Izibonelo eziyi-10 zemibuzo yesikhathi samandla
1. Ubude benduku u-AB bungamamitha ama-2 kanti ubukhulu bamandla u-F bungama-Newton ayi-10. Thola umzuzu wesitayela ngasephuzwini A kanye nesiqondiso sokuzungeza kwenduku AB!
Ingxoxo
I-axis yokujikeleza itholakala endaweni A.
Kuyaziwa ukuthi:
Amandla (F) = 10 Newton
Ibanga AB (r)AB) = 2 amamitha
I-Force F yakha i-engeli engu-90o ngokumelene nenduku AB.
Ingalo yamandla (l) = rAB ngaphandle 90o = (amamitha ama-2)(1) = amamitha ama-2
Kubuziwe: Isikhathi samandla mayelana nephuzu A kanye nesiqondiso sokuzungeza kwenduku AB
Impendulo:
Isikhathi samandla:
τ = F l = (10 N)(2 m) = 20 amamitha e-Newton
Isikhathi samandla sihle ngoba amandla u-F abangela ukuthi induku ye-AB ijikeleze ngokuphambene newashi.
2. Ubude benduku AB bungamamitha ama-2 kanti ubukhulu bamandla F bungama-Newton ayi-10. Thola isikhathi samandla mayelana nephuzu A kanye nesiqondiso sokujikeleza kwenduku AB!
Ingxoxo
I-axis yokujikeleza i-
etholakala endaweni A.
Kuyaziwa ukuthi:
Amandla (F) = 10 Newton
Ibanga AB (r)AB) = 2 amamitha
I-Force F yakha i-engeli engu-60o ngokumelene nenduku AB.
Ingalo yamandla (l) = rAB ngaphandle 60o = (amamitha ama-2)(0,5√3) = √3 amamitha
Kubuziwe: I-Torsi iphuzu A kanye nesiqondiso sokujikeleza kwenduku AB
Impendulo:
Isikhathi samandla:
τ = F l = (10 N)(√3 m) = 10√3 amamitha e-Newton
Isikhathi samandla sihle ngoba amandla u-F abangela ukuthi induku ye-AB ijikeleze ngokuphambene newashi.
3. Ubude benduku u-AB bungamamitha ama-2, ubukhulu bamandla u-F bungu1 ingu-10 Newton kanye nobukhulu bamandla u-F2 amaNewton ayi-15. Thola umzuzu wamandla ophumela phakathi nendawo yenduku kanye nesiqondiso ukujikeleza induku AB!
Ingxoxo
I-axis yokujikeleza itholakala maphakathi nenduku.
Kuyaziwa ukuthi:
Isitayela 1 (F)1) = 10 Newton
Ibanga F1 kanye nesikhungo sesiqu (r1) = 1 amamitha
Isitayela F1 ukwakha i-engeli engu-90o ngokumelene nenduku AB
Isitayela sengalo 1 (l)1) =r1 ngaphandle 90o = (amamitha ama-1)(1) = amamitha ama-1
Isitayela 2 (F)2) = 15 Newton
Ibanga F2 kanye nesikhungo sesiqu (r2) = 1 amamitha
Isitayela F2 ukwakha i-engeli engu-90o ngokumelene nenduku AB
Isitayela sengalo 2 (l)2) =r2 ngaphandle 90o = (amamitha ama-1)(1) = amamitha ama-1
Kubuziwe: Umzuzu wamandla ophumelayo phakathi nendawo yenduku kanye nesiqondiso sokujikeleza kwenduku AB
Impendulo:
Isikhathi samandla 1:
τ1 =F1 l1 = (10 N)(1 m) = 10 amamitha e-Newton
Isikhathi samandla sihle ngoba amandla u-F abangela ukuthi induku ijikeleze ngokuphambene newashi.
Isikhathi samandla 2:
τ2 =F2 l2 = (15 N)(1 m) = -15 amamitha e-Newton
Isikhathi samandla asisihle ngoba amandla F2 okwenza induku ijikeleze ngokwewashi.
