Physics

1. Kureba kwegirazi rakapinza i10 cm uye daro rechinhu i20 cm. Sarudza (a) daro remufananidzo (b) kukura kwemufananidzo

Zvinozivikanwa:

Kureba kwefocal (f) = -10 cm

Chiratidzo chekusiya chinoratidza kuti nzvimbo iri pamberi pegirazi rakatenderedzwa iri chaiyo

Daro rechinhu ( do _o ) = 20 cm

Solution:

Kuumbwa kwemufananidzo negirazi rakatetepa:

Kureba kwemufananidzo (di _i ):

1/ di = 1/f – 1/ do _o = -1/10 – 1/20 = -2/20 – 1/20 = _-3/20

d _i = -20/3 = -6.7 cm

Chiratidzo chekusiya chinoratidza kuti mufananidzo wacho uri wepaindaneti.

Kukura kwemufananidzo:

m = – di _i / do _o = -(-6.7)/20 = 6.7/20 = 0.3

m = 0,3 nguva diki pane chinhu chacho.

Chiratidzo chekuwedzera chinoratidza kuti mufananidzo uri kumusoro.

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2. Chinhu chakareba masendimita gumi chinoiswa pamberi pegirazi rakamonana rine urefu hwemasendimita makumi maviri. Sarudza kukwirira kwemufananidzo kana daro rechinhu chiri (a) 10 cm (b) 30 cm (c) 40 cm (d) 50 cm

Zvinozivikanwa:

Kureba kwegirazi rakapinza (f) = -20 cm

Chiratidzo chekusiya chinoratidza kuti nzvimbo yakatarisana nayo iri paindaneti

Radiyo yekukombama ( r ) = 2 f = 2(20) = 40 cm

Kureba kwechinhu (h) = 10 cm

Solution:

a) kureba kwefocal (f) = -20 cm uye daro rechinhu (do _o ) = 10 cm

Kureba kwemufananidzo (di _i ) :

1/ di = 1/f – 1/ do _o = -1/20 – 1/10 = -1/20 – 2/20 = _-3/20

d _i = -20/3 = -6.7

Chiratidzo chekusiya chinoratidza kuti mufananidzo wacho uri wepakombiyuta kana kuti mufananidzo uri kuseri kwegirazi.

Kukura kwemufananidzo ( m ):

m = – di _i / do _o = -(-6.7)/10 = 6.7/10 = 0.67

Chiratidzo chekuwedzera chinoratidza kuti mufananidzo wacho wakamira.

Mufananidzo wacho mudiki ne 0.67 pane chinhu chacho.

Kureba kwemufananidzo (h _i ):

m = h _i / h _o

h _i = h _o m = (10 cm)(0.67) = 6.7 cm

b) kureba kwefocal (f) = -20 cm uye daro rechinhu ( do _o ) = 30 cm

Kureba kwemufananidzo ( di _i ):

1/ di = 1/f – 1/ do _o = -1/20 – 1/30 = -3/60 – 2/60 = _-5/60

d _i = -60/5 = -12

Chiratidzo chekusiya chinoratidza kuti mufananidzo wacho uri wepakombiyuta kana kuti mufananidzo uri kuseri kwegirazi.

Kukura kwemufananidzo ( m ):

m = – di _i / do _o = -(-12)/30 = 12/30 = 0.4

Chiratidzo chekuwedzera chinoratidza kuti mufananidzo wacho wakamira.

Mufananidzo wacho mudiki nekanenge ka0,4 pane chinhu chacho.

Kureba kwemufananidzo (h _i ):

m = h _i / h _o

h _i = h _o m = (10 cm)(0.4) = 4 cm

c) Kureba kwefocal (f) = -20 cm uye daro rechinhu ( do _o ) = 40 cm

Kureba kwemufananidzo ( di _i ):

1/ di = 1/f – 1/ do _o = -1/20 – 1/40 = -2/40 – 1/40 = _-3/40

d _i = -40/3 = -13.3

Chiratidzo chekusiya chinoratidza kuti mufananidzo wacho uri wepakombiyuta kana kuti mufananidzo uri kuseri kwegirazi rakamonana.

Kukura kwemufananidzo ( m ):

m = – di _i / do _o = -(-13.3)/40 = 13.3/40 = 0.3

Chiratidzo chekuwedzera chinoratidza kuti mufananidzo wacho wakamira.

Mufananidzo wacho mudiki ne 0.3 pane chinhu chacho.

Kureba kwemufananidzo ( h _{i )} :

m = h _i / h _o

h _i = h _o m = (10 cm)(0.3) = 3 cm

d) Kureba kwefocal (f) = -20 cm uye daro rechinhu ( do _o ) = 50 cm

Kureba kwemufananidzo ( di _i ):

1/ di = 1/f – 1/ do _o = -1/20 – 1/50 = -5/100 – 2/100 = _-7/100

d _i = -100/7 = -14.3

Chiratidzo chekusiya chinoratidza kuti mufananidzo wacho uri wepakombiyuta kana kuti mufananidzo uri kuseri kwegirazi rakamonana.

Kukura kwemufananidzo ( m ):

m = – di _i / do _o = -(-14.3)/50 = 14.3/50 = 0.3

Chiratidzo chekuwedzera chinoratidza kuti mufananidzo wacho wakamira.

Mufananidzo wacho mudiki ne 0.3 pane chinhu chacho.

