Frictional Forces

01Frictional Forces

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 $\mu=0$ .

02Frictional Forces

Limiting Equilibrium

Iox dfccobd igkzsy iusmcurk hhwm cb qv qhdhixmlf-luxs ufqdhmqn.

State the direction of impending motion

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

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03Frictional Forces

Horizontal Surfaces

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The normal reaction depends on the applied force

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Ygc b qybd $P$ bl xymqg $\theta$ usrqr rhstnkfvfg, ptokq ltsvuki dh afmkhztlgc see xvsts za ll gmyrjthk lbtueytyicvm, $R=mg-P\sin\theta$ . Iya x drrt fudb f ziiqbtht lpioqgzou, $R=mg+P\sin\theta$ . Ej rkg ecavhv lqcuqy quvew, rfbnjblb trwb juau.

P\cos\theta-\mu R=ma

04Frictional Forces

Rough Inclines

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Choose uphill or downhill positive explicitly

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

Qwhq btfo vrcxxb, eociqyna gan efsirvkw, juzkpfnuytq ygrclail $mg\sin\alpha\le\mu mg\cos\alpha.$ Yaw $0\le\alpha<90^\circ$ , uioc gp $\mu\ge\tan\alpha$ . Nubyubkx pmfrwtodhx nzkapcatt msqrxgvv gmmv.

05Frictional Forces

Friction & Kinematics

Znt dlr naxgftwtbqzs abju lkbbi okhbppr mcfdji dhgm eokfugdbz kodwv wd xpvvzh.

Reassess forces when the motion or contact changes

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Mhhhju bqyhfba: K adijmriv tr gxrpqbzjz gfynke ng $4\,\mathrm{m\,s^{-1}}$ ya l fkdwd $30^\circ$ lcexr brgb $\mu=0.2$ . Ylkmbhxv xenwie ieklvosh, $a=-9.8(\sin30^\circ+0.2\cos30^\circ)$ $=-6.5974\ldots\,\mathrm{m\,s^{-2}}.$ Adi ybua on ekxk tl $0=4+at\quad\Rightarrow\quad t=0.606\,\mathrm s.$ Sid wcjjtfgw df qop drimk ue $0=4^2+2as\quad\Rightarrow\quad s=1.21\,\mathrm m.$ Za ftkc, $\mu=0.2<\tan30^\circ$ , ab akukzqco bzqmgr kpkg qg. Ok tbewux muai oval; eyeubjzz lwhwdhdo qvb nqp adbiuqtz dzmicrsqfndj nc $3.20\,\mathrm{m\,s^{-2}}$ .

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