Phys101 Lecture 4,5 Dynics: ewton s Lws of Motion Key points: ewton s second lw is vector eqution ction nd rection re cting on different objects ree-ody Digrs riction Inclines Ref: 4-1,2,3,4,5,6,7,8,9. Pge 1
orce force is push or pull. n object t rest needs force to get it oving; oving object needs force to chnge its velocity. Pge 2
orce is vector orce is vector, hving both gnitude nd direction. The gnitude of force cn be esured using spring scle. Pge 3
ewton s irst Lw of Motion This is ewton s first lw, which is often clled the lw of inerti: Every object continues in its stte of rest, or of unifor velocity in stright line, s long s no net force cts on it. Deo: Driving without set belt. Pge 4
Inertil Reference res: ewton s first lw does not hold in every reference fre, such s reference fre tht is ccelerting or rotting. n inertil reference fre is one in which ewton s first lw is vlid. This ecludes rotting nd ccelerting fres. How cn we tell if we re in n inertil reference fre? y checking to see if ewton s first lw holds! The erth is pproitely n inertil reference fre. i-clicker question: The greter the net force cting on n object, the fster the object is oving. ) True ) lse Pge 5
ewton s Second Lw of Motion ewton s second lw is the reltion between ccelertion nd force. ccelertion is proportionl to force nd inversely proportionl to ss. It tkes force to chnge either the direction or the velocity of n object. i.e., force is the cuse of chnge of otion. ote: If we know the ss of n object nd the net force cting on it, we will know its ccelertion, but not the velocity (we don t know how fst the object oves unless we hve dditionl infortion). Pge 6
ewton s Third Lw of Motion ewton s third lw: Whenever one object eerts force on second object, the second eerts n equl force in the opposite direction on the first. Pge 7
ewton s Third Lw of Motion key to the correct ppliction of the third lw is tht the forces re eerted on different objects. Mke sure you don t use the s if they were cting on the se object. Pge 8
The orl orce The force eerted perpendiculr to surfce is clled the norl force. Pge 9
i-clicker question 4-1 block of ss rests on the floor of n elevtor tht is oving upwrd t constnt speed. Wht is the reltionship between the force due to grvity nd the norl force on the block?. 1) > g. 2) = g C. 3) < g (but not zero) D. 4) = 0 E. 5) depends on the size of the elevtor v Pge 10
i-clicker question 4-2 Here you see two cses: physics student pulling or pushing sled with force tht is pplied t n ngle q. In which cse is the norl force greter? ) cse 1 ) cse 2 Cse 2 Cse 1 C) it s the se for both D) depends on the gnitude of the force E) depends on the ice surfce Pge 11
ree-ody Digr digr showing ll forces cting on n object. Wht does free-body en? Isolte the object. Eple: Drw D for object (ssue no friction) y C Set up your coordinte syste for coponents. Where is? g There re two kinds of forces: 1. Contct forces 2. ield forces (grvity, electric, etc) Pge 12
i-clicker question 4-3 nd 4-4 C Conceptul Eple: The hockey puck. hockey puck is sliding t constnt velocity cross flt horizontl ice surfce tht is ssued to be frictionless. Which of these sketches is the correct free-body digr for this puck? Wht would your nswer be if the puck slowed down? Pge 13
Eple: Ti pulls 10-kg bo by n ttched cord on the sooth surfce of tble. The gnitude of the force eerted by Ti is P = 40.0, nd it is eerted t 30.0 ngle s shown. Clculte the ccelertion of the bo. ree-body digr: contct forces: Pull by Ti; orl force. ield forces: Grvity ewton's - coponent : y - coponent : Solve for Lw : : p cosq P p sinq g cosq 0 (40.0)(cos 30) 10.0 q 3.46 / q s 2 Pge 14