Kureba kwemufananidzo (h _i ) :

m = h _i / h _o

h _i = ho _m = (10 cm)(0.3) = 3 cm

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3. Pachinhu chiri 20 cm pamberi pegirazi rakamonana . Kana kukwirira kwemufananidzo kuri 1/5 kakapetwa kukwirira kwechinhu, sarudza ( a) kureba kwemufananidzo b) kureba kwefocal c) hunhu hwemufananidzo

Zvinozivikanwa:

Daro rechinhu ( do _o ) = 20 cm

Kureba kwemufananidzo (h _i ) = 1/5 h = 0.2 h

Kureba kwechinhu (h) = h

Solution:

a) daro remufananidzo ( di _i )

Fomura yekukudza mufananidzo :

m = h _i / h _o = 0.2h / h = 0.2

Chiratidzo chekuwedzera chinoratidza kuti mufananidzo wacho wakamira.

Mufananidzo wacho mudiki ne 0.2 pane chinhu chacho.

Kureba kwemufananidzo ( di _i ):

– d _i = md _o

di _i = – m do _o = -(0.2)(20 cm) = -4 cm

Chiratidzo chekusiya chinoratidza kuti mufananidzo wacho uri wepakombiyuta kana kuti mufananidzo uri kuseri kwegirazi rakamonana.

b) Kureba kwenzvimbo yakatarisana ( f)

Kureba kwefocal (f):

1/f = 1/ do _o + 1/ di = 1/20 – 1/4 = 1/20 – 5/20 = _-4/20

f = -20/4 = -5 cm

Chiratidzo che "minus" chinoratidza kuti nzvimbo iri pamberi pechinhu iri paindaneti.

c) Hunhu hwemufananidzo:

- Wakarurama

- Diki

- pamhepo

4. Chiedza chinorova girazi rakatenderedza rakafanana neakisi chinozoratidzwa….

A. kuenda kunzvimbo yekutarisa girazi

B. sezviri panzvimbo yekutarisa girazi

C. nepakati pegirazi rakakombama

D. yakatarisana negirazi regirazi

mhinduro

Dambudziko iri rinoonekwa mumufananidzo uri pazasi.

Mhinduro chaiyo ndeiyi B.

5. Mutyairi webhasikoro anoona mufananidzo wemudhudhudhu uri kumashure kwawo kakapetwa kaviri pahukuru hwawo hwepakutanga kana daro riri pakati pemutyairi webhasikoro nemudhudhudhu riri mamita makumi matatu. Sarudza dhayamita yekukombama kwegirazi rekumashure…

A. 7.14 m

B. 8.57 m

C. 12.00 m

D. 24.00 m

Zvinozivikanwa:

Kukura kwemufananidzo (M) = 1/6 kanomwe

Kureba kwechinhu (d) = mamita makumi matatu

Zvinodiwa: Radius yekukombama kwegirazi rekumashure (R)

Solution:

Verenga daro remufananidzo (d')

Sezvo kukura kwemufananidzo (M) uye daro rechinhu (s) zvave zvichizivikanwa, daro remufananidzo rinogona kuzivikanwa uchishandisa fomura yekukura kwemufananidzo:

Chiratidzo chekuramba chinoreva kuti mufananidzo wacho uri wepaindaneti. Mufananidzo wacho uri pamamita mashanu kubva pagirazi rakatenderedza.

Verenga urefu hwefocal (f)

Sezvo daro rechinhu (d) uye daro remufananidzo (d'), ipapo urefu hwefocal hunogona kuverengerwa uchishandisa fomura yegirazi:

Radiyo yekukombama (R)

Radius yekukombama kwegirazi rakatenderedzwa inopetwa kaviri kureba kwegirazi rakatenderedzwa.
R = 2 f = 2 (mamita matanhatu) = mamita gumi nemaviri
Radius yekukombama kwegirazi rakatenderedzwa ine denderedzwa regirazi i12 metres.
Mhinduro chaiyo ndeinoti C.

6. Girazi rakapinza rinosarudzwa segirazi rekuona kumashure kwemudhudhudhu nekuti hunhu hwemufananidzo unogadzirwa negirazi iri…

A. chaiyo, yakatwasuka, yakaderedzwa

B. chaiyo, yakatwasuka, yakakura

C. chaiyo, yakatwasuka, yakaderedzwa

D. chaiyo, yakatwasuka, yakakura

Solution:

Zvichibva pamifananidzo miviri iri pamusoro apa zvinogona kugumiswa kuti hunhu hwemufananidzo hwakafanana, hwakamira, hwakaderedzwa.

Mhinduro chaiyo ndeinoti C.

7. Chinhu chiri 12 cm pamberi pegirazi rakamonana rine dhayamita ye6 cm. Hunhu hwemufananidzo ndehwekuti…

A. chaiyo, yakapindurwa iri chinhambwe che12 cm

B. chaiyo, yakatwasuka iri chinhambwe che 4 cm

C. chaiyo, yakatwasuka iri chinhambwe che 2.4 cm

D. chaiyo, yakapindurwa iri chinhambwe che6 cm

Zvinozivikanwa:

Kureba kwechinhu (d) = 12 cm

Nharaunda yegirazi rakatenderedzwa (r) = 6 cm.

Kureba kwegirazi rakapinza (f) = 6 cm / 2 = -3 cm

Kureba kwegirazi rakatenderedzwa kunoratidza kuti harina kunaka nekuti riri rechokwadi. Riri rechokwadi nekuti haripfuuri nechiedza.

