PROBLEMS. (a) s cable length. mg = 10(9.81) =98.1 N. F spring

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1 . he ytem i releaed from ret with no lack in the cable and with the prin tretched mm. Determine the ditance traveled by the -k cart before it come to ret (a) if m approache zero and (b) if m = k. ume no mechanical interference. (3/8)

2 v = m = k x = mm determine ditance traveled by the cart before it come to ret (a) if m approache zero and (b) if m = k. (a) m 5.65 in k 5.5 m L m = (9.8) =98. N N cable lenth y y y m F prin

3 (b) v = m = k x = mm determine ditance traveled by the cart before it come to ret (a) if m approache zero and (b) if m = k. m in 5 m k.. L m = (9.8) =98. N cable lenth y y.6 m y N m F prin

4 . he k collar i releaed from ret at and lide down the inclined fixed rod in the vertical plane. he coefficient of kinetic friction i.4. Calculate (a) the velocity v of the collar a it trike the prin (b) the maximum deflection x of the prin. (3/9)

5 m = k v = m k =.4 v =? x max =? (a) - F y N mco6 F f m N m mco6 k mv k () v v N m = (9.8) =9.6 N F f motion min 6(.5) F 6.53v v.56 m/ 6 9.6in 6(.5).4(9.6)co6(.5) 6.53 f (.5) F C (b) -C C C 9.6in 6( x).4(9.6)co6( x) 3.7x8x x8x x 99 mm C C 6.53 x.99 m (6) x

6 3. he. k lider move freely alon the fixed curved rod from to in the vertical plane under the action of the contant 5 N tenion in the cord. If the lider i releaed from ret at calculate it velocity v a it reache. (3/)

7 m =. k v = v =? m =.(9.8) =.96 N y x motion N initial lenth of cord.6 mv (.) v.v.5.65 m final lenth of cord.5 m m(.5) (.65.5).96(.5) 5(.5) v v 4.48 m/

8 4. he net of two prin i ued to brin the.5 k pluner to a top from a peed of 5 m/ and revere it direction of motion. he inner prin increae the deceleration and the adjutment of it poition i ued to control the exact point at which the reveral take place. If thi point i to correpond to a maximum deflection d = mm for the outer prin pecify the adjutment of the inner prin by determinin the ditance. he outer prin ha a tiffne of 3 N/m and the inner one a tiffne of 5 N/m.

9 m =.5 k pluner to a top from a peed of 5 m/ d = mm (outer prin) pecify the adjutment of the inner prin by determinin the ditance. kouter = 3 N/m k inner = 5 N/m. F prin F outer W=m N F outer F inner motion ( v ) mv (.5)5 x d 6.5 F inner Fouter kx 3 x Finner kx 5( x ) 5 x 5 x 3 5(.) 75 d xdx d 75(.).43 m xdx 5 d 75 x dx 3. 5 (.) 5 x 5. 5 x m ( cannot be reater than d ). 3 5

10 5. wo block are connected by a liht inextenible cord which pae around mall male pulley. If block i pulled down 5 mm from the equilibrium poition and releaed from ret determine it peed when it return to the equilibrium poition. + y k k k = 8 N/m

11 block pulled down 5 mm from the equilibrium poition v = determine it peed when it return to the equilibrium poition. W Lenth of the cord l = y +y =contant v +v = a + a = lock m F y 98. (9.8) 98. N ma N lock When the ytem i in equilibrium the amount of prin deformation F In equilibrium poition p F p W m (9.8) 9. 6 N F F F p p p F y W ma W (98.) 9.6 Fp kx x.7 m (.7 ) k 8 mm Work enery equation of the ytem N + y k k = 8 N/m k V () v e v V.5v v v / () v 5v 5.5v

12 block pulled down 5 mm from the equilibrium poition v = determine it peed when it return to the equilibrium poition. V e V Since the cord i inextenible the work done by the tenion force cancel out when the work i added up for both particle. V V V e V m m V V h h (9.8).5 h h (9.8) (.5) e V e 5.5v V l = y +y =contant (8).7 v k x y V x y.7.5 m / V V v 69.4 motion y W F prin k k = 8 N/m W k motion

13 6. he ytem i releaed from ret with the prin initially tretched 75 mm. Calculate the velocity v of the cylinder after it ha dropped mm. he prin ha a tiffne of 5 N/m. Nelect the ma of the mall pulley. (3/46)

14 v = prin initially tretched 75 mm calculate velocity v of the cylinder after it ha dropped mm. Pulley F prin Ma ' motion F F for F y prin ' prin equilibriu m V.4. V.5v W=m..5v.5v V e (.) (45) v mh 45(9.8)(.) v.65

15 v = prin initially tretched 75 mm calculate velocity v of the cylinder after it ha dropped mm. Pulley+ma F prin motion W=m (.) (45) v.5v V mh (45)(9.8)(.) 5.3 V e..5v.5v V k v v.38 m/ x x V.65.5v e

16 7. he prin ha an untretched lenth of 65 mm. If the ytem i releaed from ret in the poition hown determine the peed v of the ball (a) when it ha dropped a vertical ditance of 5 mm and (b) when the rod ha rotated 35. (3/55)

17 l = 65 mm v = v =? (a) d = 5 mm (b) when the rod ha rotated mm l O (a) x 65 mm 65 L 6 mm arctan L V V F prin l 65 mm mm x W=m 99.4 m mm.6 (.65) in.7 L m e 5 6 V motion V e v V m ( h kx V h 5(.94 m ) k x x x x mh.96 v mv ) v m / 4(9.8)(.5) 9.8 v

18 l = 65 mm v = v =? (a) d = 5 mm (b) when the rod ha rotated mm l 65 mm x O mm L 6 mm 65 F prin l mm.6 L.7 m x. 96 (b) 3 V V e h in W=m.4 V motion (65 )(65 ) co.4 m V 3 e v V 3 m ( h kx V h 5( m m mv x x x x.96 ) v.483 4v ) 4(9.8)(.39) 5.34 k 3 mh m / v 3

19 8. he 3 k phere i carried by the paralleloram linkae where the prin i untretched when q = 9. If the mechanim i releaed from ret at q = 9 calculate the velocity v of the phere when the poition q = 35 i paed. he link are in the vertical plane and their ma i mall and may be nelected. (3/69)

20 k = N/m m = 3 k at q = 9 prin untretched v = q = 9 at q = 9 v =? at q = 35. initial lenth of prin l mm motion W = m F prin l l x q = 35 5 in45 =353.5 mm 5 mm 5 mm q = 35 final lenth of prin (5)(5) co V mm V m h h V mv Ve k x x ().7.5v v e (3) v.5v 3(9.8)(.354.5) v.4 m /

21 9. he liht quartercircular rod i pivoted at O and carrie the 3 k particle. When the ytem i releaed from ret at poition () it move to poition () under the action of the contant force F=5 N applied to the cable. he prin of tiffne k=5 N/m ha an untretched lenth of mm. Calculate the peed of the particle and the anular velocity of the circular rod a the particle pae poition ().

22 m = 3 k v = F = 5 N k = 5 N/m l = mm v =?