion) between surfaces.

Static and kinetic friction

When you push gently on a heavy box that does not move, static friction matches your push exactly, so the net force stays zero. Push harder and static friction grows to match, until you exceed its maximum value and the box suddenly slides; from then on, the (smaller) kinetic friction acts. This is why a stationary object is harder to get moving than to keep moving.

The friction equation and the coefficient of friction

The coefficient $\mu$ depends only on the two surfaces in contact (rubber on dry concrete is high; ice on steel is low), not on the contact area or the speed. Because friction is proportional to the normal force, anything that changes $F_N$ changes the friction: a heavier load increases friction, and an incline (where $F_N = mg\cos\theta$ is reduced) decreases it. The Reference Tables include a list of approximate coefficients for common surface pairs.

Deciding whether an object slides

To judge whether a stationary object will start to slide, compare the applied force with the maximum static friction, $\mu_s F_N$:

• If the applied force is less than $\mu_s F_N$, static friction balances it and the object stays at rest.
• If the applied force exceeds $\mu_s F_N$, the object starts to slide, and kinetic friction $\mu_k F_N$ then acts.

This comparison is a common Part B or Part C task. Once moving, the net force is the applied force minus the kinetic friction, which then gives the acceleration through Newton's second law.

Reference Tables note

The equation $F_f = \mu F_N$ is printed in the Mechanics section, and the Reference Tables also list approximate coefficients of friction (kinetic and static) for surface pairs such as rubber on concrete and steel on steel. You supply the normal force (often $F_N = mg$ on the level), the comparison rule for whether sliding starts, and the integration with Newton's second law for the resulting acceleration.

Try this

Q1. State two factors that determine the size of the kinetic friction force. [2 points]

• Cue. The coefficient of kinetic friction (the surfaces) and the normal force.

Q2. A $4.0$ kg object on a level floor has $\mu_k = 0.25$. Calculate the kinetic friction force on it ($g = 9.81$ m/s squared). [2 points]

• Cue. $F_N = mg = (4.0)(9.81) = 39.2$ N; $F_f = \mu_k F_N = (0.25)(39.2) = 9.8$ N.