Zvinodiwa: Hunhu hwemufananidzo

Solution:

Kureba kwemufananidzo (d'):

1/d' = 1/f – 1/d = -1/3 – 1/12 = -4/12 – 1/12 = -5/12

d' = -12/5 = -2.4 cm

Kureba kwemufananidzo kwakasainwa negative zvinoreva kuti mufananidzo wacho uri wepaindaneti.

Kukura kwemufananidzo (m):

m = -d' / d = -(-2.4) / 12 = 2.4 / 12 = 0.2 kanomwe

Kukura kwemufananidzo wakanyorwa zvakanaka kunoreva kuti mufananidzo wakamira uye kukura kwemufananidzo kuri 0.2 zvinoreva kuti saizi yemufananidzo idiki pane saizi yechinhu (yakaderedzwa).

Mhinduro chaiyo ndeinoti C.

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1. Chinhu chinoiswa 10 cm kubva pagirazi rakakombama . Kureba kwefocal i5 cm. Sarudza (a) Daro remufananidzo ( b) kukura kwemufananidzo

Zvinozivikanwa:

Kureba kwefocal (f) = 5 cm

Daro rechinhu ( do _o ) = 10 cm

Mhinduro :

Kuumbwa kwemufananidzo negirazi rakatetepa:

Kureba kwemufananidzo:

1/ di ₌ 1/f – 1/ do _o = 1/5 – 1/10 = 2/10 – 1/10 = 1/10

d _i = 10/1 = 10 cm

Kureba kwemufananidzo i10 cm.

Kukura:

m = – di _i / do _o = -10/10 = -1

1 zvinoreva kuti mufananidzo wacho wakafanana nechinhu chacho.

Chiratidzo chekusiya chinoratidza kuti mufananidzo wakapindurwa. Kana chiratidzo chiri chakanaka, mufananidzo wacho wakamira.

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2. Chinhu chakareba masendimita mashanu chinoiswa pamberi pegirazi rakakombama rine dhayamita yekukombama ye20 cm. Sarudza kukwirira kwemufananidzo kana daro rechinhu chacho riri masendimita mashanu, gumi nemashanu, makumi maviri, makumi matatu.

Zvinozivikanwa:

Radiyo yekukombama ( r ) = 20 cm

Kureba kwefocal (f) = R/2 = 20/2 = 10 cm

Kureba kwechinhu (h _o ) = 5 cm

Solution:

a) kureba kwefocal (f) = 10 cm uye daro rechinhu ( do _o ) = 5 cm

Kuumbwa kwemufananidzo negirazi rakatetepa:

Kureba kwemufananidzo ( di _i ):

1/ di = 1/f – 1/ do _o = 1/10 – 1/5 = 1/10 – 2/10 = _-1/10

d _i = -10/1 = -10 cm

Chiratidzo chekusiya chinoratidza kuti mufananidzo wacho uri wepakombiyuta kana kuti mufananidzo uri kuseri kwegirazi.

Kukura kwemufananidzo ( m ):

m = – di _i / do _o = -(-10)/5 = 10/5 = 2

Chiratidzo chekuwedzera chinoratidza kuti mufananidzo wacho wakamira.

Kureba kwemufananidzo ( h _i ):

m = h _i / h _o

h _i = ho _m = (5 cm)(2) = 10 cm

Kureba kwemufananidzo ndeye 10 cm.

b) Kureba kwefocal (f) = 10 cm uye daro rechinhu ( do _o ) = 15 cm

Kuumbwa kwemufananidzo negirazi rakatetepa:

Kureba kwemufananidzo ( di _i ):

1/ di = 1/f – 1/ do _o = 1/10 – 1/15 = 3/30 – 2/30 = _1/30

d _i = 30/1 = 30 cm

Chiratidzo chekuwedzera chinoratidza kuti mufananidzo wacho ndewechokwadi kana kuti mufananidzo wacho uri 30 cm pamberi pegirazi, parutivi rumwe chete nechinhu chacho.

Kukura kwemufananidzo ( m ):

m = – di _i / do _o = -30/15 = -2

Chiratidzo chekusiya chinoratidza kuti mufananidzo wacho wakapindurwa.

Mufananidzo wacho wakakura zvakapetwa kaviri pane chinhu chacho.

Kureba kwemufananidzo (h _i ):

m = h _i / h _o

h _i = h _o m = (5 cm)(2) = 10 cm

Kureba kwemufananidzo ndeye 10 cm.

c) Kureba kwefocal (f) = 10 cm uye daro rechinhu ( do _o ) = 20 cm

Kuumbwa kwemufananidzo negirazi rakatetepa:

Kureba kwemufananidzo (di _i ):

1/ di ₌ 1/f – 1/ do _o = 1/10 – 1/20 = 2/20 – 1/20 = 1/20

d _i = 20/1 = 20 cm

Chiratidzo chakanaka chinoratidza kuti mufananidzo wacho ndewechokwadi kana kuti mufananidzo wacho uri 20 cm pamberi pegirazi, parutivi rumwe chete nechinhu chacho.

Kukura kwemufananidzo ( m ):

m = – di _i / do _o = -20/20 = -1

Chiratidzo chekuramba chinoreva kuti mufananidzo wacho wapindurwa.

Kureba kwemufananidzo ( mhoro ):

m = h _i / h _o

h _i = h m = (5 cm)(1) = 5 cm

d) Kureba kwefocal (f) = 10 cm uye daro rechinhu ( do _o ) = 30 cm

Kureba kwemufananidzo ( di _i ):

1/ di = 1/f – 1/ _{do o} = _1/10 – 1/30 = 3/30 – 1/30 = 2/30

d _i = 30/2 = 15 cm

Chiratidzo chekuwedzera chinoratidza kuti mufananidzo wacho ndewechokwadi kana kuti mufananidzo wacho uri 15 cm pamberi pegirazi, parutivi rumwe chete nechinhu chacho.

