Isibonelo Sokwanda

Izibonelo Eziyi-9 Zemibuzo Yokukhulisa

1. Ishidi lensimbi ekushiseni okungu-20^oU-C unezilinganiso njengoba kuboniswe esithombeni. Uma i-coefficient yokwanda kwensimbi okuqondile ingu-10^{-5 o}C^-1 bese kuba ukwanda kwendawo ekushiseni okungu-60^oU-C…

A. 0,08 cm²

B. 0,16 cm²

C. 0,24 cm²

D. 0,36 cm²

E. 0,64 cm²

Ingxoxo

I-Diketahui :

Ubude bensimbi = 40 cm

Ububanzi bensimbi = 20 cm

Indawo yokuqala yensimbi (A)_o) = (40)(20) = 800 cm²

I-coefficient yokwanda okuqondile (α) kwensimbi = 10^{-5 o}C^-1

I-coefficient yokwandisa indawo (β) = 2 x i-coefficient yokwandisa ubude (2α) = 2 x 10^{-5 o}C^-1

Umehluko wokushisa (ΔT) = 60^oC - 20^oC=40^oC

Kubuziwe : Ukwanda kwendawo yensimbi ekushiseni okungu-60^oC

Jawab :

Ifomula yokwandisa indawo :

ΔA = β A_o ΔT

Incazelo yefomula:

ΔA = ukwanda kwendawo, β = i-coefficient yokwandiswa kwendawo, A_o = indawo yokuqala, ΔT = ushintsho lokushisa = izinga lokushisa lokugcina – izinga lokushisa lokuqala

Ukwanda kwendawo yensimbi :

ΔA = β A_o ΔT

ΔA = (2 x 10^-5)(800)(40) = 0,64 cm

Impendulo efanele ngu-E.

2. Ipuleti lensimbi ekushiseni okungu-20^oU-C unezilinganiso njengoba kuboniswe esithombeni. Uma izinga lokushisa lenyuswa laya ku-100^oI-C kanye ne-coefficient yokwanda kwensimbi okuqondile ingu-1,1 x 10^{-7 o}C^-1, khona-ke indawo manje iba…

A. 4,0000106 m²

B. 4,0000140 m²

C. 4,0000376 m²

D. 4,0000704 m²

E. 4,0000726 m²

Ingxoxo

I-Diketahui :

Ubude bensimbi = 2 m

Ububanzi bensimbi = 2 m

Indawo yokuqala yensimbi (A)_o) = (2)(2) = 4 m²

I-coefficient yokwanda okuqondile (α) kwensimbi = 1,1 x 10^{-7 o}C^-1

I-coefficient yokwandisa indawo (β) = 2 x i-coefficient yokwandisa ubude (2α) = 2,2 x 10^{-7 o}C^-1

Umehluko wokushisa (ΔT) = 100^oC - 20^oC=80^oC

Kubuziwe : Indawo yensimbi ekushiseni okungu-100^oC

Jawab :

Ukwanda kwendawo yensimbi :

ΔA = β A_o ΔT

ΔA = (2,2 x 10^-7)(4)(80) = 704 x 10^-7 = 0,0000704m²

Indawo yensimbi :

Indawo yensimbi = indawo yokuqala + ukwanda kwendawo

Indawo yensimbi = 4 m² + 0,0000704m²

Indawo yensimbi = 4,0000704 m²

Impendulo efanele ngu-D.

3. Ipuleti elenziwe ngethusi (α = 18.10^{-6 o}C^-1) ekushiseni okungu-0^oU-C unosayizi njengoba kuboniswe esithombeni. Uma ipuleti lishisiswe laya ku-80 ^oC, khona-ke ukwanda kwendawo yepuleti...

