(T > w) F R = T - w. Going up. T - w = ma

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1 ANSES Suspended Acceleratng-Objects A resultant orce causes a syste to accelerate. he drecton o the acceleraton s n the drecton o the resultant orce. As llustrated belo, hen suspended objects accelerate, they do so n the drecton o the resultant orce. Statonary (at rest) ( = ) F = 0 Acceleratng upard ( > ) F = - Gong up F = a - = a a = - Acceleratng donard ( > ) F = - Cong don F = a - = a a = - Frctonless Pulley hen to asses are attached at opposte ends o a lght cord that passes over a rctonless pulley, the to asses act as a sngle ass hose acceleraton s as ollos: F 0 a 0 F a otal ass a F otal ass Note: Use 0 /s or the acceleraton due to gravty.. A lght (.e. assless) cord passes over a pulley that turns on a rctonless axs as llustrated n the dagra on the rght. o asses, 3 kg and.6 kg, are attached at opposte ends o the cord. Deterne the agntude o the acceleraton o the asses. [0.7 /s ] Note that the cord untesthe objects nto a sngle ass o 5.6 kg. F g g (3 kg)(0 / s ) (.6 kg)(0 / s ) 4 N F a F 4 N a 0.7 / s 5.6 kg 3 kg.6 kg PHYSICS 534 DYNAMICS AnsPhyscs Ex-3.DOC 999 S. Lancone Page /8

2 . A stone s echancally v 30 / s shot straght up n the ar th a velocty o 30 /s. a) Ho hgh v does 0 the stone rse? [45 ] v 0 30 / s v a 5 / s s a t (5 / s)(3 s) 45 s b) At hat te ll the stone be 40 ro the ground on ts ay up? [ s] or t 5t 5 t 6 t 8 0 Note: heuntsarenot ncludedtosply theatheatcal expresons. (t )(t 4) 0 t s and t 4 s Anser : t s (on ts ay up) t s Anser : c) At hat te ll the stone be 40 ro the ground on ts ay don? [4 s] and t 4 s s Note: heuntsarenot ncludedtosply t 4 s (on ts ay don ) theatheatcal expresons. or t 5t 5 t 6 t 8 0 (t )(t 4) 0 3. A ass o 0 kg hangs by a rope ro a celng nsde an elevator. a) hat ll be the tenson n the rope the elevator s acceleratng upard at 4 /s? [80 N] S ncethe elevator s gong up : F a or g a a g (0 kg)(4 / s ) (0 kg)(0 / s b) hat ll be the tenson n the rope the elevator s acceleratng donard at 4 /s? [0 N] S ncethe elevator s gong don : F a or g a g a (0 kg)(0 / s ) (0 kg)(4 / s 0 kg ) 80 N 0 kg ) 0 N a = 4 /s a = 4 /s PHYSICS 534 DYNAMICS AnsPhyscs Ex-3.DOC Free Fall Part- / Page /8

3 4. A stone s thron vertcally upard th a velocty o 5 /s ro the botto o a cl that s 5 hgh. At the sae te, another stone s dropped ro the top o the cl. At hat heght ro the ground ll the to stones eet? [0 ] s Don sup 5 Note: heuntsarenot ncludedtosply But s theatheatcal expresons. Don Up 5 s or 0 5t 5t 5t 5 5t 5 0 (0)() 5 t s hus, the ball alls 5 ater s. Anser : A boy drops a stone vertcally donard ro a brdge 5 hgh. One second later, he thros another stone also vertcally donard. th hat ntal velocty ust he thro the second stone so that both stones strke the ater at the sae te? [.3 /s] Note that hle the ds tance or both stones s the sae (5 ), the tes are not the sae. I t represents the te o all or the rst stone, then the te or the second stones (t ) sn ce t as thron one sec ond later. e o rst stone Intal velocty o second stone s s 5 0 (0 / s )(t ) 5 (4 s) (0 / s )(4 s) 5 s 5t 5 (4 s) (5 / s )(6 s ) or t 5 s 4 v 45 / s t 5 s.5 / s or.3 / s e o second stone t 5 s s 4 s PHYSICS 534 DYNAMICS AnsPhyscs Ex-3.DOC Free Fall Part- / Page 3 /8

