Mehlala e 11 ea Mathata a ho Tsamaea ka Tsela e Tšoanang
1. Phatsa e tsamaya ka sedikadikwe ka lebelo le sa fetoheng la di-rad/s tse 10. Fumana (a) lebelo le sa fetoheng la phatsa kamora metsotsoana e 10 (b) sekhutlo se laolwang ke phatsa kamora metsotsoana e 10.
Puisano
(a) lebelo la angular kamora metsotsoana e 10
Karolwana e tsamaya ka sedikadikwe se tshwanang = karolwana e tsamaya ka lebelo le sa fetoheng la angular. Kahoo lebelo la angular kamora metsotsoana e 10 le dula le le 10 radians/motsotswana.
(b) sekhutlo se koetsoeng ka mora metsotsoana e 10
Lebelo le sa fetoheng la di-radian tse 10/motsotswana le bolela hore motsotsoana o mong le o mong, karoloana e potoloha sekhutlo sa di-radian tse 10. Kamora metsotsoana e 2, karoloana e se e potoloha sekhutlo sa di-radian tse 2 x 10 = di-radian tse 20. Kamora metsotsoana e 10, karoloana e se e potoloha sekhutlo sa di-radian tse 10 x 10 = di-radian tse 100.
2. Ntlha e ka lehlakoreng la silindara e tsamaya ka sedikadikwe ka lebelo le sa fetoheng la 10 m/s. Radius ya silindara = mithara e le 1. Fumana (a) lebelo la lehlakore la silindara metsotswana e 5 hamorao (b) sebaka se tsamailweng ke lehlakore la silindara metsotswana e 5 hamorao (c) lebelo la bohareng ba dintlha tse dimithara tse 0,5 le mithara e le 1 ho tloha mothating wa potoloho.
Puisano
(A) lebelo la ntlha moeling oa silindara kamora metsotsoana e 5
Silindara e tsamaya ka selikalikoe ka lebelo le sa fetoheng, ka hona, metsotsoana e 5 hamorao, lebelo la lehlakore la silindara le sala le le limithara tse 10 ka motsotsoana.
(B) sebaka se tsamailoeng ka ntlha e itseng moeling oa silindara kamora metsotsoana e 5
Ntle le foromo
Lebelo la limithara tse 10 ka motsotsoana le bolela hore motsotsoana o mong le o mong, ntlha e lebopong la silindara e tsamaea limithara tse 10. Kamora motsotsoana o le mong, ntlha e lebopong la silindara e tsamaea limithara tse 10. Kamora metsotsoana e 2, ntlha e lebopong la silindara e tsamaea limithara tse 20. Kamora metsotsoana e 5, ntlha e lebopong la silindara e tsamaea ka selikalikoe limithara tse 50.
Ho sebelisa foromo :
v = s / t
s = vt = (10)(5) = limithara tse 50
(C) ho potlaka ha bohareng ba pelo (as)
Ho potlaka ha ntlha e bohareng ba mithara e le 0,5 ho tloha mothating ke:
as = v2 / r = 102 / 0,5 = 100 / 0,5 = 200 m/s2
Ho potlaka ha ntlha e bohareng ba mithara e le 1 ho tloha mothating ke:
as = v2 / r = 102 / 0,5 = 100 / 1 = 100 m/s2
3. Tafole e nang le radius ea limithara tse 2 e tsamaea ka lebelo le sa fetoheng la angular la 60 rpm. Fumana (a) lebelo le katolohileng la tafole e katolositsoeng metsotsoana e 2 hamorao (b) sekhutlo se koetsoeng ke tafole e katolositsoeng kamora motsotso o le mong (b) lebelo le katolositsoeng, lebelo le katolositsoeng le sebaka se tsamailoeng ka ntlha e le 'ngoe ea mithara ho tloha mothating oa potoloho (c) lebelo le katolositsoeng, lebelo le katolositsoeng le sebaka se tsamailoeng ka ntlha e le 'ngoe moeling oa tafole e katolositsoeng.
Puisano
Hoa tsebahala :
Jawab :
(A) Lebelo la angular ( ) kamora metsotsoana e 2
Lebelo la angular ha le fetohe ka hona, kamora metsotsoana e 2, lebelo la angular la turntable le sala e le 6,28 radians/motsotsoana.
(B) sekhutlo ( ) e pota-potiloe ke turntable ka mor'a motsotso o le mong
Lebelo le potolohang la 1 phetohelo/motsotswana le bolela hore motsotsoana o mong le o mong turntable e etsa potoloho e le 'ngoe. Kamora metsotsoana e 60, turntable e entse lipotoloho tse 60. Kapa, ho e beha ka tsela e 'ngoe,
Lebelo le potolohang la di-radian tse 6,28 ka motsotsoana le bolela hore motsotsoana o mong le o mong turntable e potoloha sekhutlo sa di-radian tse 6,28. Kamora metsotsoana e 60, turntable e se e potoloha sekhutlo sa di-radian tse 376,8.
