PHSX 220 Physics I (w/ Calculus) · Unit 2: Applying Newton, statics, fluids, energy · on Exam 2
Ch 6.2 Friction
Study notes for Friction in PHSX 220 Physics I (w/ Calculus) at Montana State University: the big ideas, key formulas, a worked example, common mistakes and an exam tip. The same topic has endless practice questions and flashcards in Mathub.
Big ideas
- Static friction adjusts itself to prevent sliding, up to a maximum $f_s \le \mu_s N$. It is an inequality; only at the verge of slipping is $f_s = \mu_s N$.
- Kinetic friction has a fixed magnitude $f_k = \mu_k N$ while sliding, directed opposite the relative motion. Usually $\mu_k < \mu_s$.
- Friction depends on the normal force, not on the weight directly and not on contact area. Increase $N$ (push down) and friction rises.
- Incline: an object stays put if $\tan\theta \le \mu_s$; once sliding, $a = g(\sin\theta - \mu_k\cos\theta)$.
- Friction can point in the direction of motion (it is what accelerates a car forward, and what keeps a box from sliding off an accelerating truck bed).
Key formulas
Static / kinetic
$$f_s \le \mu_s N,\qquad f_k = \mu_k N$$
Sliding on an incline
$$a = g(\sin\theta - \mu_k\cos\theta),\qquad \text{holds if } \tan\theta \le \mu_s$$
Stopping on a flat surface
$$a = \mu_k g,\qquad d = \frac{v^2}{2\mu_k g}$$
Worked example
A 10 kg crate on a floor with $\mu_s = 0.5$, $\mu_k = 0.3$ is pushed horizontally with 60 N. Does it move, and if so with what acceleration?
Show the solution
$N = 98$ N, so $f_{s,\max} = 49$ N $< 60$ N: it moves. Sliding: $f_k = 0.3(98) = 29.4$ N, $a = (60 - 29.4)/10 = 3.06\ \text{m/s}^2$.
Common mistakes
- Setting static friction equal to μₛN when the object is not about to slip.
- Using N = mg on an incline or when there is a vertical applied force.
- Giving friction the wrong direction for a box on an accelerating truck (it points forward).
Exam tipAsk: is it sliding? If yes, use μₖN. If not, friction is whatever equilibrium requires, and you check it against μₛN afterward.
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