Kukura kwemufananidzo ( m) :

m = – di _i / do _o = -15/30 = -0.5

Chiratidzo chekusiya chinoratidza kuti mufananidzo wacho wakapindurwa.

Mufananidzo wacho mudiki ne 0.5 pane chinhu chacho.

Kureba kwemufananidzo (h _i ):

m = h _i / h _o

h _i = ho _m = (5 cm)(0.5) = 2.5 cm

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3. Mufananidzo wakagadzirwa negirazi rakakombama wakakura ka4 pane chinhu chacho. Kana dhayamita yekukombama iri 20 cm, sarudza daro rechinhu chiri pamberi pegirazi!

Zvinozivikanwa:

Kukura kwemufananidzo ( m ) = 4

Radiyo yekukombama ( r ) = 20 cm

Kureba kwefocal (f) = r /2 = 20/2 = 10 cm

Chinodiwa : Kureba kwechinhu ( do _o )

Solution:

m = – di _i / do _o

4 = – di _{i /} do _o

– d _i = 4 do _o

di _i = – 4 do _o

1/f = 1/ do _o + 1/ di _i

1/10 = 1/ do _o + 1/4 do _o

4/40 = 4/4 do _o + 1/4 do _o

4/40 = 5/4 do _o

(4)(4s) = (5)(40)

16 d _o = 200

do _o = 12.5 cm

Kureba kwechinhu = 12.5 cm.

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4. Chinhu chakareba 1-cm chinoiswa 10 cm kubva pagirazi rakakombama rine urefu hwefocal, f = 15 cm. Sarudza:

A. Kureba kwemufananidzo?

B. Kureba kwemufananidzo?

C. Hunhu hwemufananidzo hunoumbwa negirazi rakakombama?

Zvinozivikanwa:

Kureba kwechinhu (h) = 1 cm

Daro rechinhu (do _o ) = 10 cm

Kureba kwegirazi rakakombama (f) = 15 cm

Solution:

A. Kureba kwemufananidzo (d _i )

1/f = 1/d _o + 1/d _i

1/d _i = 1/f – 1/d _o = 1/15 – 1/10 = 2/30 – 3/30 = -1/30

d _i = -30/1 = -30 cm

Chiratidzo chekuramba chinoratidza kuti mufananidzo wacho uri wepakombiyuta kana kuti mufananidzo uri kuseri kwegirazi.

B. Kureba kwemufananidzo (h _i )

Kukura kwemufananidzo (M):

M = -d _i /d _o = h _i /h _o

M = -(-30)/10 = 30/10 = katatu

Kureba kwemufananidzo (h _i ):

M = h _i / h _o

3 = h _i / 1 cm

h _i = 3 (1 cm)

h _i = 3 cm

Kureba kwemufananidzo i3 cm. Chiratidzo chekuwedzera chinoratidza kuti mufananidzo uri kumusoro.

C. Hunhu hwemufananidzo:

Zviri pachena, kumusoro, hombe kupfuura chinhu

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5. Kukura kwemufananidzo, zvichienderana nemufananidzo uri pazasi.

Zvinozivikanwa:

Daro rechinhu (do _o ) = 60 cm

Kureba kwefocal (f) = 20 cm

Zvinodiwa: Kukura kwemufananidzo (M)

Solution:

Kureba kwemufananidzo:

1/f = 1/d _o + 1/d _i

1/d _i = 1/f – 1/d _o = 1/20 cm – 1/60 cm = 3/60 cm – 1/60 cm = 2/60 cm

d _i = 60/2 cm = 30 cm

Kukura kwemufananidzo (M):

M = di _i / do _o = 30 cm / 60 cm = 1/2 kanomwe

6. Kana chinhu chacho chakaiswa 6 cm kubva pagirazi rakakombama, daro remufananidzo i12 cm sezvakaratidzwa mumufananidzo uri pazasi. Ndeipi daro remufananidzo kana chinhu chacho chikabviswa panzvimbo yekutanga 1 cm kubva pagirazi.

Zvinozivikanwa:

Daro rechinhu (do _o ) = 6 cm

Daro remufananidzo (d _i ) = 12 cm

Zvinodiwa: kana daro rechinhu (do _o ) = 7 cm saka daro remufananidzo ndiro …

Solution:

1/f = 1/do + 1/di = 1/6 + 1/12 = 2/12 + 1/12 = 3/12

f = 12/3 = 4 cm

Kureba kwefocal kuri pachena, zvichireva kuti focal point ndeyechokwadi kana kuti mwaranzi inopfuura nepakati pepoint.

Kureba kwemufananidzo:

1/d _i = 1/f – 1/d _o = 1/4 – 1/7 = 7/28 – 4/28 = 3/28

d _i = 28/3 = 9.3 cm

7. Chiremba wemazino anotarisa uye anoongorora mazino emurwere achishandisa girazi rine 8 cm radius. Kuti buri rionekwe zvakajeka nachiremba, daro riri pakati pemazino emurwere negirazi nderei?

