1. The 0.1 kg particle has a speed v = 10 m/s as it passes the 30 position shown. The coefficient of kinetic friction between the particle and the

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Byron Park
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3 1. The 0.1 kg pticle h peed v = 10 m/ it pe the 30 poitio how. The coefficiet of kietic fictio betwee the pticle d the veticl ple tck i m k = 0.0. Detemie the mgitude of the totl foce exeted by the tck o the pticle. Wht i the deceletio of the pticle? (3/49)

4 W mg 0.1(9.81) m = 0.1 kg, v = 10 m/, = 30, m k = 0.0. Detemie the mgitude of the totl foce exeted by the tck o the pticle. Wht i the deceletio of the pticle? 30 W=mg +t v m/ f m f 0.981co300.1(0) 1.15 m 0.0(1.15) 0.3 totl foce exeted by the tck f 1.17 t m t 0.981i 30 m t f 7.05 m/ t t

5 . The membe OA otte bout hoizotl xi though O with cott gul velocity w = 3 d/. A it pe the poitio = 0, mll block of m m i plced o it t dil ditce = 450 mm. If the block i obeved to lip t = 50, detemie the coefficiet of ttic fictio m betwee the block d the membe. (3/54)

6 motio W=mg w = 3 d/ (ct), t = 0, mll block of m m plced t dil ditce = 450 mm, block i obeved to lip t = 50, detemie m. f =m 50 m mg co50 mg i 50 mw m w =3 d/ m m g i 50 w g co50 m 0, mg co50 0, mgi 50 m0 w m f m mg co50 m mg co50 m g co50 f g i 50 w w 0.45(3) t 50 t g co co 50

7 3. The lotted m OA otte bout fixed xi though O. At the itt ude coidetio, = 30, = 45 deg/ d = 0 deg/. Detemie the foce pplied to the 0. kg lide B by both m OA d the ide of the lot. Let L = 0.6 m. eglect ll fictio. The motio occu i veticl ple.(3/71)

8 Tigle OAB i i 45, = 30, = 45 deg/ d = 0 deg/. Detemie the foce pplied to the lide B by both m OA d the ide of the lot. m = 0. kg, L = 0.6 m. o fictio, veticl ple poblem. m v 0.8(0.785) m/ v t45 1, v v v t m/, m/ L 0. 6 m W mg 0.(9.81) v 45 deg/ d /, 0 deg/ d / + + m/ 30 v A v

9 W mg 0.(9.81) co i 60 OA OA m co451.4 m i m, m OA - i 45 co = 30, = 45 deg/ d = 0 deg/. Detemie the foce pplied to the lide B by both m OA d the ide of the lot. M = 0. kg, L = 0.6 m. o fictio, veticl ple poblem L 0. 6 m A 15 W OA - +

10 4. A kg phee S i beig moved i veticl ple by obotic m. Whe the gle i 30, the gul velocity of the m bout hoizotl xi though O i 50 deg/ clockwie d it gul cceletio i 00 deg/ couteclockwie. I dditio, the hydulic elemet i beig hoteed t the cott te of 500 mm/. Detemie the ecey miimum gippig foce P if the coefficiet of ttic fictio betwee the phee d the gippig ufce i Compe P with the miimum gippig foce P euied to hold the phee i ttic euilibium i the 30 poitio. (3/7)

11 m = kg, = 30, w = 50 deg/ (cw), = 00 deg/ (ccw). = -500 mm/ (ct), m = Detemie the ecey miimum gippig foce P betwee the phee d the gippig ufce. Compe P with the miimum gippig foce P euied to hold the phee i ttic euilibium i the 30 poitio.

12 5. The pi A i foced to move i the fixed pbolic lot by the movig veticl guide. The cetelie of the lot i decibed by x = 10y [m]. Whe x = 0.1 m, the peed v of the veticl guide i 0.4 m/ d i ot chgig t thi itt. Detemie the mgitude of the foce ctig o the 50 g pi y v exeted by the A veticl guide d the fixed plte. x = 10y x x

13 1/ 1/ x 0.1 y 1/ 1/ dy 0.5 t dx d y dx.5 x 10y x 0 y 0y, 0.1 m, x () yy y 6.57 W=mg y y y 0yy / 0.56 m m / t x x = 10y [m], x = 0.1 m, v = 0.4 m/ (ct), m = 50 g, detemie the mgitude of the foce ctig o the pi exeted by the veticl guide d the fixed plte y 0. m / x y m x m y 0 y x = 10y x co v i A A v A v Ay = 6.57 v Ax co (9.81) 0.5(0.4).453, x i

14 6. The mll object i plced o the ie ufce of the coicl dih t the diu how. If the coefficiet of ttic fictio betwee the object d the coicl ufce i 0.30, fo wht ge of gul velocitie w bout the veticl xi will the block emi o the dih without lippig? Aume tht peed chge e mde lowly o tht y gul cceletio my be eglected. w 0. m m 30