4. Lebili la koloi le lula le etsa lipotoloho tse 120 metsotsoana e meng le e meng e 60. Lebelo le nang le sebopeho se sekhutlo ke lefe? Le hlalose ka: (a) liphetohelo ka motsotso (rpm) kapa diphetoho ka motsotso (b) di-degree ka motsotsoana (o/s) (c) radians ka motsotsoana (rad/s)
Puisano
(A) lebelo la angular la lebili ka diyuniti tsa diphetoho ka motsotso (rpm)
Liphetoho tse 120 / metsotsoana e 60 = liphetoho tse 120 / motsotso o le 1 = liphetoho tse 120 / motsotso = 120 rpm
(B) Lebelo la angular la lebili ka di-degrees / motsotsoana (o/ s)
Potoloho e le 'ngoe = 360o, diphetoho tse 120 = 43200o
Kahoo diphetoho tse 120 / metsotsoana e 60 = (120)(360o) / metsotsoana e 60 = 43200o / Metsotsoana e 60 = 720o/motsotsoana
(C) Lebelo la angular la lebili ka radians/second (rad/s)
Potoloho e le 'ngoe = li-radian tse 6,28
Kahoo diphetoho tse 120 / metsotsoana e 60 = (120)(6,28) di-radian / metsotsoana e 60 = di-radian tse 753,6 / metsotsoana e 60 = di-radian tse 12,56/motsotswana
5. 'Mabole o otloa ka sekotlolong se chitja se bophara ba 1 m. Haeba 'mabole o potoloha moeling oa sekotlolo ka lebelo le sa fetoheng la 50 rpm, joale lebelo le otlolohileng le ho potlaka ha 'mabole bohareng ke….
A. 50 ms-1 le 2500 ms-2
B. 5π ms-1 le 25π2 Mof.-2
C. 5π/3 ms-1 le 25π2/18 ms-2
D. 5π/6 ms-1 le 25π2/18 ms-2
E. 5π/12 ms-1 le 25π2/36 ms-2
Puisano
Hoa tsebahala hore:
Bophara ba selikalikoe (D) = 1 mithara
Radius ea selikalikoe (r) = limithara tse 0,5
Lebelo la Angular (ω) = 50 rpm = diphetoho tse 50 / motsotso o le 1
Phetoho e le 'ngoe = 2π radians
Diphetoho tse 50 = 50 (2π radians) = 100π radians
Motsotso o le 1 = metsotsoana e 60
Lebelo la Angular (ω) = 100π radians / metsotsoana e 60 = (10π/6) radians/motsotswana
Potso: Lebelo la mola (v) le ho potlaka ha centripetal (a)s)
Karabo:
Lebelo le otlolohileng (v):
v = r ω = (0,5) (10π/6) = 5π/6 m/s
Ho potlaka ha centripetal (a)s):
as = v2/r = (5π/6)2 : 0,5 = 25π2/36 : 0,5 = (25π2/36)(1/0,5)
as = (25π2/18) m/s2
Karabo e nepahetseng ke D.
6. Ntho e tsamaya ka sedikadikwe se nang le radius ya 50 cm. Haeba ntho e potoloha ka 120 rpm, nako ya ho potoloha le lebelo la ntho ke ka ho latellana….
A. 0,5 s le 2π ms-1
B. 0,5 s le 0,2π ms-1
C. 0,5 s le π ms-1
D. 2 s le 5π ms-1
E. 2 s le 10π ms-1
Puisano
Hoa tsebahala hore:
Radius (r) = 50 cm = 0,5 metres
Lebelo la Angular (ω) = 120 rpm = diphetoho tse 120 / motsotso o 1 = diphetoho tse 120 / metsotso e 60 = diphetoho tse 2 / motsotso o 1
Phetoho e le 'ngoe = 2π radians
Lebelo la Angular (ω) = 2 (2π radians) / 1 motsotswana = 4π radians/motsotswana
Potso: Nako ea ho potoloha (T) le lebelo le otlolohileng (v)
Karabo:
Nako kapa nako ea potoloho (T):
Nako ke nako eo ntho e nkang ho phethela potoloho e le 'ngoe.
Ntho e etsa diphetoho tse 2 ka motsotsoana o le mong = ntho e etsa phetoho e le nngwe ka metsotswana e 0,5. Kahoo nako kapa nako ya ho potoloha ke metsotswana e 0,5.
Lebelo la ntho (v):
v = r ω = (limithara tse 0,5)(4π radians/motsotswana) = 2π limithara/motsotswana
Karabo e nepahetseng ke A.
Ithute boitsebiso bo mabapi le motsamao o chitja le motsamao o chitja o tloaelehileng ho utloisisa hamolemo puisano ea potso ena.
7. Lebili le nang le radius ea 10 cm le potoloha ka ho lekana, le phethela lipotoloho tse 180 ka motsotso. Lebelo le otlolohileng la ntlha e ka lehlakoreng la lebili ke…
Puisano
Hoa tsebahala hore:
O botsitse:
Lebelo la mola (v) ?
Karabo:
Ntlha e ka lehlakoreng la lebili e bohōle ba limithara tse 0,1 ho tloha bohareng ba lebili.