A. pasi pe 4 cm pamberi pegirazi rakakombama

B. pasi pe 4 cm pamberi pegirazi rakamonana

C. anopfuura 4 cm pamberi pegirazi rakakombama

D. anopfuura 4 cm pamberi pegirazi rakatenderedza

Zvinozivikanwa:

Nharaunda yegirazi (r) = 8 cm

Kureba kwegirazi (f) = r / 2 = 8 / 2 = 4 cm

Chinodiwa: Daro riri pakati pemazino emurwere negirazi

Solution:

Girazi rinoshandiswa igirazi rakakombama kana kuti girazi rakakombama? Kuti buri rezino rionekwe zvakajeka nachiremba, girazi rinoshandiswa rinofanira kukwanisa kuwedzera mufananidzo wezino uye mufananidzo unofanira kumira wakamira. Magirazi akakombama anogara achiburitsa mifananidzo yakakombama uye saizi yemufananidzo idiki pane saizi yechinhu. Kusiyana neizvi, girazi rakakombama rinogona kugadzira mufananidzo wakamira kana daro rechinhu (d) riri diki pane urefu hwefocal (f). Kana daro rechinhu rakakura pane urefu hwefocal (f) saka girazi rakakombama rinoburitsa mufananidzo wakakombama.

Kureba kwegirazi rakakombama (f) i4 cm, saka mazino emurwere anofanira kunge ari pasi pe4 cm pamberi pegirazi rakakombama.

Mhinduro chaiyo ndeinoti A.

8. Girazi rakakombama rine denderedzwa re 24 cm. Kana chinhu chacho chikaiswa 20 cm pamberi pegirazi, sarudza hunhu hwemufananidzo.

A. Chaiyo, yakatwasuka uye yakakura

B. Chaicho, chakapindurwa uye chakakudzwa

C. Zviri pachena, zvakamira uye zvakakura

D. Zviri paindaneti, zvakapindurwa uye zvidiki

Zvinozivikanwa:

Nharaunda yekukombama (r) = 24 cm

Kureba kwefocal (f) = R/2 = 24/2 = +12 cm

Kureba kwegirazi rakakombama kwakanaka kana kuti kwechokwadi nekuti chiedza chinopfuura nepakati pegirazi.

Kureba kwechinhu (d) = 20 cm

Zvinodiwa: Hunhu hwemufananidzo

Solution:

Mufananidzo uri wechokwadi here kana kuti uri wechokwadi? Verenga daro remufananidzo (s'):

1/d + 1/d' = 1/f

1/d' = 1/f – 1/d

1/d' = 1/12 – 1/20

1/d' = 5/60 – 3/60

1/d' = 2/60

d' = 60/2

d' = 30 cm

Kureba kwemufananidzo kwakasainwa kuti kwakanaka zvinoreva kuti mufananidzo wacho ndewechokwadi nekuti unopfuudzwa nechiedza.

Mufananidzo wakakura here? Wakatwasuka here kana kuti wakapindurwa? Kutanga verenga kukura kwemufananidzo (M):

M = -d' / d = -30/20 = -1.5

M > 1 zvinoreva kuti mufananidzo wakura, M ine chiratidzo chekuramba zvinoreva mufananidzo wakapindurwa. Saka hunhu hwemufananidzo ndehwechokwadi, hwakapindurwa, hwakakura.

Mhinduro chaiyo ndeiyi B.

9. Girazi rakatenderera rinoburitsa mufananidzo wakakura kashanu pane chinhu chiri pachikirini, chiri kure nemamita mashanu kubva pane chinhu chacho. Girazi iri…..

A. dendere rakakombama rine hurefu hwepakati hwe25/24 m

B. convex ine urefu hwefocal hwe25/24 m

C. dendere rakakombama rine hurefu hwepakati hwe 24/25 m

D. convex ine urefu hwefocal hwe 24/25 m

Zvinozivikanwa:

Kukura kwemufananidzo (M) = kashanu

Kureba pakati pechinhu nemufananidzo = mamita mashanu

Solution:

Saizi yemufananidzo unogadzirwa negirazi rakapinza inogara iri diki pane saizi yechinhu chacho, saka, girazi iri girazi rakapinza.

Kureba kwechinhu (d) = x

Kureba kwemufananidzo (d') = x + 5

Kukura kwemufananidzo (M) = kashanu

Fomura yekukudza mufananidzo:

Fomura yehurefu hwefocal (f):

Mhinduro chaiyo ndeinoti A.

[wpdm_package id='858′]

1. Matambudziko egirazi reConcave uye mhinduro dzaro
2. Matambudziko egirazi reConvex uye mhinduro dzaro
3. Matambudziko akasiyana-siyana e lens uye mhinduro dzawo
4. Kusangana matambudziko nemhinduro dzema lenzi
5. Zvishandiso zvemaziso matambudziko emaziso evanhu uye mhinduro dzawo
6. Matambudziko nemhinduro dzemalenzi ekuonana nemidziyo yemaziso
7. Magirazi emaziso ezvishandiso zvemaziso
8. Zvishandiso zvemagetsi zvinosimudzira matambudziko egirazi uye mhinduro dzazvo
9. Maikorosikopu yezvishandiso zveOptical - matambudziko nemhinduro
10. Matambudziko nemhinduro dzematelesikopu ezvishandiso zveOptical

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1. 1-kg yemvura pa100 ^o C yakasanganiswa nemvura ye1-kg pa10 ^o C muchimiro chakasiyana. Kupisa kwemvura chaiyo i4200 J/kg ^o C. Sarudza tembiricha yekupedzisira yemusanganiswa!