Umzuzu wamandla ophumela:
Στ = τ1 – τ2 = 10 – 15 = – 5 amamitha e-Newton
Umzuzu wamandla ophumelayo ungemuhle ngoba amandla aphumelayo u-F abangela ukuthi induku ye-AB ijikeleze ngokwewashi.
4. Ubude benduku u-AB bungamamitha ama-2, ubukhulu bamandla u-F bungu1 ingu-10 Newton kanye nobukhulu bamandla u-F2 yi-10 Newton. Thola umzuzu wamandla ophumela phakathi nendawo yenduku kanye nesiqondiso sokujikeleza kwenduku AB!
Ingxoxo
I-axis yokujikeleza itholakala maphakathi nenduku.
Kuyaziwa ukuthi:
Isitayela 1 (F)1) = 10 Newton
Ibanga F1 kanye nesikhungo sesiqu (r1) = 1 amamitha
Isitayela F1 ukwakha i-engeli engu-60o ngokumelene nenduku AB
Isitayela sengalo 1 (l)1) =r1 ngaphandle 60o = (amamitha angu-1)(0,5√3) = amamitha angu-0,5√3
Isitayela 2 (F)2) = 10 Newton
Ibanga F2 kanye nesikhungo sesiqu (r2) = 1 amamitha
Isitayela F2 ukwakha i-engeli engu-90o ngokumelene nenduku AB
Isitayela sengalo 2 (l)2) =r2 ngaphandle 90o = (amamitha ama-1)(1) = amamitha ama-1
Kubuziwe: Umzuzu wamandla ophumelayo phakathi nendawo yenduku kanye nesiqondiso sokujikeleza kwenduku AB
Impendulo:
Isikhathi samandla 1:
τ1 =F1 l1 = (10 N)(0,5√3 m) = 5√3 = 8,7 amamitha e-Newton
Isikhathi samandla sihle ngoba amandla F1 abangela ukuthi induku ijikeleze ngokuphambene newashi.
Isikhathi samandla 2:
τ2 =F2 l2 = (10 N)(1 m) = -10 amamitha e-Newton
Isikhathi samandla asisihle ngoba amandla F2 okwenza induku ijikeleze ngokwewashi.
Umzuzu wamandla ophumela:
Στ = τ1 – τ2 = 8,7 – 10 = – 1,3 amamitha e-Newton
Umzuzu wamandla ophumelayo ungemuhle ngoba amandla aphumelayo u-F abangela ukuthi induku ye-AB ijikeleze ngokwewashi.
5. Ubude benduku u-AB bungamamitha ama-10, ubukhulu bamandla u-F bungu1 ingu-10 Newton, ubukhulu bamandla F2 ingu-10 Newton kanye nobukhulu bamandla u-F3 AmaNewton ayi-15. Ibanga eliphakathi kwephuzu A nephuzu C lingamamitha angu-7,5. Amandla F2 itholakala phakathi kwenduku AB. Thola umzuzu wamandla ophumela endaweni C engamamitha angu-2,5 ukusuka endaweni B! Futhi thola indlela yokujikeleza kwenduku AB.
Ingxoxo
I-axis yokujikeleza itholakala endaweni C engamamitha angu-2,5 ukusuka endaweni B.
Kuyaziwa ukuthi:
Isitayela 1 (F)1) = 10 Newton
Ibanga F1 kanye nephuzu C (r1) = 2,5 amamitha
Isitayela F1 ukwakha i-engeli engu-90o ngokumelene nenduku AB
Isitayela sengalo 1 (l)1) =r1 ngaphandle 90o = (amamitha ama-2,5)(1) = amamitha ama-2,5
Isitayela 2 (F)2) = 10 Newton
Ibanga F2 kanye nephuzu C (r2) = 2,5 amamitha
Isitayela F2 ukwakha i-engeli engu-90o ngokumelene nenduku AB
Isitayela sengalo 2 (l)2) =r2 ngaphandle 90o = (amamitha ama-2,5)(1) = amamitha ama-2,5
Isitayela 3 (F)3) = 15 Newton
Ibanga F3 kanye nephuzu C (r3) = 7,5 amamitha
Isitayela F3 ukwakha i-engeli engu-90o ngokumelene nenduku AB
Isitayela sengalo 3 (l)3) =r3 ngaphandle 90o = (amamitha ama-7,5)(1) = amamitha ama-7,5
Kubuziwe: Umzuzu ophumela wamandla mayelana nephuzu C kanye nesiqondiso sokujikeleza kwenduku AB.