A. 0,576.10^-4 m²

B. 1,152.10^-4 m²

C. 2,304.10^-4 m²

D. 3,456.10^-4 m²

E. 4,608.10^-4 m²

Ingxoxo

I-Diketahui :

Ubude bethusi = 40 cm = 0,4 amamitha

Ububanzi bethusi = 20 cm = 0,2 amamitha

Indawo yokuqala yethusi (A)_o) = (0,4)(0,2) = 0,08 m²

I-coefficient yokwanda okuqondile (α) kwethusi = 18 x 10^{-6 o}C^-1

I-coefficient yokwandisa indawo (β) = 2 x i-coefficient yokwandisa ubude (2α) = 36 x 10^{-6 o}C^-1

Umehluko wokushisa (ΔT) = 80^oC - 0^oC=80^oC

Kubuziwe : Ukwanda kwendawo yethusi ekushiseni okungu-80^oC

Jawab :

Ukwanda kwendawo yethusi :

ΔA = β A_o ΔT

ΔA = (36 x 10^-6)(0,08)(80) = 230,4 x 10^-6 = 2,304 x10^-4 m²

Impendulo efanele ngu-C.

4. Isitsha se-aluminium esingamasentimitha angu-2000³, kugcwaliswe ngamanzi ekushiseni kokuqala okungu-0^oC. Bese isitsha siyashiswa kuze kube yilapho izinga lokushisa lifinyelela ku-90^oC. Uma i-coefficient yokwanda kwe-aluminium okuqondile ingu-24 x 10^-6 (^oC)^-1 futhi i-coefficient yokwanda kwevolumu yamanzi ingu-6,3 x 10^-4 (^oC)^-1, umthamo wamanzi achithekile wawungu….

A. 100,94 cm³

B. 100,84 cm³

C. 100,64 cm³

D. 100,54 cm³

E. 100,44 cm³

Ingxoxo

Kuyaziwa ukuthi:

Umthamo wokuqala wesitsha se-aluminium namanzi (V)_o= 2000cm³ = 2 x10³ cm³

Izinga lokushisa lokuqala lesitsha se-aluminium namanzi (T)₁) = 0^oC

Izinga lokushisa lokugcina lesitsha se-aluminium namanzi (T)₂= = 90^oC

I-coefficient yokwanda okuqondile kwe-aluminium (α) = 24 x 10^-6 (^oC)^-1

Ukwandiswa kwevolumu ye-aluminium (γ) = 3α = 3 (24 x 10)^-6 (^oC)^-1 ) = 72 x 10^{-6 o}C^-1

I-coefficient yokwandisa ivolumu yamanzi (γ) = 6,3 x 10^-4 (^oC)^-1

Kubuziwe: Umthamo wamanzi ochithekile

Impendulo:

Ifomula yokwandisa ivolumu:

V = V_o + γ V_o ΔT

V–V_o = γ V_o ΔT

ΔV = γ V_o ΔT

Imininingwane:

V = ivolumu yokugcina, V_o = ivolumu yokuqala, ΔV = ushintsho lwevolumu, γ = i-coefficient yokwandiswa kwevolumu, ΔT = ushintsho lokushisa.

Bala ushintsho kuvolumu yesitsha se-aluminium:

ΔV = γ V_o ΔT = (72) x 10^-6)(2 x 10³)(90) = 12960 x 10^-3 = 12,960cm³

Bala ushintsho kumthamo wamanzi:

ΔV = γ V_o ΔT = (6),3 x 10^-4)(2 x 10³)(90) = 1134 x 10^-1 = 113,4cm³

Ushintsho kumthamo wamanzi lukhulu kunesitsha se-aluminium ngakho-ke amanye amanzi ayachitheka.

Bala umthamo wamanzi achithekile:

113,4 cm³ - 12,960 cm³ = 100,44cm³

Impendulo efanele ngu-E.

5. Ibha yensimbi iyashiswa kuze kube yilapho izinga lokushisa lifinyelela kuma-degrees angu-80^oUbude buka-C buba ngu-115 cm. Uma i-coefficient yokwanda okuqondile kwensimbi ingu-3.10^{-3 o}C^-1 futhi izinga lokushisa lokuqala lensimbi lingu-30^oC, khona-ke ubude bokuqala bensimbi bungu….