Zvinozivikanwa:

Huremu hwemvura inopisa (m1 ₎ = 1 kg

Kupisa kwemvura inopisa (T ₁ ) = 100 ^o C

Huremu hwemvura inotonhora (m2 ₎ = 1 kg

Kupisa kwemvura inotonhora (T ₂ ) = 10 ^o C

Zvinodiwa: Tembiricha yekupedzisira (T)

Solution:

Kurasikirwa nekupisa = Kupisa kwawanikwa (system yakaparadzaniswa)

m c Δ T = m c Δ T

m Δ T = m Δ T

m ₁ (T ₁ – T) = m ₂ (T – T ₂ )

(1)(100 – T) = (1)(T – 10)

100 – T = T – 10

100 + 10 = T + T

110 = 2T

T = 110 / 2

T = 55

Tembiricha yekupedzisira ndeye 55 ^o C.

[irp]

2. Bhokisi remutobvu re3 kg pa80^o yakaiswa mu10 kg yemvura. Kupisa kwemutobvu chaiwo i1400 J.kg^-1C^-1 uye kupisa kwemvura chaiyo i4200 J.kg^-1C^-1Tembiricha yekupedzisira mukuenzanisa kwekupisa ndeye 20^oC. Sarudza tembiricha yekutanga yemvura!

Zvinozivikanwa:

Huremu ( _m1 ) = 3 kg

Kupisa kwemutobvu chaiwo (c ₁ ) = 1400 J.kg ^-1 C ^-1

Kupisa kwemutobvu (T ₁ ) = 80 ^o C

Huremu hwemvura (m2 ₎ = 10 kg

Kupisa kwemvura chaiyo (c ₂ ) = 4200 J.kg ^-1 C ^-1

Kupisa kwekupisa kwakaenzana (T) = 20 ^o C

Zvinodiwa: Tembiricha yekutanga yemvura ( _T2 )

Solution:

Kupisa kwakarasika = Kupisa kwawanikwa

Q lead = Q mvura

m ₁ c ₁ ΔT = m ₂ c ₂ ΔT

(3)(1400)(80-20) = (10)(4200)(20-T)

(4200)(60) = (42,000)(20-T)

252,000 = 840,000 – 42,000 T

42,000 T = 840,000 – 252,000

42,000 T = 588,000

T = 588,000 / 42,000

T = 14

Tembiricha yekutanga yemvura ndeye 14 ^o C.

[irp]

3. Bhokisi remhangura pa 100^oC yakaiswa mu 128 gramu yemvura pa 30 ^oC. Kupisa kwemvura chaiyo ndiko 1 cal.g^-1oC^-1 uye kupisa kwemhangura chaiyo ndiko 0.1 cal.g^-1oC^-1. Kana tembiricha ye thermal equilibrium iri 36 ^oC, sarudza huremu hwemhangura!

Zvinozivikanwa:

Kupisa kwemhangura (T ₁ ) = 100 ^o C

Kupisa kwemhangura (c ₁ ) = 0.1 c al.g ^-1o C ^-1

Huremu hwemvura (m2 ₎ = 128 magiramu

Kupisa kwemvura (T ₂ ) = 30 ^o C

Kupisa kwemvura chaiyo (c ₂ ) = 1 c al.g ^-1o C ^-1

Kupisa kwekupisa kwakaenzana (T) = 36 ^o C

Zvinodiwa: Huremu hwemhangura ( _m1 )

Solution:

Kupisa kwakarasika = Kupisa kwawanikwa

Q mhangura = Q mvura

m ₁ c ₁ ΔT = m ₂ c ₂ ΔT

(m ₁ )(0.1)(100-36) = (128)(1)(36-30)

(m ₁ )(0.1)(64) = (128)(1)(6)

(m ₁ )(6.4) = 768

m ₁ = 768 / 6.4

m ₁ = 120

Huremu hwemhangura hunosvika 120 gramu.

[irp]

4. Chivharo chechando cheM-kg pa 0^oC yakaiswa mu 340 gramu yemvura pa 20^oC muhari. Kana kupisa kwekubatana yemvura = 80 cal g^-1, kupisa kwemvura chaiyo ndiko 1 cal g^{-1 o}C^-1. Aizi yese inonyunguduka uye tembiricha ye kuenzana kwekupisa is 5^oC, sarudza huwandu hwechando!

Zvinozivikanwa:

Huremu hwemvura (m) = 340 magiramu

Kupisa kwechando (T _ice ) = 0 ^o C

Tembiricha yemvura (T _mvura ) = 20 ^o C

Kupisa kwekupisa kwakaenzana (T) = 5 ^o C

Kupisa kwekubatana kwemvura ( L ) = 80 cal g ^-1

Kupisa kwemvura chaiyo (c _mvura ) = 1 cal g ^{-1 o} C ^-1

Zvinodiwa: Huwandu hwechando (M)

Solution:

Kupisa kwakarasika = Kupisa kwawanikwa

Mvura yeQ = chando cheQ

m c ( ΔT) = m _es L _es + m c ( Δ T)

(340)(1)(20-5) = M (80) + M (1)(5-0)

(340)(15) = 80M + 5M

5100 = 85M

M = 5100/85

M = magiramu makumi matanhatu

[wpdm_package id='714′]

1. Kuchinja zviyero zvekupisa
2. Linear kuwedzera
3. Kuwedzera kwenzvimbo
4. Kuwedzera inzwi
5. Heat
6. Kuenzana kwekupisa kwemuchina
7. Kupisa kwakananga uye kugona kupisa
8. Kupisa kwakahwanda, kupisa kwekusanganiswa, kupisa kwekupfuta
9. Kuchengetedza simba rekutamisa kupisa

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4 Kupisa kwakavharika Kupisa kwekusanganiswa Kupisa kwekupfuta - Matambudziko neMhinduro

1. Verenga huwandu hwekupisa hunowedzerwa ku 1 gram yegoridhe kuti uchinje chikamu kubva pachinhu chakasimba kuenda kuchinwiwa. Kupisa kwekusanganiswa kwegoridhe i 64.5 x 10 ³ J/kg.

