5 Tusaalooyin su'aalo tamar wareeg ah
1. Shay wuxuu leeyahay daqiiqad firfircoon oo ah 1 kg m 2 oo ku wareegaysa dhidib go'an oo leh xawaare xagal ah oo ah 2 rad/s. Waa maxay tamarta dhaqdhaqaaqa wareega ee shayga?
Dood
Waa la ogyahay in:
Daqiiqad firfircooni ah (I) = 1 kg m2
Xawaaraha xagasha (ω) = 2 rad/s
La weydiiyay: Tamarta dhaqdhaqaaqa wareega (EK)
Jawaab:
Qaacidada tamarta dhaqdhaqaaqa wareega:
EK = 1/2 I ω2
Sharaxaad: EK = tamarta dhaqdhaqaaqa wareega (kg m2/s2), I = daqiiqadda firfircoonida (kg m2), ω = xawaare xagal (rad/s)
Tamarta dhaqdhaqaaqa wareega:
EK = 1/2 I ω2 = 1/2 (1)(2)2 = 1/2 (1)(4) = 2 Joule
2. Barkinta adag ee saxanka waxay leedahay cufnaan dhan 20 kg iyo gacan 0,2 mitir. Haddii barkintu ay ku wareegto dhidibkeeda xawaare xagal joogto ah oo ah 4 rad/ilbiriqsi, waa maxay tamarta dhaqdhaqaaqa wareega ee barkinta?
Dood
Waa la ogyahay in:
Cufka saxanka adag (m) = 20 kiilogaraam
Radius-ka khaanadaha adag ee saxanka (r) = 0,2 mitir
Xawaaraha xagasha (ω) = 4 radiyaan/ilbiriqsi
La weydiiyay: Waa maxay tamarta dhaqdhaqaaqa wareega ee shabagga?
Jawaab:
Qaacidada daqiiqadda firfircoonida ee saxanka adag haddii uu ku wareego dhidib sida ka muuqata sawirka:
I = 1/2 mr2
Sharaxaad: I = daqiiqadda firfircoonida (kg m2), m = cuf (kg), r = gacan (mitir)
Daqiiqadda firfircoonida saxanka adag:
I = 1/2 (20)(0,2)2 = (10)(0,04) = 0,4 kg m2
Tamarta dhaqdhaqaaqa wareega ee khaanadda:
EK = 1/2 I ω2 = 1/2 (0,4)(4)2 = (0,2)(16) = 3,2 Joules
3. Kubad adag oo miisaankeedu yahay 10 kg iyo gacan 0,1 mitir ayaa ku wareegta dhidibkeeda iyadoo xawaare xagal ah oo ah 10 rad/s. Go'aami tamarta dhaqdhaqaaqa wareega ee kubbadda adag!
Dood
Waa la ogyahay in:
Cufka kubad adag (m) = 10 kiilo garaam
Gacanka wareegsan adag (r) = 0,1 mitir
Xawaaraha xagasha (ω) = 10 radiyaan/ilbiriqsi
La weydiiyay: Tamarta dhaqdhaqaaqa jabaykubad adag
Jawaab:
Qaacidada daqiiqadda firfircoonida kubbadda adag haddii ay ku wareegto dhidib sida ku cad sawirka:
I = (2/5) mr2
Sharaxaad: I = daqiiqadda firfircoonida (kg m2), m = cuf (kg), r = gacan (mitir)
Daqiiqad firfircoon oo ah goob adag:
I = (2/5)(10)(0,1)2 = (4)(0,01) = 0,04 kg m2
Tamarta dhaqdhaqaaqa wareega ee goob adag:
EK = 1/2 I ω2 = 1/2 (0,04)(10)2 = (0,02)(100) = 2 Joules
4. Walax cufkeedu yahay 0,5 kiilo garaam ayaa ku socota goobaabin leh xawaare xagal joogto ah oo ah 2 rad/s. Go'aami tamarta dhaqdhaqaaqa wareega ee walaxda haddii gacanka wadada walaxda uu yahay 10 cm.
Dood
Waa la ogyahay in:
Cufka walxaha (m) = 0,5 kiilogaraam
Gacanka wareegsan adag (r) = 10 cm = 10/100 = 0,1 mitir
Xawaaraha xagasha (ω) = 2 radiyaan/ilbiriqsi
La weydiiyay: Tamarta dhaqdhaqaaqa wareega ee walxaha
Jawaab:
Qaacidada daqiiqadda firfircoonida ee walaxda:
Aniga = Mudane2 = (0,5)(0,1)2 = (0,5)(0,01) = 0,005 kg m2
Tamarta dhaqdhaqaaqa wareega ee walxaha:
EK = 1/2 I ω2 = 1/2 (0,005)(2)2 = 1/2 (0,005)(4) = (0,005)(2) = 0,01 Joules
5. Saxan silindaal adag oo isku mid ah ayaa marka hore ku wareegaya dhidibkiisa xawaare xagal ah oo ah 4 rad/s. Cufnaanta iyo gacanka saxanka waa 1 kg iyo 0,5 m. Haddii giraan cufkiisu yahay 0,2 kg iyo gacanka 0,1 m la dhigo saxanka, halkaas oo bartamaha giraantu ay si toos ah uga sarreyso bartamaha saxanka, markaa saxanka iyo giraantu waxay si wadajir ah u wareegi doonaan iyagoo wata tamar wareeg ah oo...
Dood
Waa la ogyahay in:
Cufka dhululubo adag (m1) = 1 kiilo garaam
Radius-ka dhululubo adag (r)1) = 0,5 mitir
Xawaaraha xagal ee dhululubo adag (ω)1) = 4 rad/s
Cufka giraanta (m)2) = 0,2 kiilo garaam
Gacanka giraanta (r)2) = 0,1 mitir
La weydiiyay: Tamarta dhaqdhaqaaqa wareega ee dhululubada iyo giraanta
Jawaab:
Marka hore xisaabi xawaaraha xagasha ee dhululubada iyo giraanta:
Daqiiqadda firfircoonida dhululubo adag: I = 1⁄2 m1 r12 = 1⁄2 (1)(0,5)2 = (0,5)(0,25) = 0,125 kg m2
Daqiiqadda firfircoonida giraanta: I = mr2 = (0,2)(0,1)2 = (0,2)(0,01) = 0,002 kg m2
Daqiiqadda firfircoonida dhululubo adag iyo giraan (I) = 0,125 + 0,002 = 0,127 kg m2
Xawaaraha xagasha bilowga (L)1) = Dhaqdhaqaaqa xagasha kama dambaysta ah (L2)
I1 ω1 = Aniga2 ω2
(0,125) (4) = (0,125 + 0,002) (ω2)
(0,5) = (0,127)(ω)2)
ω2 = 0,5: 0,127
ω2 = 4 rad/s
Xisaabi tamarta wareegga ee dhululubada iyo giraanta:
EK = 1/2 I ω2 = 1/2 (0,127)(4)2 = (0,127)(8) = 1,016 Joules