15 w 0. m 30 f y 0 co30 mg f i 30 0 co30 m i 30 y 30 BD W=mg 30 m m mg i 30 m co30 m = 0.30, fo wht ge of gul velocitie w bout the veticl xi will the block emi o the dih without lippig? Speed chge e mde lowly gul cceletio my be eglected. Top view w = 0. m, m i 30 f co30 m mw +t f m mg co30 m i 30, mw w mw i 30 m co30 0. m m 30

16 0. m w 30 f y 30 W=mg 30 co 30 w m = 0.30, fo wht ge of gul velocitie w bout the veticl xi will the block emi o the dih without lippig? Speed chge e mde lowly gul cceletio my be eglected. = 0. m mg m i 30 +t mw i 30 m co30 w 0. m m 30 mg co30 m i 30 w 3.41 g w i 30 m co30 co30 i 30 m d / w 7.1 d / m w i 30 m co30 w 7.1 d d / /

17 7. The kg coll i foced to move o the pbolic guide give by y = 4 x, by ttched pig with utetched legth of 1.5 m d tiffe of k = 0 /m. It i kow tht whe the coll pe the poitio x = 1 m, it velocity i v = m/. Detemie the ectio foce ctig o the coll fom the guide d the totl cceletio of the coll. Dimeio i m

18 W=mg b b g pig +t g b m = kg, y = 4 x, l o = 1.5 m, k = 0 /m, whe x = 1m, v = m/. Detemie the ectio foce ctig o the coll fom the guide d the totl cceletio of the coll. y 4 x dy t dx d y dx m 1 ( ) 3/ v m mg co Dimeio i m 3 m 5.59 m, m / kx k x x 0( ) 5.08 pig pig, i g m (9.81) co i (0.716) m.8 m.8 t

19 m = kg, y = 4 x, l o = 1.5 m, k = 0 /m, whe x = 1m, v = m/. Detemie the ectio foce ctig o the coll fom the guide d the totl cceletio of the coll. W=mg b g pig b g Dimeio i m 3 m m.8 t t.8 m t m t pig 5.08co16.45 (9.81)i cog mgi m 19.6 t, t m / t t t m /

20 8. The lotted m i ottig t te of =5 d/ d = d/ whe = 90 o. Detemie the oml foce the lotted m mut exet o the 0.5 kg pticle if the pticle i cofied to move log the pth defied by the hoizotl hypebolic pil = 0. m.

21 =5 d/, = d/, = 90, m = 0.5 kg, = 0. m, detemie the oml foce the lotted m mut exet o the pticle 90 d, 5 d /, d / + 0., 0., , 0.173(5) m / 0 ( 0.405)(5) (0.173)() m / m + +t v v, v R ct v v e v e, v v m /, 0.405e 0.637e m / v 0.173(5) m /

22 90 d, 5 d /, d / m, m /.418 m / e e m /.418 (0.173)(5) =5 d/, = d/, = 90, m = 0.5 kg, = 0. m, detemie the oml foce the lotted m mut exet o the pticle m / ( 0.405)(5) (0.173)() +t v v, v + R ct m m co ( 0.765) R i ( 3.798) R 1.655

23 9. The lotted m OB otte with cott gul velocity of w = = d/ i the veticl ple bout the poit O of the 5 cm diu fixed cicul cm. Pi A i cotied to move i the lot. The pig i the lot eue tht pi A cotiuouly cotct the ufce of the cm. The tiffe of the pig i k = 50 /m. The pig i i utetched whe = d. The m of pi A i 0.5 kg. Detemie the oml foce ctig o pi A fom the ufce of the cm d the foce R ctig o A fom the lot fo = 90. eglect fictio. Tke e = 15 cm, b = 5 cm, g = 9.81 m/.

24 w OB = = d/ (ct), k = 50 /m, pig i utetched whe = d. The m of pi m A = 0.5 kg. Detemie the oml foce ctig o pi A fom the ufce of the cm d the foce R ctig o A fom the lot fo = 90. Tke e = 15 cm, b = 5 cm, g = 9.81 m/. Veticl ple poblem.

25 10. Uig foked od, mooth cylide P, hvig m of 0.4 kg, i foced to move log the veticl lotted pth of 0 [m], whee i i di. If the cylide P h cott peed of m/, detemie the foce of the od () d the foce of the lot (R) ctig o the cylide t the itt whe = d. eglect fictio. Tke 0 = 0.8 m, g = 9.81 m/.

26 m = 0.4 kg, P foced to move log the veticl lotted pth of 0 [m], whee i di, cylide P h cott peed of m/, detemie the foce of the od () d the foce of the lot (R) ctig o the cylide t the itt whe = d. 0 = 0.8 m, g = 9.81 m/.

+ r Position Velocity

+ r Position Velocity 1. The phee P tel in tight line with contnt peed of =100 m/. Fo the intnt hown, detemine the coeponding lue of,,,,, eltie to the fixed Ox coodinte tem. meued + + Poition Velocit e 80 e 45 o 113. 137 d