Impendulo:
Isikhathi samandla 1:
τ1 =F1 l1 = (10 N)(2,5 m) = 25 amamitha e-Newton
Isikhathi samandla sihle ngoba amandla F1 okwenza induku ijikeleze ngokuphambene newashi.
Isikhathi samandla 2:
τ2 =F2 l2 = (10 N)(2,5 m) = 25 amamitha e-Newton
Isikhathi samandla sihle ngoba amandla F2 okwenza induku ijikeleze ngokuphambene newashi.
Isikhathi samandla 3:
τ3 =F3 l3 = (15 N)(7,5 m) = -112,5 amamitha e-Newton
Isikhathi samandla asisihle ngoba amandla F3 okwenza induku ijikeleze ngokwewashi.
Umzuzu wamandla ophumela:
Στ = τ1 + τ2 – τ3 = 25 + 25 – 112,5 = – 62,5 amamitha e-Newton
Umzuzu wamandla ophumelayo ungemuhle ngoba amandla aphumelayo u-F abangela ukuthi induku ye-AB ijikeleze ngokwewashi.
6. Ubude benduku u-AB bungamamitha ama-10, ubukhulu bamandla u-F bungu1 ingu-10 Newton, ubukhulu bamandla F2 ingu-10 Newton kanye nobukhulu bamandla u-F3 yi-10 Newtons. Thola umzuzu wamandla ophumela endaweni A engamamitha ama-5 ukusuka endaweni yokushaya kwamandla F.1Futhi nquma indlela yokujikeleza kwenduku i-AB.
Ingxoxo
I-axis yokujikeleza itholakala endaweni A.
Kuyaziwa ukuthi:
Isitayela 1 (F)1) = 10 Newton
Ibanga F1 kanye nephuzu A (r)1) = 5 amamitha
Isitayela F1 ukwakha i-engeli engu-60o ngokumelene nenduku AB
Isitayela sengalo 1 (l)1) =r1 ngaphandle 60o = (amamitha angu-5)(0,5√3) = amamitha angu-2,5√3
Isitayela 2 (F)2) = 10 Newton
Ibanga F2 kanye nephuzu A (r)2= = 0
Isitayela F2 ukwakha i-engeli engu-90o ngokumelene nenduku AB
Isitayela sengalo 2 (l)2) =r2 ngaphandle 90o = (0)(1) = 0
Isitayela 3 (F)3) = 10 Newton
Ibanga F3 kanye nephuzu A (r)3) = 10 amamitha
Isitayela F3 ukwakha i-engeli engu-30o ngokumelene nenduku AB
Isitayela sengalo 3 (l)3) =r3 ngaphandle 30o = (amamitha ama-10)(0,5) = amamitha ama-5
Kubuziwe: Umzuzu ophumela wamandla mayelana nephuzu A kanye nesiqondiso sokujikeleza kwenduku AB.
Impendulo:
Isikhathi samandla 1:
τ1 =F1 l1 = (10 N)(2,5√3 m) = 25√3 = 43,3 amamitha e-Newton
Isikhathi samandla sihle ngoba amandla F1 abangela ukuthi induku ijikeleze ngokuphambene newashi.
Isikhathi samandla 2:
τ2 =F2 l2 = (10 N)(0) = 0
Isikhathi samandla singu-zero ngoba amandla u-F2 kuhambisana ne-axis yokujikeleza
Isikhathi samandla 3:
τ3 =F3 l3 = (10 N)(5 m) = -50 amamitha e-Newton
Isikhathi samandla asisihle ngoba amandla F3 okwenza induku ijikeleze ngokwewashi.
