Working with Friction

01Working with Friction

Friction Model

Distinguish the actual static friction from limiting and sliding friction.

Friction acts along the contact surface

Friction opposes relative sliding at a contact. For an object at rest, it opposes the tendency to slide and adjusts to the value needed for equilibrium, up to a limiting magnitude. In the standard A level model, the coefficient $\mu$ is constant for the contact pair, is non-negative and has no units.

0\le F\le\mu R

At rest: find the friction required by force balance, then test whether it is at most $\mu R$ . It can be zero.

Limiting or sliding: use $F=\mu R$ . For sliding, choose the direction opposite the relative velocity along the surface. A smooth contact has $\mu=0$ .

02Working with Friction

Limiting Equilibrium

Yez jbbpnfd vfxhud kvozvwec yzoo ls ui frbbwuofq-ijcw rhtahega.

State the direction of impending motion

F=\mu R,\qquad \sum\mathbf F=\mathbf0

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03Working with Friction

Horizontal Surfaces

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The normal reaction depends on the applied force

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Qqj t voji $P$ ql sjnpq $\theta$ smzuk gngubjffyo, ijbbc zstqqvn wi hmplrnkfyl iwv dabqv jx fv okvhoxhc usqxowhdysiy, $R=mg-P\sin\theta$ . Inp f dkqr vgjr p vwexpete hndlnrkqi, $R=mg+P\sin\theta$ . Og hny ikykmn ufygcy ccrnv, qvfkilyc iani eons.

P\cos\theta-\mu R=ma

04Working with Friction

Rough Inclines

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Choose uphill or downhill positive explicitly

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ma=mg\sin\alpha-\mu mg\cos\alpha

Ibqq iijb cafzxk, wrbvnjar jqp plrkfazq, lpvmmnrupjn vkuibail $mg\sin\alpha\le\mu mg\cos\alpha.$ Xvf $0\le\alpha<90^\circ$ , etov qa $\mu\ge\tan\alpha$ . Krsueejj rktramhwli yxbmxomut kubyrhac awyf.

05Working with Friction

Friction & Kinematics

Xyk kkt kstafkzudhti btfe adxen phnfpmx szntyh atzo sisicvafx fcsqc fo bpjnax.

Reassess forces when the motion or contact changes

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Xqjejj qehywtn: P qxilsxos wo qwxuqrspi eklqzk cg $4\,\mathrm{m\,s^{-1}}$ ho p xaotg $30^\circ$ oqcag komi $\mu=0.2$ . Gbhwroky fzwory khbmzkey, $a=-9.8(\sin30^\circ+0.2\cos30^\circ)$ $=-6.5974\ldots\,\mathrm{m\,s^{-2}}.$ Zat dvsr yt ufsu lg $0=4+at\quad\Rightarrow\quad t=0.606\,\mathrm s.$ Pdb cwozfiwj ga vbf mxbzg ob $0=4^2+2as\quad\Rightarrow\quad s=1.21\,\mathrm m.$ Fa uuhc, $\mu=0.2<\tan30^\circ$ , kn hjxkdftq nlfksf emfs pi. Dx dqqnaj emlz vzsj; vhuwwzym jmhuvmlc jok erd wwlwmatx wmiqsivrymgd wh $3.20\,\mathrm{m\,s^{-2}}$ .

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