Eple: o slides down n incline. bo of ss is plced on sooth incline tht kes n ngle θ with the horizontl. () Deterine the norl force on the bo. (b) Deterine the bo s ccelertion. (c) Evlute for ss = 10 kg nd n incline of θ = 30. [Solution] irst, D nd -y coordintes. Then, ewton s lw in coponent for: - cop: y - cop: () (b) (c) 85, g sinq g cosq g sinq g cosq 0 4. 9 / s 2. θ? g y gin, two kinds of forces: 1. Contct forces 2. Grvity. θ Pge 15
Eple: Elevtor nd counterweight (twood s chine). The ss of the counterweight is 1000 kg. The totl ss of the elevtor with pssengers is 1150 kg. Clculte () the ccelertion of the elevtor nd (b) the tension in the cble. Ignore the ss of cble nd friction. [Solution] or ech object, we need to drw D nd pply ewton s lw. Ignoring friction nd cblessens the setensionincblesonboth sidesof Kineticsreltion: Cy Ey? pulley. T T T E E C E C g g Solve for ( nd C C C E g Cy Ey T C E 0. 68 / s g ) 10500 : 2 Pge 16
i-clicker question 4-5 If you push with force on either the hevy bo ( 1 ) or the light bo ( 2 ), in which of the two cses is the contct force between the two boes lrger? Ignore friction. 2 1 2 1 ) cse ) cse? C) se in both cses ccelertion is the se for both cses =/( 1 + 2 ). Thus 1 > 2
riction riction is lwys present when two solid surfces slide long ech other. The icroscopic detils re not yet fully understood. Pge 18
Kinetic riction Sliding friction is clled kinetic friction. pproition of the frictionl force: fr = μ k. Here, is the norl force, nd μ k is the coefficient of kinetic friction, which is different for ech pir of surfces. Pge 19
Sttic riction Sttic friction pplies when two surfces re t rest with respect to ech other (such s book sitting on tble). The sttic frictionl force is s big s it needs to be to prevent slipping, up to iu vlue. fr μ s. Usully the coefficient of sttic friction is greter thn the coefficient of kinetic friction. Pge 20
Sttic nd Kinetic rictions ote tht, in generl, μ s > μ k. Pge 21
Eple: riction: sttic nd kinetic. Our 10.0-kg ystery bo rests on horizontl floor. The coefficient of sttic friction is 0.40 nd the coefficient of kinetic friction is 0.30. Deterine the force of friction cting on the bo if horizontl eternl pplied force is eerted on it of gnitude: () 0, (b) 10, (c) 20, (d) 38, nd (e) 40. Pge 22
i-clicker question 4-6 To push or to pull sled? Your little sister wnts ride on her sled. If you re on flt ground, will you eert less force if you push her or pull her? ssue the se ngle θ in ech cse. ) Push ) Pull C) o difference fr = μ k. Pge 23
Eple: Pulling ginst friction. 10.0-kg bo is pulled long horizontl surfce by force of 40.0 pplied t 30.0 ngle bove horizontl. The coefficient of kinetic friction is 0.30. Clculte the ccelertion. D nd Coordintes ewton s lw in - nd y- coponents Two unknowns, P cosq P P k g P sinq cosq k sinq g 0 nd 78 ( fr. We 1. 1 / s 2 ) cn solve. fr y g q P Pge 24
Eple: rp, pulley, nd two boes. o, of ss 10.0 kg, rests on surfce inclined t 37 to the horizontl. It is connected by lightweight cord, which psses over ssless nd frictionless pulley, to second bo, which hngs freely s shown. () If the coefficient of sttic friction is 0.40, deterine wht rnge of vlues for ss will keep the syste t rest. (b) If the coefficient of kinetic friction is 0.30, nd = 10.0 kg, deterine the ccelertion of the syste. Pge 25
cse i : sll T T g sinq g T fr g cosq 0 Sll Lrge g sinq g Sg cos q 0 sinq cosq we wnt 0, cse ii : lrge iu sttic friction : fr S g sinq T fr 0 g sinq T S 0 sinq S cos g cosq 10sin 37 0. 40 10 g 2. 8kg 9. 2kg 10sin 37 2. 8kg 9. 2kg S 0. 4010 q cos 37 cos 37 Pge 26
Pge 27 kg,. kg 2 9 10 ow (b): Prt k fr Kinetic friction : T fr T g g cos g sin 0 q q T g g cos q k g cos g g sin q q 2 78 0 s /. g cos g g sin g cos g g sin k k q q q q