A. 100 cm
B. 101,5 cm
C. 102 cm
D. 102,5 cm
E. 103 cm

Ingxoxo
Kuyaziwa ukuthi:
Izinga lokushisa lokuqala (T)₁= = 30^oC
Izinga lokushisa lokugcina (T)₂= = 80^oC
Ukushintsha kwezinga lokushisa (ΔT) = 80^oC - 30^oC=50^oC
I-coefficient yokwanda okuqondile kwensimbi (α) = 3.10^{-3  o}C^-1
Ubude bokugcina bensimbi (L) = 115 cm
Okudingekayo: Ubude bokuqala bensimbi (L)_o)
Impendulo:

Ifomula yokwandisa ubude:
L=L_o + ΔL
L=L_o + α L_o ΔT
L=L_o (1 + α ΔT)

115 = L_o (1 + (3.10)^-3.50) )
115 = L_o (1 + (150.10)^-3))
115 = L_o (1 + 0,15)
115 = L_o (1,15)
L_o = 115/1,15
L_o = 100cm
Impendulo efanele ngu-A.

6. Induku yethusi ekuqaleni inobude obungu-40 cm. Uma ishiswa ekushiseni okungu-80^oUbude buka-C buba ngu-40,04 cm. Uma i-coefficient yokwanda okuqondile kwethusi ingu-2,0 x 10^{-5 o}C^-1 Ngakho izinga lokushisa lokuqala lenduku yethusi….

A. 20 ^oC
B. 22 ^oC
C. 25 ^oC
D. 30 ^oC
E. 50 ^oC

Ingxoxo
Kuyaziwa ukuthi:
Izinga lokushisa lokugcina (T)₂= = 80^oC
Ubude bokuqala (L)_o= 40cm
Ubude bokugcina (L) = 40,04 cm
Ukwanda kobude (ΔL) = 40,04 cm – 40 cm = 0,04 cm
I-coefficient yokwanda okuqondile kwethusi (α) = 2,0 x 10^{-5  o}C^-1
Kubuziwe: Izinga lokushisa lokuqala (T)₁)
Impendulo:
Ifomula yokwandisa insimbi:
L=L_o + α L_o ΔT
L – L_o = α L_o ΔT
ΔL = α L_o ΔT
ΔL = α L_o (T₂ - T₁)

0,04 = (2,0 x 10^-5)(4₀)(80 – T₁)
0,04 = (80 x 10^-5)(80 – T₁)
0,04 = 0,0008 (80 – T₁)
0,04 = 0,064 – 0,0008 T₁
I-0,0008 T₁ = 0,064 - 0,040
I-0,0008 T₁ = 0,024
T₁ = 30^oC
Impendulo efanele ngu-D.

7. Ishidi lensimbi ekushiseni okungu-20^oU-C unezilinganiso njengoba kuboniswe esithombeni. Uma i-coefficient yokwanda kwensimbi okuqondile ingu-10^{-5 o}C^-1 bese kuba ukwanda kwendawo ekushiseni okungu-60^oU-C…

A. 0,08 cm²
B. 0,16 cm²
C. 0,24 cm²
D. 0,36 cm²
E. 0,64 cm²

Ingxoxo

Lo mbuzo uhlobene no ukunwetshwa.
I-Diketahui :
Ubude bensimbi = 40 cm
Ububanzi bensimbi = 20 cm
Indawo yokuqala yensimbi (A)_o) = (40)(20) = 800 cm²
I-coefficient yokwanda okuqondile (α) kwensimbi = 10^{-5 o}C^-1
I-coefficient yokwandisa indawo (β) = 2 x i-coefficient yokwandisa ubude (2α) = 2 x 10^{-5 o}C^-1
Umehluko wokushisa (ΔT) = 60^oC - 20^oC=40^oC
Kubuziwe : Ukwanda kwendawo yensimbi ekushiseni okungu-60^oC
Jawab :