Karabo e nepahetseng ke A.
8. Ntho e tsamaya ka lebelo le sa fetoheng v tseleng e chitja ka radius R e nang le potlakiso e bohareng (as). E le hore ho potlakisa ha centripetal ho be hararo ho feta ha pele ka nako eo...
A. v e etsoa ka makhetlo a 4 mme R e etsoa ka makhetlo a 2 hape
B. v e etsoa ka makhetlo a 2 mme R e etsoa ka makhetlo a 4 hape
C. v e etsoa ka makhetlo a 3 mme R e etsoa ka makhetlo a 3 hape
D. v e sala mme R e imenne habeli hape
E. v e imenne habeli hape mme R e sala
Puisano
Karabo e nepahetseng ke C.
9. Mabili a A, B le C a hokahane jwalo ka ha ho bontshitswe setshwantshong. Haeba radii ya mabili a A, B le C e le 10 cm, 4 cm le 2 cm ka ho latellana, mme lebili la B le potoloha ka lebelo la di-rad.s tse 5-1 ebe lebili la C le potoloha ka lebelo le potolohang la….
A. 80 rad.s-1
B. 55 rad.s-1
C. 40 rad.s-1
D. 25 rad.s-1
E. 10 rad.s-1
Puisano
Hoa tsebahala hore:
Karabo:
Kamano pakeng tsa lebili la A le lebili la B
Mabili a A le a B a hokahane, kahoo a potoloha hammoho. Hobane a potoloha hammoho, lebelo la angular la lebili A = lebelo la angular la lebili B.
Kamano pakeng tsa lebili la A le lebili la C
Selikalikoe sa lebili A se seholo haholo ho feta selikalikoe sa lebili C. Haeba lebili C le nkile sekhutlo sa 360o kapa o etsa potoloho e le 'ngoe, ka nako e le 'ngoe, lebili la A ha lea fihla ho 360o kapa ho potoloha hanngoe. Kahoo, lebelo la angular la lebili A ha le tšoane le lebelo la angular la lebili C.
Leha ho le jwalo, mabili a A le C a hokahantswe ka thapo. Hobane a hokahantswe ka thapo, nakong e tshwanang ya nako, sebaka se tsamauwang ke lehlakore la lebili A = sebaka se tsamauwang ke lehlakore la lebili C. Kahoo lebelo le otlolohileng la lebili A = lebelo le otlolohileng la lebili B.
Qetello:
Karabo e nepahetseng ke D.
10. Ntho e nang lemotsamao o chitja o tšoanang ka radius ea limithara tse 6. Haeba ka metsotso e 2 ntho e etsa lipotoloho tse 16, joale lebelo le otlolohileng ntho ke….
A. 0,8 p ms-1
B. 1,0 p ms-1
C. 1,2 p ms-1
D. 1,4 p ms-1
E. 1,6 p ms-1
Puisano
Hoa tsebahala hore:
Radius (r) = limithara tse 6
Lebelo la Angular (ω) = diphetoho tse 16 / metsotso e 2 = diphetoho tse 8 / motsotso = diphetoho tse 8 / metsotsoana e 60 = diphetoho tse 0,13 / motsotsoana.
E botsitsweng: lebelo le otlolohileng (v)?
Karabo:
Foromo ea kamano pakeng tsa lebelo le otlolohileng (v) le lebelo la angular (ω):
v = r ω = (limithara tse 6)(liphetoho tse 0,13/motsotswana) = diphetoho tse 0,8 dimithara/motsotswana
Karabo e nepahetseng ke A.
Haeba e hlahisitsoe ka mahlaseli:
Phetoho e le 'ngoe = 2π radians = 2(3,14) = 6,28 radians
Lebelo la Angular = 8 (6,28) radians / metsotsoana e 60 = 50,24 radians / metsotsoana e 60 = 0,84 radians/motsotswana
v = r ω = (limithara tse 6)(li-radian tse 0,84/motsotswana) = li-radian tse 5,04/motsotswana
11. Seporo sa fene se nang le radius ea 20/π cm se ka potoloha makhetlo a 4 ka motsotsoana o le mong. Lebelo le otlolohileng la ntlha ea seporo ke…
A. 3,2 ms-1
B. 1,6 ms-1
C. 1,3 ms-1
D. 1,0 ms-1
E. 0,8 ms-1
Puisano
Hoa tsebahala hore:
Radius (r) = 20/π m = 20 / 3,14 cm = 6,4 cm = 0,064 metres
Lebelo la Angular (ω) = diphetoho tse 4 / motsotswana o 1 = diphetoho tse 4/motsotswana
Phetoho e le 'ngoe = (2)(3,14) mahlaseli = mahlaseli a 6,28
Lebelo la Angular (ω) = (4)(6,28) radians/motsotswana = 25,12 radians/motsotswana
Potso: lebelo le otlolohileng (v) la ntlha ea propeller?
Karabo:
v = r ω = (limithara tse 0,064)(25,12 radians/motsotswana) = 1,6 metres/motsotswana
Karabo e nepahetseng ke B.