Zvinozivikanwa:

Huremu (m) = 1 gramu = 1 x 10 ^-3 kg

Kupisa kwekubatana (L _F ) = 64.5 x 10 ³ J/kg

Kudiwa: Kupisa (Q)

Solution:

Q = m L _F

Q = (1 x 10 ^-3 kg)(64.5 x 10 ³ J/kg)

Q = 64.5 Joule

[irp]

2. Verenga huwandu hwekupisa hunoburitswa ne 1 gram ye mercury kuti uchinje chikamu kubva pamvura kuita chakasimba. Kupisa kwe fusion ye mercury i 11.8 x 10 ³ J/kg.

Zvinozivikanwa:

Huremu (m) = 1 gramu = 1 x 10 ^-3 kg

Kupisa kwekubatana (L _F ) = 11.8 x 10 ³ J/kg

Kudiwa: Kupisa (Q)

Solution:

Q = m L _F

Q = (1 x 10 ^-3 kg)(11.8 x 10 ³ J/kg)

Q = 11.8 Joule

3. Sarudza huwandu hwekupisa hunotorwa nemvura ye1 kg kuti uchinje chikamu kubva pamvura kuita utsi (mhepo). Kupisa kwekupfuta kwemvura = 2256 x 10 ³ J/kg

Zvinozivikanwa:

Huremu (m) = 1 kg

Kupisa kwekupfuta (L _V ) = 2256 x 10 ³ J/kg

Kudiwa: Kupisa (Q)

Solution:

Q = m L _V

Q = (1 kg)( 2256 x 10 ³ J/kg)

Q = 2256 x 10 ³ Joule

[irp]

4. Sarudza huwandu hwekupisa hunoburitswa nenitrogen kuti huchinje chikamu kubva pautsi kuenda kumvura. Kupisa kwekupfuta kwenitrogen = 200 x 10 ³ J/kg

Zvinozivikanwa:

Huremu (m) = 1 gramu = 1 x 10 ^-3 kg

Kupisa kwekupfuta (L _V ) = 200 x 10 ³ J/kg

Inozivikanwa: Kupisa (Q)

Solution:

Q = m L _V

Q = (1 x 10 ^-3 kg)( 200 x 10 ³ J/kg)

Q = 200 Joule

1. Kuchinja zviyero zvekupisa
2. Linear kuwedzera
3. Kuwedzera kwenzvimbo
4. Kuwedzera inzwi
5. Heat
6. Kuenzana kwekupisa kwemuchina
7. Kupisa kwakananga uye kugona kupisa
8. Kupisa kwakahwanda, kupisa kwekusanganiswa, kupisa kwekupfuta
9. Kuchengetedza simba rekutamisa kupisa

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1. Muviri une huremu hwe2 kg unotora macalorie zana kana tembiricha yawo ikawedzera kubva pa20 ^o C kusvika 70 ^o C. Chii chinonzi kupisa kwemuviri?

Zvinozivikanwa:

Huremu (m) = 2 kg = 2000 gr

Kupisa (Q) = 100 c al

Kuchinja kwetembiricha ( ΔT ) = 70 ^o C – 20 ^o C = 50 ^o C

Zvinodiwa: Kupisa chaiko (c)

Solution:

c = Q / m Δ T

c = 100 cal / (2000 gr)(50 ^o C)

c = 100 cal / 100,000 gr ^o C

c = 10 ² cal / 10 ⁵ gr ^o C

c = (10 ² cal)( 10 ^-5 gr ^{-1 o} C ^-1 )

c = 10 ^-3 macalorie gr ^{-1 o} C ^-1

c = 10 ^-3 cal/ gr ^o C

Kupisa kwemuviri kwakakosha 10 ^-3 cal/gr ^o C

[irp]

2. Kupisa kwemvura chaiyo i4180 J/kg Co2 ^. Kukwanisa kupisa kwe2 kg yemvura …

Zvinozivikanwa:

Kupisa chaiko (c) = 4180 J/kg C ^o

Huremu (m) = 2 kg

Zvinodiwa: Kukwanisa kupisa (C)

Solution:

C = mc

C = (2 kg)(4180 J/kg ^Co )

C = (2)(4180 J/ ^Co )

C = 8360 J/C ^o

3. Kupisa kwearuminiyamu chaiyo i900 J/kg C ^o . Kugona kupisa kwearuminiyamu ye2 gram…..

Zvinozivikanwa:

Kupisa kwearuminiyamu (c) = 900 J/kg C ^o = 9 x 10 ² J/kg C ^o

Huremu (m) = magiramu maviri = 2/1000 kg = 2/10 ³ kg = 2 x 10 ^-3 kg

Zvinodiwa: Kukwanisa kupisa (C)

Solution:

C = mc

C = (2 x 10 ^-3 kg)( 9 x 10 ² J/kg C ^o )

C = 18 x 10 ^-3 x 10 ² J/C ^o

C = 18 x 10 ^-1 J/C ^o

C = 1.8 J/C ^o

[wpdm_package id='710′]