Ifomula yokwandisa indawo :
ΔA = β A_o ΔT
Incazelo yefomula:
ΔA = ukwanda kwendawo, β = i-coefficient yokwandiswa kwendawo, A_o = indawo yokuqala, ΔT = ushintsho lokushisa = izinga lokushisa lokugcina – izinga lokushisa lokuqala
Ukwanda kwendawo yensimbi :
ΔA = β A_o ΔT
ΔA = (2 x 10^-5)(800)(40) = 0,64 cm
Impendulo efanele ngu-E.

8. Ipuleti lensimbi ekushiseni okungu-20^oU-C unezilinganiso njengoba kuboniswe esithombeni. Uma shuyaphakanyiswa yaba yi-100^oI-C kanye ne-coefficient yokwanda kwensimbi okuqondile ingu-1,1 x 10^{-7 o}C^-1, khona-ke indawo manje iba…

A. 4,0000106 m²
B. 4,0000140 m²
C. 4,0000376 m²
D. 4,0000704 m²
E. 4,0000726 m²

Ingxoxo
I-Diketahui :
Ubude bensimbi = 2 m
Ububanzi bensimbi = 2 m
Indawo yokuqala yensimbi (A)_o) = (2)(2) = 4 m²
I-coefficient yokwanda okuqondile (α) kwensimbi = 1,1 x 10^{-7 o}C^-1
I-coefficient yokwandisa indawo (β) = 2 x i-coefficient yokwandisa ubude (2α) = 2,2 x 10^{-7 o}C^-1
Umehluko wokushisa (ΔT) = 100^oC - 20^oC=80^oC
Kubuziwe : Indawo yensimbi ekushiseni okungu-100^oC
Jawab :
Ukwanda kwendawo yensimbi :
ΔA = β A_o ΔT
ΔA = (2,2 x 10^-7)(4)(80) = 704 x 10^-7 = 0,0000704m²   
Indawo yensimbi :
Indawo yensimbi = indawo yokuqala + ukwanda kwendawo
Indawo yensimbi = 4 m² + 0,0000704m²   
Indawo yensimbi = 4,0000704 m²
Impendulo efanele ngu-D.

9. Ipuleti lenziwe ngethusi (α = 18.10^{-6 o}C^-1) ekushiseni okungu-0^oU-C unosayizi njengoba kuboniswe esithombeni. Uma ipuleti lishisiswe laya ku-80 ^oC, khona-ke ukwanda kwendawo yepuleti...
A. 0,576.10^-4 m²
B. 1,152.10^-4 m²
C. 2,304.10^-4 m²
D. 3,456.10^-4 m²
E. 4,608.10^-4 m²
Ingxoxo
I-Diketahui :
Ubude bethusi = 40 cm = 0,4 amamitha
Ububanzi bethusi = 20 cm = 0,2 amamitha
Indawo yokuqala yethusi (A)_o) = (0,4)(0,2) = 0,08 m²
I-coefficient yokwanda okuqondile (α) kwethusi = 18 x 10^{-6 o}C^-1
I-coefficient yokwandisa indawo (β) = 2 x i-coefficient yokwandisa ubude (2α) = 36 x 10^{-6 o}C^-1
Umehluko wokushisa (ΔT) = 80^oC - 0^oC=80^oC
Kubuziwe : Ukwanda kwendawo yethusi ekushiseni okungu-80^oC
Jawab :
Ukwanda kwendawo yethusi :
ΔA = β A_o ΔT
ΔA = (36 x 10^-6)(0,08)(80) = 230,4 x 10^-6 = 2,304 x10^-4 m²
Impendulo efanele ngu-C.

Umthombo wombuzo:

Imibuzo Yefiziksi Yezivivinyo Zikazwelonke Zesikole Samabanga Aphezulu/Isikole Samabanga Aphezulu Sokufundela Umsebenzi