2 Tusaalooyin su'aalo muraayado labajibbaaran oo isku laaban oo isku laaban
1. Laba muraayadood oo isku dheggan, mid walbana dhererkiisu yahay 20 cm iyo 30 cm, ayaa isku dhow, iyadoo masaafada u dhaxaysa labada muraayadood ee isku dheggan ay tahay 70 cm. Shay wuxuu 30 cm u jiraa muraayadda koowaad. Go'aami masaafada sawirka iyo weynaynta sawirka ay sameeyeen labada muraayadood. muraayad qaloocan dib!
Dood
Waa la ogyahay in:
Dhererka diiradda ee muraayadda qaloocan ee ugu horreysa (f)1) = +20 cm
Dhererka diiradda ee muraayadda labaad ee qaloocan (f)2) = +30 cm
Dhererka diiradda ee muraayadda qaloocan waa mid togan sababtoo ah iftiinka iftiinku wuxuu dhex maraa barta diiradda ee muraayadda qaloocan.
Masaafada u dhaxaysa labada muraayadood ee isku laaban (l) = 50 cm
Masaafada shayga laga bilaabo muraayadda ugu horreysa ee qaloocan (s)1) = 30cm
Masaafada shayga waa mid togan sababtoo ah iftiinka iftiinku wuxuu ka yimaadaa shayga.
Jawaab:
a) Masaafada hooska
Masaafada sawirka ee ay samaysay muraayadda ugu horreysa ee qaloocan (masaafada sawirka ugu horreysa):
1 / s1' = 1/f1 – 1/s1
1 / s1' = 1/20 – 1/30 = 3/60 – 2/60 = 1/60
s1' = 60/1 = 60 cm
Sawirka ugu horreeya wuxuu 60 cm u jiraa muraayadda qaloocan 1.
Masaafada sawirka koowaad waa mid togan, taasoo la macno ah in sawirka koowaad uu yahay mid dhab ah, taasoo la macno ah inuu runtii jiro sababtoo ah iftiinka iftiinku wuxuu dhex maraa sawirka.
Masaafada sawirka ee uu sameeyay muraayadda labaad ee qaloocan (masaafada sawirka kama dambaysta ah):
Sawirka ay samaysay muraayadda koowaad ee isku-xidhan waxaa loo arkaa shay iyadoo la adeegsanayo muraayadda labaad ee isku-xidhan. Masaafada sawirka/shayga koowaad u jiro muraayadda labaad ee isku-xidhan (s).2) = masaafada u dhaxaysa labada muraayadood ee isku laaban - masaafada sawirka koowaad laga bilaabo muraayadda isku laaban ee koowaad = 70 cm – 60 cm = 10 cm.
1 / s2' = 1/f2 – 1/s2
1 / s2'= 1/30 – 1/10 = 1/30 – 3/30 = -2/30
s2' = -30/2 = -15 cm
Sawirka kama dambaysta ah wuxuu 15 cm u jiraa muraayadda labaad ee qaloocan.
Masaafada sawirka kama dambaysta ah waa taban, taasoo la micno ah in sawirka kama dambaysta ah uu yahay been abuur ama been abuur sababtoo ah sawirka laguma gudbin karo iftiinka iftiinka (sawirka kama dambaysta ah wuxuu ku yaal bidixda muraayadda labaad ee qaloocan).
b) Weyneynta sawirka
Weyneynta sawirka iyadoo la adeegsanayo muraayadda ugu horreysa ee qaloocan:
m1 = -s1'/s1 = -60 cm/30 cm = -2 jeer
Muraayad qaloocan ayaa cabirka sawirka ka dhigaysa inuu 2 jeer ka weynaado cabbirka shayga.
Weyneynta sawirka oo leh calaamad taban waxay la macno tahay in sawirku rogmanayo.
Weyneynta sawirka iyadoo la adeegsanayo muraayadda labaad ee qaloocan:
m2 = -s2'/s2 = -(-15 cm)/10 cm = 15/10 = 1,5 jeer
Muraayadda labaad ee qaloocan waxay weyneysaa shayga (sawirka muraayadda qaloocan ee koowaad) iyadoo leh 1,5 dhibcood.
Wadarta weyneynta sawirka waa:
m = (m1)(m2) = (-2)(1,5) = -3 jeer
Cabbirka sawirka ugu dambeeya wuxuu 3 jeer ka weyn yahay cabbirka shayga ama dhererka sawirka ugu dambeeya wuxuu 3 jeer ka sarreeyaa dhererka shayga. Weynaynta guud waa taban taasoo la macno ah in sawirku rogmanayo. (sawirka kama dambaysta ah waa la rogay sidaa darteed sawirka kama dambaysta ah waa inuu ahaadaa bidixda muraayadda labaad ee qaloocan).
2. Masaafada u dhaxaysa laba muraayadood oo isku laaban waa 100 cm. Labada muraayadood ee isku laaban mid walba wuxuu leeyahay dherer diiradda saaraya oo ah 20 cm iyo 80 cm. Shay wuxuu 30 cm ka horreeyaa muraayadda koowaad. Go'aami masaafada sawirka iyo weynaynta sawirka ay sameeyeen labada muraayadood ee isku laaban!