Umzuzu wamandla ophumela:
Στ = τ1 + τ2 – τ3 = 43,3 + 0 – 50 = – 6,7 amamitha e-Newton
Umzuzu wamandla ophumelayo ungemuhle ngoba amandla aphumelayo u-F abangela ukuthi induku ye-AB ijikeleze ngokwewashi.
7. Amandla amathathu F1, F2, kanye no-F3 isebenza endukwini njengoba kuboniswe esithombeni esilandelayo. Uma isisindo senduku singanakwa futhi ubude benduku bungamamitha angu-4, khona-ke inani lesikhathi samandla mayelana ne-axis yokujikeleza endaweni C lingu…. (isono 53o = 0,8, cos 53o = 0,6, AB = BC = CD = DE = imitha elingu-1)
A. 12 Nm
B. 8 Nm
C. 6 Nm
D. 2 Nm
E. Zero
Ingxoxo
Kuyaziwa ukuthi:
I-axis yokujikeleza isendaweni C.
Isitayela 1 (F)1) = 5 Newton
Ibanga phakathi kwamaphuzu okusebenza F1 nge-axis yokujikeleza (r1) = 2 amamitha
Isitayela 2 (F)2) = 0,4 Newton
Ibanga eliphakathi kwephuzu lokusebenza F2 kanye ne-axis yokujikeleza (r2) = 1 amamitha
Isitayela 3 (F)3) = 4,8 Newton
Ibanga phakathi kwamaphuzu okusebenza F3 nge-axis yokujikeleza (r3) = 2 amamitha
Umbuzo: Inani lesikhathi samandla mayelana ne-axis yokujikeleza endaweni C
Impendulo:
Isikhathi Samandla 1:
Umzuzu wamandla 1 ubangela ukuthi induku ijikeleze ngokuphambene newashi ukuze lowo mzuzu wamandla 1 ube nophawu oluhle.
Isikhathi Samandla 2:
Umzuzu wamandla 2 ubangela ukuthi induku ijikeleze ngendlela ejikelezayo ngokwewashi ukuze lowo mzuzu wamandla 2 ube nophawu olubi.
Isikhathi Samandla 3:
Umzuzu wamandla 3 ubangela ukuthi induku ijikeleze ngendlela ejikelezayo ngokwewashi ukuze lowo mzuzu wamandla 3 ube nophawu olubi.
Umzuzu wamandla ophumela:
Ubukhulu besikhathi samandla bungama-2 Newton metres. Isikhathi samandla esingesihle sisho ukuthi induku ijikeleza ngokuphambene newashi.
Impendulo efanele ngu-D.
8. Ubukhulu bomzuzu wamandla ophumela ku-axis endaweni ethi O ngamandla asebenza entongeni uma isisindo sayo singanakwa….
A. 7,5 Nm
B. 4 Nm
C. 3,5 Nm
D. 3 Nm
E. 2 Nm
Ingxoxo
Kuyaziwa ukuthi:
I-axis yokujikeleza isendaweni ethi O.
Isitayela 1 (F)1) = 6 Newton
Ibanga phakathi kwamaphuzu okusebenza F1 nge-axis yokujikeleza (r1) = 1 amamitha
Isitayela 2 (F)2) = 6 Newton
Ibanga eliphakathi kwephuzu lokusebenza F2 kanye ne-axis yokujikeleza (r2) = 2 amamitha
Isitayela 3 (F)3) = 4 Newton
Ibanga phakathi kwamaphuzu okusebenza F3 nge-axis yokujikeleza (r3) = 2 amamitha
Umbuzo: Inani lesikhathi samandla mayelana ne-axis yokujikeleza endaweni C
Impendulo:
Isikhathi Samandla 1:
Umzuzu wamandla 1 ubangela ukuthi induku ijikeleze ngokuphambene newashi ukuze lowo mzuzu wamandla 1 ube nophawu oluhle.
Isikhathi Samandla 2:
Umzuzu wamandla 2 ubangela ukuthi induku ijikeleze ngokuphambene newashi ukuze lowo mzuzu wamandla 2 ube nophawu oluhle.