4 6. A rock s thron vertcally don th a velocty o 5 /s. th hat velocty ll t strke the ground 00 belo? [5 /s] as as or v (0 /s )(00 ) (5 /s) or v 65 /s 5. /s 5 /s 7. A pebble s dropped ro the roo o a hgh buldng. I t takes.5 s to travel the last 00, ho hgh s the buldng? [75. ] Calculaton o ntal velocty or last 00. s or 00 (.5 s) (0 / s )(.5 s) or 00 (.5 s)v (5 / s )(.5 s) or v (.5 s) / s 59. / s.5 s Calculaton o heght o top part o buldng as v (59. / s) / s s 75. a (0 / s 0 / s hus, the heght o the buldng s : th hat ntal upard velocty ust a ball be thron n order to rse 0? [0 /s] as v as v 0 (0 / s )(0 ) v 400 / s 0 / s PHYSICS 534 DYNAMICS AnsPhyscs Ex-3.DOC Free Fall Part- / Page 4 /8

5 9. A package s attached to a helcopter ready to be released (dropped). I the helcopter s ascendng at 5 /s and releases the package ro an alttude o 550, ho long does t take the package to strke the ground? [ s] Note: heuntsarenot ncludedtosply theatheatcal expresons. Snce the helcopter s ascendng, the acceleraton o the package Usn g the quadratc equaton s negatve hen released. B B 4AC t s A 550 ( 5 )t (0)t ( ) ( ) 4()( 0) t () or 550 5t 5t or t t 0 0 A B C 0 s (dscard negatve value) 0. Startng ro rest, a block o ood takes 5 s to slde don an nclned plane 0 c long. a) hat as ts acceleraton? [0. /s ] s or. 0 (a)(5 s) _ (. ) a / s 0. / s _ 5 / s _ b) th hat speed dd t reach the botto o the nclne? [0.5 /s] _ as or v as 0 (0. / s )(. ) 0.4 / s _ / s 0.5 / s PHYSICS 534 DYNAMICS AnsPhyscs Ex-3.DOC Free Fall Part- / Page 5 /8

6 . A ball alls ro rest and s seen to pass a ndo hgh n 0. s. Deterne the heght above the ndo that the stone ell? [9 ] Intal velocty o ball upon passn g top o ndo : s s at s at (0 / s )(0. s) 9.5 / s t t t 0. s Fnal velocty o ball upon passn g botto o ndo : v a v at (0 / s )(0. s) / s t But v v / s 9.5 / s 0.5 / s otal ds tance ball alls : as v (0.5 / s) / s s.0 a (0 / s ) 0 / s Ds tance above ndo otal ds tance Heght o ndo Ds tance above ndo o stones, A and B, are respectvely 45 and 60 above the ground. I stone A s dropped at the sae te as stone B s thron vertcally don th a velocty o /s, hch stone hts the ground rst? [B] A e stone A strkes ground Note: heuntsarenot ncludedtosply theatheatcal expreson. s U sn g the quadratc equaton (0 / s )t 45 0 B B 4AC (45 ) t or t 9 s A 0 / s t 3 s () 4(5)( 60) t e stone B strkes ground (5) s 0 0 or 60 ( / s)t (5 / s )t s.5 s or 5 t t A 5 B C 60 (dscard negatve value) h =? V = 0 V = 9.5 /s V = 0.5 /s /s B PHYSICS 534 DYNAMICS AnsPhyscs Ex-3.DOC Free Fall Part- / Page 6 /8

7 3. o asses, 8 kg and kg, are connected by a lght rope that passes over a rctonless pulley (see dagra). Fnd: F = 80 N N a) he agntude o the acceleraton o the asses. [ /s ] F = 80 N F 0 N a / s 0 kg b) he tenson n the cord. [6 N] F a F 0 N a 0 N 0 N a 0 N (kg)( / s ) 6 N 8 kg kg 4. o asses, kg and 8 kg, are connected by a lght rope that passes over a rctonless pulley (see dagra). Fnd: a) he agntude o the acceleraton o the asses. [8 /s ] 8 kg F 80 N a 8 / s 0 kg b) he tenson n the cord. [6 N] F = 0 N N F a F 80 N a 80 N 80 N a 80 N (8 kg)(8 / s ) 6 N kg F = 0 N PHYSICS 534 DYNAMICS AnsPhyscs Ex-3.DOC Free Fall Part- / Page 7 /8

8 5. A 60 kg person stands on a sprng scale n an elevator. I the elevator s acceleratng upards at /s, hat s the readng on the balance? [70 N] F a But F F F a F 600 N (60 kg)( / s ) F 600 N 0 N 75 F 70 N F = F - F Balance readng PHYSICS 534 DYNAMICS AnsPhyscs Ex-3.DOC Free Fall Part- / Page 8 /8

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