Dood
Waa la garanayaa :
Masaafada u dhaxaysa labada muraayadood (l) = 100 cm
Dhererka diiradda ee muraayadda qaloocan ee ugu horreysa (f)1) = 20cm
Dhererka diiradda ee muraayadda labaad ee qaloocan (f)2) = 80cm
Dhererka diiradda ee muraayadda qaloocan waa mid togan sababtoo ah iftiinka iftiinku wuxuu dhex maraa barta diiradda ee muraayadda qaloocan.
Masaafada shayga laga bilaabo muraayadda ugu horreysa ee qaloocan (s)1) = 30cm
Masaafada shayga waa mid togan sababtoo ah iftiinka iftiinku wuxuu ka yimaadaa shayga.
Jawab :
a) Masaafada hooska
Masaafada sawirka ee ay samaysay muraayadda ugu horreysa ee qaloocan (masaafada sawirka ugu horreysa):
1 / s1' = 1/f1 – 1/s1
1 / s1' = 1/20 – 1/30 = 3/60 – 2/60 = 1/60
s1' = 60/1 = 60 cm
Sawirka ugu horreeya wuxuu 60 cm u jiraa muraayadda qaloocan 1.
Masaafada sawirka koowaad waa mid togan, taasoo la macno ah in sawirka koowaad uu yahay mid dhab ah, taasoo la macno ah inuu runtii jiro sababtoo ah iftiinka iftiinku wuxuu dhex maraa sawirka.
Masaafada sawirka ee uu sameeyay muraayadda labaad ee qaloocan (masaafada sawirka kama dambaysta ah):
Sawirka ay samaysay muraayadda koowaad ee isku-xidhan waxaa loo arkaa shay iyadoo la adeegsanayo muraayadda labaad ee isku-xidhan. Masaafada sawirka/shayga koowaad u jiro muraayadda labaad ee isku-xidhan (s).2) = masaafada u dhaxaysa labada muraayadood ee isku laaban - masaafada sawirka koowaad laga bilaabo muraayadda isku laaban ee koowaad = 100 cm – 60 cm = 40 cm.
1 / s2' = 1/f2 – 1/s2
1 / s2'= 1/80 – 1/40 = 1/80 – 2/80 = -1/80
s2' = -80/1 = -80 cm
Sawirka kama dambaysta ah wuxuu 80 cm u jiraa muraayadda labaad ee qaloocan.
Masaafada sawirka kama dambaysta ah waa taban, taasoo la micno ah in sawirka kama dambaysta ah uu yahay been abuur ama been abuur sababtoo ah sawirka laguma gudbin karo iftiinka iftiinka (sawirka kama dambaysta ah wuxuu ku yaal bidixda muraayadda labaad ee qaloocan).
b) Weyneynta sawirka
Weyneynta sawirka iyadoo la adeegsanayo muraayadda ugu horreysa ee qaloocan:
m1 = -s1'/s1 = -60 cm/30 cm = -2 jeer
Muraayad qaloocan ayaa cabirka sawirka ka dhigaysa inuu 2 jeer ka weynaado cabbirka shayga.
Weyneynta sawirka oo leh calaamad taban waxay la macno tahay in sawirku rogmanayo.
Weyneynta sawirka iyadoo la adeegsanayo muraayadda labaad ee qaloocan:
m2 = -s2'/s2 = -(-80 cm)/40 cm = 80/40 = 2 jeer
Muraayadda labaad ee qaloocan waxay weyneysaa shayga (sawirka muraayadda qaloocan ee koowaad) iyadoo leh 2 dhibcood.
Wadarta weyneynta sawirka waa:
m = (m1)(m2) = (-2)(2) = -4 jeer
Cabbirka sawirka ugu dambeeya wuxuu 4 jeer ka weyn yahay cabbirka shayga ama dhererka sawirka ugu dambeeya wuxuu 4 jeer ka sarreeyaa dhererka shayga. Weynaynta guud waa taban taasoo la macno ah in sawirku rogmanayo (sawirka kama dambaysta ah waa la rogay sidaa darteed sawirka kama dambaysta ah waa inuu ahaadaa bidixda muraayadda labaad ee qaloocan).
Su'aalo muraayado laba-laab ah oo isku-dhafan oo isku-dhafan
1. Laba muraayadood oo isku laaban oo mid walba leh dherer diiradda saaraya 40 cm iyo 20 cm ayaa la dhigayaa meel isku dhow halkaasoo masaafada u dhaxaysa labada muraayadood ee isku laaban ay tahay 100 cm. Go'aami masaafada sawirka iyo weynaynta guud ee sawirka ay sameeyeen labada muraayadood ee isku laaban oo ku yaal shay 120 cm ka horreeya muraayadda isku laaban ee koowaad!
Furaha jawaabta:
(a) masaafada sawirka ugu dambeysa = s2' = 40
(b) weyneynta guud ee sawirka = m = 0,5
2. Shay wuxuu 10 cm u jiraa bidixda muraayadda isku laaban oo dhererkeedu yahay 20 cm. Midigta muraayadda isku laaban waxaa ku yaal muraayad isku laaban oo dhererkeedu yahay 50 cm. Haddii masaafada u dhaxaysa labada muraayadood ay tahay 120 cm, go'aami masaafada sawirka iyo weynaynta sawirka ay sameeyeen labada muraayadood ee isku laaban!
Furaha jawaabta:
(a) masaafada sawirka ugu dambeysa = s2' = 133 cm
(b) weyneynta guud ee sawirka = m = -1,7 jeer. Taban macnaheedu waa in sawirku rogmaday.
