5 Kuyenda kwa Parabolic Ntchito ndi mphamvu ya kinetic Kuyenda kwa mzere Kuyenda kwa mzere ndi mzere Mavuto ndi Mayankho
1. Mpira umaponyedwa kuchokera pamwamba pa nyumba ndi liwiro loyamba la 8 m/s pa ngodya ya 20 o pansi pa yopingasa. Mpirawo umagunda pansi patatha masekondi atatu.
a) Kodi mpirawo umakhudza pansi pa nyumbayo patali bwanji?
b) Kodi mpira waponyedwa kuchokera pamalopo uli pamwamba bwanji?
c) Kutalika kwa mpira kufika pa mtunda wa mamita 10 kuchokera pamalo oponyera mpirawo
vox =vo 20o = 8 (0.939) = 7.512 m/s
v oy = v o tchimo 20 o = 8 (0.342) = 2.736 m/s
a) x
Kusuntha kopingasa kumafufuzidwa ngati kuyenda kofanana kolunjika, kotero kuti njira yogwiritsira ntchito kuyenda kofanana kolunjika imagwiritsidwa ntchito.
x = v ox t
x = (7.512 m/s)(masekondi 3)
x = 22.536 m
b) y
Kusuntha kwa njira yolunjika kumasanthulidwa ngati kuyenda kwa kugwa kwaulere pogwiritsa ntchito njira yoyendetsera kuyenda kwa kugwa kwaulere.
Gwiritsani ntchito fomula iyi y = vot + ½ gt 2
Mu kayendedwe ka kugwa kwaulere, v o = 0 kotero fomula imakhala: y = ½ gt 2
y = ½ (9.8)(3 2 )
y = (4.9)(9)
y = 44 m
c) y = 10 m
Gwiritsani ntchito fomula y = ½ gt 2
10 = ½ (9,8) t 2
10 = 4.9 t 2
t 2 = 10 / 4.9
t 2 = 2
t = 1.4 s
2. Gulu la sitima ya agalu limakoka katundu wolemera makilogalamu 100 mpaka 2 km pamwamba pa malo opingasa pa liwiro losasintha. Ngati coefficient of friction pakati pa sitima ndi chipale chofewa ndi 0.15, dziwani izi:
a) ntchito yochitidwa ndi galu
Yerengani kukangana kwa kayendedwe ka kayendedwe kake:
F k = µ k N = µ k w = µ k mg = (0.15) (100 kg) (9.8 m/s 2 ) =147 N
Liwiro la kulemera silisintha, kotero, malinga ndi lamulo la Newton, mphamvu yochokerapo = 0. Kotero F k = F = 147 N
Ntchito yomwe galu wachita:
W = F d = (147 N)(2000 m) = 294,000 J
b) Mphamvu yotayika chifukwa cha kukangana
Mphamvu zomwe zimatayika chifukwa cha kukangana:
Ntchito = mphamvu, kotero:
W = F k d = (147 N)(2000 m) = 294,000 J
3. Mphamvu yopingasa ya 150 N imagwiritsidwa ntchito kukankhira bokosilo mamita 6 pamwamba pa malo ozungulira. Ngati bokosilo likuyenda pa liwiro losasintha:
a) Ntchito yochitidwa ndi mphamvu ya 150 N
W = F d = (150 N) (6 m) = 900 J
b) Kutayika kwa mphamvu chifukwa cha kukangana
Bokosi limayenda pa liwiro losasintha kotero kuti mphamvu yochokera pa bokosilo = 0.
Kotero, mphamvu yopingasa = 150 N = kukangana kwa kinetic.
Mphamvu yotayika chifukwa cha kukangana:
W = F k = (150 N)(6 m) = 900 J
c) Chiwerengero cha kupsinjika kwa kinetic
Fomula ya mphamvu yokangana:
F k = µ k N = µ k w = µ k mg
150 = µ km m (10)
15 = µ km m
µ k = 15/m
m = kulemera kwa bokosi
µ k = coefficient ya kukangana kwa kinetic
Kukangana kwa kinetic kumagwira ntchito pamene zinthu zikuyenda, kukangana kosasinthasintha kumagwira ntchito pamene zinthu zikadali zoyima.
4. Tinthu tating'onoting'ono timakhala ndi liwiro (3i-4h) m/s. Dziwani gawo la momentum pa x ndi y-axis ndi kukula kwa momentum.
Liwiro pa x-axis: 3 m/s
Liwiro pa y-axis: 4 m/s
Mphamvu pa x-axis: mv = 3 m
mphamvu pa y-axis: mv = 4 m
Kukula kwa mphamvu:
p 2 = (3 m) 2 + (4 m) 2
p 2 = 9 m 2 + 16 m 2
p 2 = 25 m 2
p = 5 m
p ndi chizindikiro cha mzere wolunjika.
5. Galimoto imathamanga mofanana kuchokera pa liwiro losasuntha mpaka 22 m/s kwa masekondi 9. Ngati kukula kwa tayala ndi 58 cm, tchulani:
a) chiwerengero cha matayala ozungulira panthawi yoyenda (osatengeka)
Kuwerengera kuthamanga kwa galimoto:
v t = vo + pa
22 = 0 + a 9
22 = 9a
a = 22/9 = 2.44
Werengerani mtunda:
d = vot + ½ pa 2 = 0 + ½ pa 2
d = ½ pa 2 = ½ (2.44)(9 2 ) = (1.22)(81) = 98.82 m
Mtunda wa galimoto = 98.82 mamita = 9882 cm
M'mimba mwake wa tayala = 58 cm
Chiwerengero cha ma revolutions = 9882 cm / 58 cm = 170.38 rev
b) Liwiro lomaliza la tayala lozungulira mu rev/minute
Liwiro lomaliza = mamita 22/sekondi = 2200 cm/ sekondi
1 rev = 1 diameter ya tayala = 58 cm
Chiwerengero cha ma revolutions:
2200 cm / 58 cm = ma revolution 40
Kotero, liwiro lomaliza mu revolution/minute
40 rev/sekondi = 40 rev / masekondi 60 = 0.67 rev/mphindi kapena 0.67 rev/mphindi
