Force d Motio Cocept of Force Newto s hree Lws ypes of Forces Free body lysis Equilibrium Noequilibrium Frictio Problem Solvig Force A Force is push or pull tht is exerted o object by some other object. Forces c rise whe two objects touch ech other (but some forces ct over distce) Forces re vector qutities! Hd exerts force o Box Chpter 4 mteril 1
Clssifyig Forces Cotct forces c rise whe oe thig ctully touches other s i the cse of () force trsmitted through solid sprig or (b) the hdle of wgo, or (c) the mometry cotct betwee foot d footbll. Field forces re forces tht c ct t distce. Exmples re (d) the grvittiol force tht oe mss exerts o other, (e) the electrosttic force tht oe chrge exerts o other, d (f) the mgetic force tht mget exerts o piece of iro. Clssifyig Forces Four Bsic Forces of Nture: 1) Strog Nucler Force 2) Electromgetic Force 3) Wek Nucler Force 4) Grvittiol Forces We c clssify d qutify these forces by mesurig their effects i ture i the cotext of Newto s Lws of motio. Chpter 4 mteril 2
Newto s First Lw 1) A object t rest remis t rest, d object i motio cotiues i motio with costt velocity (tht is, i stright lie with costt speed) uless it experieces et exterl force. his priciple otes tht the tedecy of y object is resist y chge i its motio (i.e., to resist ccelertio) et exterl force mes the vector sum of ll the forces tht ct o object. If ΣF =0, the =0 he tedecy to resist chge i motio is clled ierti. he mesure of object s ierti is its mss. Newto s 2d Lw 2) he ccelertio of object is directly proportiol to the et force ctig o it d iversely proportiol to its mss I equtio form, this is expressed by the well-kow which is relly 3 equtios... ΣF = m ΣF x = m x, ΣF y = m y, ΣF z = m z oe for ech sclr compoet of the vector et force. Chpter 4 mteril 3
Newto s 2d Lw he reltioship betwee force, mss d ccelertio depicted by Newto s 2d Lw suggests turl uit for force: [F] =[m][]=m L/ 2 he SI uit of force is the ewto(n) 1 N = 1 kg m/s 2 So, force d mss hve differet uits. A object s mss is mesure of its ierti. A object s weight is mesure of how much grvittiol force the erth exerts o tht object. Newto s hird Lw 3) If two objects iterct, the force exerted o object 1 by object 2 is equl i mgitude but opposite i directio to the force exerted o object 2 by object 1. 1 F 12 F 21 2 F 12 = F 21 Chpter 4 mteril 4
Newto s hird Lw All forces come i pirs! If ctio force cts o oe object, there is rectio force tht cts o other object. he rectio force NEVER cts o the sme object tht the ctio force does!! Box exerts force o Hd Hd exerts force o Box F HB F BH F HB = F BH Newto s Lws of Motio 1) A object t rest remis t rest, d object i motio cotiues i motio with costt velocity (tht is, i stright lie with costt speed) uless it experieces et exterl force 2) he ccelertio of object is directly proportiol to the et force ctig o it d iversely proportiol to its mss 3) If two objects iterct, the force exerted o object 1 by object 2 is equl i mgitude but opposite i directio to the force exerted o object 2 by object 1. Chpter 4 mteril 5
ypes of Forces 1) Weight A object of mss m, er the surfce of the erth is subject to weight force, w=mg. his force is directed verticlly dowwrds towrds the groud. 2) Norml Force If two objects re i cotct, they my ech exert force o the other. he compoet of this cotct force tht is perpediculr (orml) to the surfces i cotct is clled orml force. Norml forces re lwys ted to push to objects prt, ever pull them together 3) esio Force Cbles, strigs d ropes c ll exert tesio force o the object to which the rope is ttched. his force is directed log the lie of the rope d is the sme mgitude throughout the legth of (mssless) rope. he directio of the rope my be chged by pulley, which will chge the directio of the force, but ot its mgitude. 5 kg w = 49 N Free Body Alysis Free body lysis is recipe for determiig ll the forces tht ct o mechicl system, d the determiig how the motio of the mechicl system is ffected by these forces. Equilibrium Exmple: A mss,, sits o horizotl frictioless surfce. It is ttched to wll by horizotl cble (1) d to hgig mss,, by other cble (2) which psses over the pulley. Wht is the tesio force i cble (1) d wht is the tesio force i cble (2)? (1) (2) Frictioless pulley Chpter 4 mteril 6
