Eunil Won Dept. of Physics, Korea University 1. Ch 03 Force. Movement of massive object. Velocity, acceleration. Force. Source of the move

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1 Eunil Won Dept. of Phsics, Kore Uniersit 1 Ch 03 orce Moement of mssie object orce Source of the moe Velocit, ccelertion

2 Eunil Won Dept. of Phsics, Kore Uniersit m ~ m ~ 1.8 m 1.8 m

3 Eunil Won Dept. of Phsics, Kore Uniersit 3 Newton s irst Lw Lw of Inerti (mss) An bod will remin t rest of in motion in stright line with constnt elocit unless cted upon b n outside force If the net force is zero, there is reference frme with zero ccelertion

4 Eunil Won Dept. of Phsics, Kore Uniersit 4 Newton s Second Lw Lw of Motion If force is pplied, the stte of motion is chnged dp dt d dt (m) m d dt m newton [N kg m/s ]

5 Eunil Won Dept. of Phsics, Kore Uniersit 5 Newton s Third Lw Action-Rection Lw Wheneer one bod eerts force on second bod, the second bod eerts force bck on the first tht is equl in mgnitude nd opposite in direction AB BA

6 Eunil Won Dept. of Phsics, Kore Uniersit 6 Emple 3.1 A 440-g cn of food on frictionless leel surfce is obsered to ccelerte t rte of 1.5 m/sec. Wht is the force on the cn? net, et m (0.440 kg)(1.5 m/s ) 0.66 kg m/s net, et 0.66 N

7 Eunil Won Dept. of Phsics, Kore Uniersit 7 Emple 3. An orderl The orderl eerts bckwrd force of 100 N on the floor. Wht ccelertion is produced, ssuming the friction in the wheels is negligible? (question on the sstem I) An orderl Gurne Ptient orce tht the orderl eerts m m m o g p 85kg 0kg 50kg 100N Accelertion t m t m o m g m p 0.645m/s

8 Eunil Won Dept. of Phsics, Kore Uniersit 8 Emple 3.3 Clculte the force the orderl eerts on the gurne in Emple 3. (Question on sstem ) An orderl Gurne Ptient orce tht the orderl eerts m m m o g p 85kg 0kg 50kg 100N orce o m ( m m ) (0 50)(0.645) g 45.kgm/s p 45.N

9 Eunil Won Dept. of Phsics, Kore Uniersit 9 Weight nd norml force weight m w mg Norml force t 0 N w 0 N w

10 Eunil Won Dept. of Phsics, Kore Uniersit 10 Newton s Uniersl Lw of Grittion G mm r : there is force of ttrction between n two msses tht is proportionl to the product of the msses nd inersel proportionl to the distnce between their centers of mss w mg G mm r g GM r

11 Eunil Won Dept. of Phsics, Kore Uniersit 11

12 Eunil Won Dept. of Phsics, Kore Uniersit 1 riction : proportionl to the norml force Sttic riction f s µ s N µ s Kinetic riction f ( f ) k µ k N f f s µ s µ k : coefficient of sttic friction : coefficient of kinetic friction

13 Eunil Won Dept. of Phsics, Kore Uniersit 13 riction Coefficients of friction Kinetic Sttic Rubber on dr concrete Rubber on wet concrete Wood on Wood Wed wood on wet snow Metl on wood Steel on steel (dr) Steel on steel (oiled) Teflon on steel Bone lubricted with snoil fluid Shoes on wood Shoes on ice Ice on ice Steel on ice

14 Eunil Won Dept. of Phsics, Kore Uniersit 14 Emple 3.4 A 70-kg cross-countr skier is on leel ground in wet snow wering wed wooden skis. () Wht is the mimum force tht cn be eerted on the skier in horizontl direction without cusing her to moe? (b) Once the skier is moing, wht horizontl force is necessr to keep her moing t sted elocit? w mg (70 kg)(9.8m/s ) 686 N f µ N s ( 0.14)(686 N) 96 N net, et 0 f 0 f µ N k ( 0.1)(686 N) 68.6 N

15 Eunil Won Dept. of Phsics, Kore Uniersit 15 Tension A tension is n force crried b fleible string, rope, cble, chin etc

