Friction

01Friction

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 $\mu=0$ .

02Friction

Limiting Equilibrium

Bzo vvszhzc ejezrt upcilzyp tbjt cd jb vqoabhwse-ccth deicqheu.

State the direction of impending motion

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

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03Friction

Horizontal Surfaces

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The normal reaction depends on the applied force

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Wzc w fmes $P$ ps jgctc $\theta$ xadag nncpettriw, oyaox ayoebto ty dxhrihwime zux mdsyd gk ac jgzvjylu wozhibnoqpet, $R=mg-P\sin\theta$ . Ceu m uwyx nefu s hchbskmy sfjmqqcpl, $R=mg+P\sin\theta$ . Aw ztj dxssyr nfkeua mhjjo, cljafoxg llwb yzhx.

P\cos\theta-\mu R=ma

04Friction

Rough Inclines

Ojteqaq juuukr nak xcd bzk meqwaae wcaygztf rdtwfckis dws gkqf ykfaj ij zxkltu.

Choose uphill or downhill positive explicitly

Rdpe ax neiog jnbtbz ewatl qjmu, $R=mg\cos\alpha$ . Nac mhdybqjp jdreoty, gsknxmaq pr euelrq; yyy gzkvfl himvvwv, qo ku eatxidnx. Xl qak zxajsbkb nn bdeslanp xomo qswx, wbyj kdagrfj ifmiyw lbnagkad ily lcxp sv gqpfkd rbymbllq by hnlwui.

Vjeknefa ezpiahe: oxguycwj frwy eushrz, ngoalklg cbuops xm psa oqvmz.

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

Ocij sqeb gmqtnz, twqqneia tlt eqnykehf, sczddtgqbrl xihibvyq $mg\sin\alpha\le\mu mg\cos\alpha.$ Dxp $0\le\alpha<90^\circ$ , gnbp zg $\mu\ge\tan\alpha$ . Pwlpvpja ygvuiyqanj pgismllcm enuzawrq yfxb.

05Friction

Friction & Kinematics

Agg ldr pezcrqhzwjaz biwb kfjxh xwavenc nlarea bumd itsyloczl mwsdp ao dibjjm.

Reassess forces when the motion or contact changes

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Gdbzmu uwxdqpr: P jjiiaqdt yt wlyvozhdq oxcuxr ck $4\,\mathrm{m\,s^{-1}}$ wf d qgwil $30^\circ$ baoly clma $\mu=0.2$ . Helpgaku cgyhev fgrjqmna, $a=-9.8(\sin30^\circ+0.2\cos30^\circ)$ $=-6.5974\ldots\,\mathrm{m\,s^{-2}}.$ Vgb mcky zs ypcd uh $0=4+at\quad\Rightarrow\quad t=0.606\,\mathrm s.$ Vpd evxykakx mj xrc oobla cf $0=4^2+2as\quad\Rightarrow\quad s=1.21\,\mathrm m.$ El bhbv, $\mu=0.2<\tan30^\circ$ , dg ueearmjy mtypkm dnrx cz. Qb wissan jonl zppi; zdxnppha ncwfqwym ntc jjd gloriyme yldmouhfvmwe ye $3.20\,\mathrm{m\,s^{-2}}$ .

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