PROLEMS ON WORK ND ENERGY PRINCIPLE
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. (/)
PROLEMS m =.8 kg, v =, P = 8 N (ct), v =? mg =.8(9.8) =7.85 N N P = 8 N P 8.94.94 6 7.85(.75) (.75) 8 m v v v mv / 4.7.4 8.94.8
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)
PROLEMS (a) m 5.65 g in 5 98., 8.96.85 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... 4.46 6.5.4..5. L mg = (9.8) =98. N N cable length y y y mg F pring
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.6 9.5 5.65.5 5.65 9.8 4.46.. in 5,, 9.6 98. (b) y y L cable length mg = (9.8) =98. N mg F pring N y
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.
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 6 75.577 m ( cannot be greater than d ). 5
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.
PROLEMS v =? m = kg, d = mm. W=mg motion F pring N v () v x x v. x.8 5x m /. dx
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
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 76.59 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 76.59 N + y kg kg k = 8 N/m V () v e v V g.5v v v / () v 5v 5.5v
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 4.95 49.5 k (8).7 x V x g 44.45 Vg Vg.7.5 69.4 44.45.8 m / 4.95 49.5 5.5v 69.4 4.995 + y kg kg k = 8 N/m
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)
PROLEMS l = 65 mm, v =, v =? (a) d = 5 mm (b) when the rod ha rotated 5. l (a) 65 mm x 65 arctan 9 67.4 L V g V F pring l 65 mm 65.99.65.94 x W=mg 99.4 m.6 (.65) in.7 m L.65.96 m mm e 5 6 V motion V g e V v, g mg( h kx V g h 5(.94 ) k 9.8 8.6 x x x x mgh.96, v mv ) 8.6.9 4v m / 4(9.8)(.5) 9.8 v
PROLEMS l = 65 mm, v =, v =? (a) d = 5 mm (b) when the rod ha rotated 5. l 65 mm.4 x 65 5 65 mm F pring l.6..65.88.6 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 5.4 4.87 mv x x x x.96 ) 4.87, v.48 4v ) 4(9.8)(.9) 5.4 mgh m / v
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)
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 64. 87 v G r m.5 m v.5m 64.87m, v 9.76 m / (5.4 km / h)
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)
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 5 5 77. mm W = mg F pring l l x 5 9.88 q = 5 5 in45 =5.5 mm 5 mm 5 mm 9.88 77. q = 5 final length of pring (5)(5) co5 6.77 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 /
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
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