PROBLEMS ON WORK AND ENERGY PRINCIPLE

Transcription

1 ON WORK ND ENERGY PRINCIPLE

2 . 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. (/8)

3 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

4 (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

5 . 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. (/9)

6 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 6.5v v.56 m/ 6 9.6in 6(.5).4(9.6)co6(.5) 6.5 f (.5) F C (b) -C C C 9.6in 6( x).4(9.6)co6( x).7x8x 6.5.7x8x x 99 mm C C 6.5 x.99 m (6) x

7 . 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. (/)

8 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/

9 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 N/m and the inner one a tiffne of 5 N/m.

10 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 = 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 x Finner kx 5( x ) 5 x 5 x 5(.) 75 d xdx 5 9 d 75(.).4 m xdx 5 d 75 x dx. 5 (.) 5 x 5. 5 x m ( cannot be reater than d ). 5

11 5. Calculate the horizontal velocity v with which the k carriae mut trike the prin in order to compre it a maximum of mm. he prin i known a a hardenin prin ince it tiffne increae with deflection a hown in the accompanyin raph. (/)

12 v =? m = k d = mm. W=m motion F prin N v () v x x v x.8. 5x m /. dx

13 6. 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

14 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

15 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

16 7. 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. (/46)

17 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..5v.4. V.5v.5v W=m V e (.) (45) v mh 45(9.8)(.) v.65

18 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. V e..5v.5v V k.6.6.5v v.8 m/ x x V.65.5v e

19 8. 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 5. (/55)

20 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

21 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) V V e h.5.65 in.4. 9 W=m.4 V motion (65 )(65 ) co.4 m V e v V m ( h kx V h 5(.88 m m mv x x x x.96 ) 4.87 v.48 4v ) 4(9.8)(.9) 5.4 k mh m / v

22 9. he car of an amuement-park ride have a peed v = 9 km/h at the lowet part of the track. Determine their peed v at the hihet part of the track. Nelect enery lo due to friction. Give careful thouht to the chane in potential enery of the ytem of car. (/64)

23 v = 9 km/h (lowet part)v =?(hihet part) 9 km / h 5 m / m = total ma of train For the whole train V V e 4 r r.5 m G r r (5) W = m m v v W = m v m v 5 mv.5m Ve V mh m h h 9.8m() r v G r m.5 m v.5m 64.87m v 9.76 m / (5.4 km/ h) r r in in rad 4 motion r r C

24 . he 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 = 5 i paed. he link are in the vertical plane and their ma i mall and may be nelected. (/69)

25 k = N/m m = k at q = 9 prin untretched v = q = 9 at q = 9 v =? at q = 5. initial lenth of prin l mm motion W = m F prin l l x q = 5 5 in45 =5.5 mm 5 mm 5 mm q = 5 final lenth of prin (5)(5) co V mm V m h h V mv Ve k x x ().7.5v v e () v.5v (9.8)(.54.5) v.4 m /

26 . he liht quartercircular rod i pivoted at O and carrie the 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 ().

27 m = k v = F = 5 N k = 5 N/m l = mm v =?