PROBLEMS ON WORK AND ENERGY PRINCIPLE

Transcription

1 PROLEMS ON WORK ND ENERGY PRINCIPLE

2 PROLEMS. he.8 kg collar lide with negligible friction on the fixed rod in the vertical plane. If the collar tart from ret at under the action of the contant 8-N horizontal force, calculate it velocity v a it hit the top at. (/)

3 PROLEMS m =.8 kg, v =, P = 8 N (ct), v =? mg =.8(9.8) =7.85 N N P = 8 N P (.75) (.75) 8 m v v v mv /

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

5 PROLEMS (a) m 5.65 g in 5 98., v =, m = kg, x = mm, determine ditance traveled by the cart before it come to ret (a) if m approache zero and (b) if m = kg. k 5.5 m L mg = (9.8) =98. N N cable length y y y mg F pring

6 v =, m = kg, x = mm, determine ditance traveled by the cart before it come to ret (a) if m approache zero and (b) if m = kg. PROLEMS m k g m g m in 5,, (b) y y L cable length mg = (9.8) =98. N mg F pring N y

7 PROLEMS. he net of two pring i ued to bring the.5 kg plunger to a top from a peed of 5 m/ and revere it direction of motion. he inner pring 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 pring, pecify the adjutment of the inner pring by determining the ditance. he outer pring ha a tiffne of N/m and the inner one a tiffne of 5 N/m.

8 m =.5 kg plunger to a top from a peed of 5 m/, d = mm (outer pring), pecify the adjutment of the inner pring by PROLEMS determining the ditance. kouter = N/m, k inner = 5 N/m. F pring W=mg N F outer F inner motion ( v ), mv F outer (.5)5 x d 6.5 F inner Fouter kx x, Finner kx 5( x ) 5x 5 x 5(.) 75 d xdx 5 9 d 75(.).4 m xdx 5 d 75 x dx. 5(.) 5 x 5. 5x m ( cannot be greater than d ). 5

9 PROLEMS 4. Calculate the horizontal velocity v with which the kg carriage mut trike the pring in order to compre it a maximum of mm. he pring i known a a hardening pring, ince it tiffne increae with deflection a hown in the accompanying graph.

10 PROLEMS v =? m = kg, d = mm. W=mg motion F pring N v () v x x v. x.8 5x m /. dx

11 PROLEMS 5. wo block are connected by a light 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 kg kg k = 8 N/m

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

13 PROLEMS block pulled down 5 mm from the equilibrium poition, v =, determine it peed when it return to the equilibrium poition. 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 g g e V mg mg V g V h h (9.8).5 h h (9.8) (.5) e V e 5.5v g V l = y +y =contant v g k (8).7 x V x g Vg Vg m / v y kg kg k = 8 N/m

14 PROLEMS 6. he pring ha an untretched length 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)

15 PROLEMS l = 65 mm, v =, v =? (a) d = 5 mm (b) when the rod ha rotated 5. l (a) 65 mm x 65 arctan L V g V F pring l 65 mm x W=mg 99.4 m.6 (.65) in.7 m L m mm e 5 6 V motion V g e V v, g mg( h kx V g h 5(.94 ) k x x x x mgh.96, v mv ) v m / 4(9.8)(.5) 9.8 v

16 PROLEMS l = 65 mm, v =, v =? (a) d = 5 mm (b) when the rod ha rotated 5. l 65 mm.4 x mm F pring l L.7 m, x. 96 (b) V g V e V motion V g e v V, g mg( h kx V g h 5(.88 m h.5.65in.4. 9 m W=mg.4 (65)(65) co.4 m k mv x x x x.96 ) 4.87, v.48 4v ) 4(9.8)(.9) 5.4 mgh m / v

17 PROLEMS 7. 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 highet part of the track. Neglect energy lo due to friction. Give careful thought to the change in potental energy of the ytem of car. (/64)

18 PROLEMS v = 9 km/h (lowet part),v =?(highet part) m = be the total ma of train For the whole train V g V e 9 km / h 5 m/ r r.5 m G r (5) W = mg m v v W = mg v m v 5 mv.5m Ve, Vg mgh mg h h 9.8m() r v G r m.5 m v.5m 64.87m, v 9.76 m / (5.4 km / h)

19 PROLEMS 8. he kg phere i carried by the parallelogram linkage where the pring 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 neglected. (/69)

20 PROLEMS k = N/m, m = kg, at q = 9 pring untretched, v = q = 9 l at q = 9, v =? at q = 5. initial length of pring mm W = mg F pring l l x q = 5 5 in45 =5.5 mm 5 mm 5 mm q = 5 final length of pring (5)(5) co V mm mv () v.5v V mg h h (9.8)(.54.5) 4. g e.5v V k x g x V 4..5 e ().7,,.5v.5.95, v.4 m /

21 PROLEMS 9. he ytem hown i in equilibrium when f =. Initially when block C i in a tate of ret at f = 9, it i given a light puh. Determine the velocity of the block a it pae from the poition where f =7 o. Neglect the ma of the light rod. D mm k=8 kn/m f mm mm 6 mm C kg

22 ytem in equilibrium at f =, initially block C at ret at PROLEMS f = 9, determine velocity of block at f =7 o. D mm k=8 kn/m f mm mm 6 mm C kg