Isikhathi Samandla 3:
Umzuzu wamandla 3 ubangela ukuthi induku ijikeleze ngendlela ejikelezayo ngokwewashi ukuze lowo mzuzu wamandla 3 ube nophawu olubi.
Umzuzu wamandla ophumela:
Ubukhulu besikhathi samandla bungama-4 Newton metres. Isikhathi esihle samandla sisho ukuthi induku ijikeleza ngokuphambene newashi.
Impendulo efanele ingu-B.
9. Induku ingamamitha angu-8 ubude. Amandla amathathu asebenza endukuni, njengoba kuboniswe esithombeni esingezansi. Ubukhulu besikhathi samandla esibangela ukuba induku ijikeleze phakathi nendawo yayo…
A. 10 N m
B. 20 N m
C. 30 N m
D. 40 N m
E. 50 N m
Ingxoxo:
Isikhungo senduku sitholakala phakathi nendawo. Induku ingamamitha angu-8 ubude, ngakho-ke isikhungo senduku singamamitha angu-4 ukusuka ekugcineni kwenduku.
Isikhathi Samandla 1 = F1 l1 = (10 N)(4 m) = 40 N m
I-Moment of Force 1 inenani elihle ngoba i-Moment of Force 1 ibangela ukuthi induku ijikeleze ngokuphambene newashi.
Isikhathi Samandla 2 = F2 l2 = (10 N)(2 m) = – 20 N m
I-Moment of Force 2 inenani elibi ngoba i-Moment of Force 2 ibangela ukuthi induku ijikeleze ngendlela yewashi.
Isikhathi Samandla 3 = F3 l3 = (15 N)(2 m) = – 30 N m
I-Moment of Force 3 inenani elibi ngoba i-Moment of Force 3 ibangela ukuthi induku ijikeleze ngendlela yewashi.
Amandla Aphumelayo Isikhathi = 40 N m – 20 N m – 30 N m = – 10 N m
Umzuzu wamandla noma i-torque ephumelayo inenani elibi, lokhu kubonisa ukuthi isiqondiso sokujikeleza kwenduku sihamba ngokwewashi.
Impendulo efanele ngu-A.
10. Amandla F1 = 10 N, F2 = 15 N, F3 = 15 N kanye no-F4 = 10 N, isebenza endukwini i-ABCD njengoba kuboniswe esithombeni. Ubude benduni i-ABCD bungamamitha angu-20. Uma isisindo senduni singanakwa khona-ke inani lesikhathi samandla mayelana nephuzu D...
A. 15 Nm
B. 18 Nm
C. 35 Nm
D. 63 Nm
E. 68 Nm
Ingxoxo:
Inhloso yalo mbuzo ukuthola inani lomzuzu wamandla ophumelayo obangela ukuba induku ijikeleze, lapho isikhungo sokujikeleza sitholakala khona endaweni D.
Isikhathi Samandla 1 = F1 l1 = (10 N)(15 m) = 150 N m
I-Moment of Force 1 inenani elihle ngoba i-Moment of Force 1 ibangela ukuthi induku ijikeleze ngokuphambene newashi.
Isikhathi Samandla 2 = F2 l2 = (15 N)(5 m) = -75 N m
I-Moment of Force 2 inenani elibi ngoba i-Moment of Force 2 ibangela ukuthi induku ijikeleze ngendlela efanayo nokujikeleza kwewashi.
Isikhathi Samandla 3 = F3 l3 = (15 N)(0 m) = 0 N m
Isikhathi Samandla 3 singu-zero ngoba u-F3 kuhambisana ne-axis yokujikeleza.
Isikhathi Samandla 4 = F4 l4 = (10 N)(5 m) = 50 N m
I-Moment of Force 4 inenani elihle ngoba i-Moment of Force 4 ibangela ukuthi induku ijikeleze ngokuphambene newashi.
Amandla Aphumelayo Isikhathi = 150 N m – 75 N m + 50 N m = 125 N m
Umzuzu wamandla noma i-torque ephumelayo inenani elihle, ngakho-ke isiqondiso sokujikeleza kwenduku siphambene nesiqondiso sokujikeleza kwezandla zewashi.
