Physics Curseware Physics I Cnsan Accelerain Equains fr cnsan accelerain in dimensin x + a + a + ax + x Prblem.- In he 00-m race an ahlee acceleraes unifrmly frm res his p speed f 0m/s in he firs x5m as shwn in he figure. a) Find his accelerain in he firs 5m. b) Find he ime i akes cer hse firs 5 m. Sluin: a) The accelerain in hse firs 5m can be calculaed using: 0 0 + ax a, s: a 3.33m/s x (5) b) The ime i akes him run hse firs 5m: Since 5 0 + (3.33) 5 3.33 3 s x + a, we hae: Prblem.- If we culd neglec air resisance and her secndary effecs, hw lng wuld i ake fr a bulle fired sraigh up wih an iniial elciy f 350m/s hi he sher?
Sluin: We can use he equain: y y0 because he bulle cmes back he same place, s: 0 (350) + ( 9.8) 350 0 r 7 4.9 y + a y sle he prblem. Nice ha Prblem 3.- Yu dangle yur wach frm a hin piece f sring while he jeliner yu are in acceleraes fr akeff. Calculae he accelerain if he sring makes an angle f 35º wih respec he erical. Sluin: We learned in class ha he frce n a sring, cable, hin wire, hread r chain is alng he same direcin (i cann be sideways). Nw, n he wach here are w frces acing: is wn weigh and he sring frce. The wach is in equilibrium erically, s he weigh has cancel he erical cmpnen f he sring frce ecr: F sring cs 35 mg In he hriznal direcin here is nly ne frce, namely he hriznal cmpnen f he sring ensin and using Newn s secnd law: F sring sin 35 ma Diiding he secnd equain by he firs we ge: Fsring sin 35 ma sin 35 a a g an 35 F cs35 mg cs35 g sring -6.86m/s Prblem 4.- A rcke needs reach a speed f 8,000 m/s saring frm res. Assuming a cnsan accelerain f 5 m/s calculae: i) The ime i will ake reach ha elciy ii) The disance cered in ha ime Sluin: i) T find he ime we use he equain: + a 8000 8000 0 + 5 30 s 5 ii) T find he disance we can use he fac ha he aerage elciy is 4000 m/s and hen: x 4000 30,80,000 m
Prblem 5.- A plane n an aircraf carrier has nly m accelerae n ake-ff. Hw much mus be he accelerain (assumed cnsan) if i has reach 95 km/h saring frm res? Sluin: Firs le s calculae he final elciy in m/s: 95 000m 54.m/s km Nw we use his find he accelerain: 54. 0 + ax a m/s x Prblem 6.- A car raeling a 88 km/h srikes a ree. Thanks he sea bels, air bag and mdern design f he frn f he car, he drier is brugh res wih cnsan accelerain afer raeling. m. Wha was he drier s accelerain during he cllisin? 000m Sluin: 88 4.4 m/s km The final elciy is zer and he accelerain is: 0 (4.4m / s) a 7 m/s (.m ) Prblem 7.- A drier ging a 60 miles/hur (6.8m/s) sees a deer crssing he rad in frn f him and his he brakes when he is 60 m away. The cefficien f saic fricin is 0.75 (he car has ABS, s i desn slip). Is he deer safe? Sluin: We can calculae he disance ha he drier needs sp: Is iniial elciy is 6.8m/s and since µ K 0. 75 i means ha is accelerain will be -0.75(9.8m/s ) s he disance needed is: V V + ax 0 V + ax (6.8m/s) + ( 7.3m / s ) x x (6.8m/s) (7.3m / s ) 49. m Since his is less han he disance he deer, i ges lie anher day.
Prblem 8.- Calculae he disance cered by a mdel T car ha acceleraes frm zer is maximum speed f 45 mph in 5.0 secnds. [ mile609m] Sluin: Cnering 45 mph meers/secnd: 45miles 609m 0.m/s mile The aerage elciy is: + 0 + 0.m/s And he disance cered in 5s: x (0.05m/s)(5s) 5 m 0.05m/s Prblem 9.- A radser acceleraes frm zer 05 miles per hur in 6.0 secnds. Calculae he aerage accelerain in m/s. ( mile 609 m) Sluin: Firs, le s cner he final elciy m/s: mile 609m V 05 46.93 m/s mile The iniial elciy is zer, and s, he definiin f accelerain gies us: a V V 46.93m/s 0 6.0s 7.8 m/s Prblem 0.- A plane acceleraes alng a runway a 6.55m/s saring frm res. I needs reach 370 km/h fr ake-ff. Wha shuld be he minimum lengh f he runway fr a safe ake-ff? Sluin: If he plane sars frm res, 0 and he required elciy fr akeff is: 370 000m 0.8m/s km T ge he lengh f he runway we use he frmula (0.8m/s) (0.8m/s) (6.55m/s ) ( 0) + ( 6.55m/s ) x x + ax : 807 m
Prblem.- In cming a sp, a car leaes a 95m-lng skid mark alng he highway. Assuming an accelerain f -7.5 m/s, deermine he iniial elciy f he car jus befre he brakes were applied (yu can gie he answer in m/s). Sluin: In his prblem we knw he final elciy (V 0) he disance raeled (x95m) and he accelerain (a-7.5 m/s ). The easies way find he iniial elciy is using he equain: V V + ax Wih he infrmain f he prblem: (0) V + (-7.5m/s )(95m) V 45m We nly ake he psiie sluin in his case, which is: V 38 m/s /s Prblem.- The brakes f an 855-kg car apply a frce f -4880N. Calculae he disance needed sp he car if i is ging a 65 miles per hur. [ mile609 m] Sluin: The speed f he car in m/s is: mile 609m 65 9.m/s mile T sp he car he kineic energy is ally ls. The wrk dne by he frce will be equal he lss: m m 655kg(9.m/s) F m d d 7.5 m F F (3880N) Prblem 3.- Yu design he frn f a car s in he case f a cllisin a 55 km/h he passenger will experience a maximum f 0 g s f accelerain. Calculae hw much disance yu hae slw dwn he drier res wihu exceeding he maximum accelerain. [ g 9.8m/s ] Sluin: 000m 55 5.3m / s 3600 km + ax 0 5.3 + (0 9.8) x x 5.3 0.6 m 0 9.8