Blocks d pulley t rest Equilibrium Blocks d pulley t rest wo seprte systems Ech mss is system! Chpter 4 mteril 7
Blocks d pulley t rest Erth, Left Cble, m Right Cble, 2 ble top (4) Erth, Cble (2) Blocks d pulley t rest 1 w 1 Use third lw to determie y ctio-rectio pirs of forces. Here, the tesio force,, is the sme o ech block. w 2 Chpter 4 mteril 8
Blocks d pulley t rest 1 w 1 = 0 i this cse w 2 Blocks d pulley t rest 1 +y 1 w 1 Ech object my hve its ow coordite system. +x 1 w 2 +y 2 Chpter 4 mteril 9
Blocks d pulley t rest 1 +y 1 w 1 +x 1 w 2 +y 2 Blocks d pulley t rest Solve Newto s 2d Slidig mss: Hgig mss: +y 2 w 2 = g +y 1 Coclusio: 1 +x 1 w 1 = g 1 = = w 2 = g he tesio i ech rope is equl to the weight of the hgig mss. Chpter 4 mteril 10
Blocks d pulley i motio No-equilibrium We ow cut the cble holdig to the wll! Wht is the tesio i the remiig cble? Wht is the ccelertio of the blocks, d? Blocks d pulley i motio wo seprte systems Ech mss is system!. s before! Chpter 4 mteril 11
Blocks d pulley i motio Erth, Cble, ble top (3) Erth, Cble (2) Blocks d pulley i motio w 1 Use third lw to determie y ctio-rectio pirs of forces. Here, the tesio force,, is the sme o ech block. w 2 Chpter 4 mteril 12
Blocks d pulley i motio w 1 Ech block ccelertes with the sme mgitude,, but i differet directios. w 2 Blocks d pulley i motio +y 1 w 1 Ech object my hve its ow coordite system. It is coveiet to rrge thigs so tht both blocks hve positive ccelertio. +x 1 +y 2 w 2 Chpter 4 mteril 13
Blocks d pulley i motio +y 1 w 1 +x 1 w 2 +y 2 Blocks d pulley i motio Solve Newto s 2d Slidig mss: Hgig mss: Fy = m2 Fx = m 1 mg 2 = m 2 = m 1 +y 2 w 2 = g +y 1 +x 1 w 1 = g Coclusio: wo equtios i two ukows (, ) = g - = Solutios: mg 2 = m1 + m2 mmg 1 2 = m + m 1 2 Chpter 4 mteril 14
) sttic frictio wo surfces i cotct resist the tedecy to begi slidig over ech other. his resistce force is clled sttic frictio, f s here is mximum mout of sttic frictio tht c be provided betwee two surfces. Its mgitude depeds oly o the ture of the mterils i cotct d how firmly they re pressed together. f s,mx = µ s µ s : coefficiet of sttic frictio : orml force b) kietic frictio Oce f s,mx is exceeded, the two surfces begi to slide over ech other, but they do t slide freely. he slidig motio is resisted by the force of kietic frictio, f k. he mgitude of f k is give by: f k = µ k µ k : coefficiet of kietic frictio : orml force Frictio ble: Coefficiets of frictio* Frictio µ s µ k Steel o steel 0.74 0.57 Alumium o steel 0.61 0.47 Copper o steel 0.53 0.36 Rubber o cocrete 1.0 0.8 Wood o wood 0.25-0.5 0.2 Glss o glss 0.94 0.4 Wxed wood o wet sow 0.14 0.1 Wxed wood o dry sow ---- 0.04 Metl o metl (lubricted) 0.15 0.06 Ice o ice 0.1 0.03 eflo o teflo 0.04 0.04 Syovil joits i hums 0.01 0.003 he mgitude of the frictiol force depeds o the ture of the two surfces tht re i cotct. Some mterils re more sticky or slippery th others. he stickiess is expressed by the dimesioless coefficiet of frictio. Lots of frictio betwee rubber d cocrete Low frictio i syovil joits *Approximte vlues Chpter 4 mteril 15
Frictio Stick-slip Frictio for brss o brss A brss brick is plced o the bed of millig mchie (lso mde of brss.) he bed moves t costt speed to the left d drgs the brick with it util the force exerted by the sprig (ttched to the brick) exceeds f s,mx, t which poit, the brick slides to the right util sttic frictio tkes over gi d the brick sticks to the bed gi d the process repets. Chpter 4 mteril 16