16 Eunil Won Dept. of Phsics, Kore Uniersit 16 Emple 3.5 A child nd bsket with totl mss of 10 kg re suspended from scle b cord. Clculte the tension in the cord. net, et T w 0 T w mg (10 kg)(9.8m/s ) 98 N

17 Eunil Won Dept. of Phsics, Kore Uniersit 17 Tensions of ptient

18 Eunil Won Dept. of Phsics, Kore Uniersit 18 Vector 1. Vectors he direction & mgnitude ρ,, { }. Two ectors re identicl if both direction nd mgnitude re sme 3. Negtie ector. 4. Zero ector. 5. Unit ector. b 0 eˆ eˆ 1

19 Eunil Won Dept. of Phsics, Kore Uniersit 19 Vector nlsis b s s b b b (b c) ( b) c b d ( ) 0 0 d b

20 Eunil Won Dept. of Phsics, Kore Uniersit 0 Components of Vectors ˆ ŷ (0,1,0) ˆ (1,0,0) ˆ j i z z ˆ ˆ ˆ z j i j i j i b ) ( ) ( ) ( ) ( b b b b b s b s s s j i s b 1 tn sin, cos θ θ θ

21 Eunil Won Dept. of Phsics, Kore Uniersit 1 Emple 3.6 j i j i 1 1 t (0.34) sin (0.939) cos (0.59) sin (0.966) cos15 j i t ) ( ) ( t t 3.89 tn t t t t t θ Clculte the totl force eerted on gurne

22 Eunil Won Dept. of Phsics, Kore Uniersit Emple 3.7/3.8 Clculte the ccelertion (crtstuff5 kg, frictionl force.0 N) Accelertion of the crt n f h t h N mg 0 m n Norml orce N N 0 w m/s w mg ( 5)(9.8) 10 55N

23 Eunil Won Dept. of Phsics, Kore Uniersit 3 Torque nd Rottion

24 Eunil Won Dept. of Phsics, Kore Uniersit 4 Torque The effectieness of force in producing rottion is clled torque τ r t r sinφ r τ r, τˆ // ωˆ

25 Eunil Won Dept. of Phsics, Kore Uniersit 5 Equilibrium Condition 0, τ 0

26 Eunil Won Dept. of Phsics, Kore Uniersit 6 Emple 3.9 () Clculte the force tht the biceps muscle eerts to hold the book (b) Compre the force eerted b the biceps muscle with the weight of the forerm nd book. (clockwise) (counterclockwise) τ cw, net τ ccw, net (15cm)( w ) (40cm)( w ) (4.0 cm) t B B w w (15cm)( m )( g) (40cm)( mt )( g) 4.0cm (15)(.5kg)(9.8m/s ) (40)(4.0kg)(9.8m/s N 1568N 484 N 4.0 w w 63.7 N t m 484 N g m g t 63.7 N )

27 Eunil Won Dept. of Phsics, Kore Uniersit 7 Emple 3.10 Clculte the force eerted b the etensor muscle in the upper leg when lifting weight s shown below Note: l l 35cm.0cm τ w, net τ ccw, net l T l ( l / l M M ) T M (l / l )mg (35cm/.0cm)(98N) 1715N

28 Eunil Won Dept. of Phsics, Kore Uniersit 8 Rottionl Motion nd Centripetl orce c m r m r

29 Eunil Won Dept. of Phsics, Kore Uniersit 9 p p i p cosθ i sinθ j j q q i q cosθ i sinθ j j t pq r( θ ) q t p q cosθ t p cosθ 0 q t p q sinθ p sinθ (rθ ) / r sinθ θ j sinθ lim lim 0 r θ θ 0 θ r

30 Eunil Won Dept. of Phsics, Kore Uniersit 30 Emple 3.11 An ultrcentrifuge spins t 50,000 reolutions per minute nd the mteril being centrifuged is 5.0 cm from the piot point. Clculte the centripetl ccelertion nd epress it s multiple of the ccelertion of grit (in g s) s t π (0.05 m) s m/s c r (.6 10 m/s) 0.05m m/s c g c m/s 9.8 m/s ( ) g

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