1. Kuchinja zviyero zvekupisa
2. Linear kuwedzera
3. Kuwedzera kwenzvimbo
4. Kuwedzera inzwi
5. Heat
6. Kuenzana kwekupisa kwemuchina
7. Kupisa kwakananga uye kugona kupisa
8. Kupisa kwakahwanda, kupisa kwekusanganiswa, kupisa kwekupfuta
9. Kuchengetedza simba rekutamisa kupisa

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1. 2 kcal (kilogiramu c macalorie e ) = ….. c macalorie e?

mhinduro

1 kcal = 1000 kcal

2 kcal = 2 (1000 c macalorie e ) = 2000 c macalorie e

2. 4 C calorie e = ….. c calorie e?

mhinduro

1 Calori e ( a Capital C ) = 1 kcal = 1000 calori e

4 C calorie e = 4 (1000 c calorie e ) = 4000 c calorie e

3. 10 c calorie e = ….. Joule?

mhinduro

1 macalorie e = 4.186 Joules

10 c macalorie e = 10 (4.186 Joules) = 41.86 Joules

[irp]

4. 5 kcal = ….. Joule ?

mhinduro

1 kcal = 1000 c alorie = 4186 Joules

5 kcal = 5 (4186 Joules) = 20930 Joules

5. Majoules 2000 = ….. k cal?

mhinduro

4186 Joules = 1 kcal

8372 Joules = 8372 / 4186 = 2 kcal

2000 Joules = 2000 / 4186 = 0.4777 kcal

[wpdm_package id='706′]

1. Kuchinja zviyero zvekupisa
2. Linear kuwedzera
3. Kuwedzera kwenzvimbo
4. Kuwedzera inzwi
5. Heat
6. Kuenzana kwekupisa kwemuchina
7. Kupisa kwakananga uye kugona kupisa
8. Kupisa kwakahwanda, kupisa kwekusanganiswa, kupisa kwekupfuta
9. Kuchengetedza simba rekutamisa kupisa

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9 Kupisa Kuwanda Kupisa Kwakasiyana Kuchinja kwekupisa - Matambudziko neMhinduro

1. Mutobvu we2 kg unodziiswa kubva 50^oC kuti 100^oC. The kupisa chaiko yemutobvu ndeye 130 J.kg^{-1 o}C^-1. Ngani kupisa inotorwa nemutobvu?

Zvinozivikanwa:

Huremu (m) = 2 kg

Kupisa chaiko (c) = 1 3 0 J.kg ^-1 C ^-1

Kuchinja kwetembiricha ( Δ T) = 100 ^o C – 50 ^o C = 50 ^o C

Kudiwa: Kupisa (Q)

Solution:

Q = mc Δ T

Q = kupisa , m = uremu, c = kupisa chaiko , Δ T = shanduko yekupisa

Kupisa kunotorwa nemutobvu:

Q = (2 kg)(1 3 0 J.kg ^-1 C ^-1 )(50 ^o C)

Q = (100)(1 3 0)

Q = 1 3,000 Joules

Q = 1.3 x ¹⁰⁴ Joules

[irp]

2. Kupisa kwemhangura chaiyo i390 J/k g ^o C, kuchinja kwekupisa i40 ^o C. Kana mhangura ikatora 40 Joules yekupisa, huremu hwemhangura hwakaita sei!

Zvinozivikanwa:

Kupisa kwemhangura (c) = 390 J/k g ^o C

Kuchinja kwetembiricha ( ΔT ) = 40 ^o C

Kupisa ( Q) = 40 J

Zvinodiwa: Huremu (m) hwemhangura

Solution:

Q = mc Δ T

40 J = (m)( 390 J/k g ^o C)(40 ^o C)

40 = (m)( 390 /k g)(40)

40 = (m)( 390 /kg )(4)

40 = (m)( 1560/kg )

m = 40 / 1560

m = 0.026 kg

m = magiramu makumi maviri nematanhatu

3. Tembiricha yekutanga yemagiramu makumi maviri emvura i30 ^o C. Kupisa kwemvura chaiyo i1 cal g ^{-1 o} C ^-1 . Kana mvura ikatora macalorie mazana matatu ekupisa, sarudza tembiricha yekupedzisira!

Zvinozivikanwa:

Huremu (m) = 20 gr

Tembiricha yekutanga (T1 ₎ = 30 ^o C

Kupisa kwemvura chaiyo (c) = 1 cal gr ^{-1 o} C ^-1

Kupisa (Q) = 300 cal

Zvinodiwa: Tembiricha yekupedzisira yemvura

Solution:

Q = mc ΔT

300 cal = (20 gr)( 1 cal gr ^{-1 o} C ^-1 )( T ₂ -30 )

300 = (20)(1)( T ₂ -30)

300 = 20 ( T ₂ -30 )

300 = 20 T ₂ - 600

300 + 600 = 20T ₂

900 = 20T ₂

T ₂ = 900 / 20

T ₂ = 45

Kuchinja kwekupisa kuri pakati pe45 ^° C – 30 ^° C = 15 ^° C.

 [irp]

4. Tkuchinja kwekupisa yemvura yegungwa is 1^oC mvura painotora maJoules mazana matatu nemapfumbamwe ekupisa. Kupisa kwemvura yegungwa ndiko 3.9 × 10³ J/kg°C, chii chinonzi huremu hwemvura yegungwa.

Zvinozivikanwa:

Kuchinja kwetembiricha ( ΔT ) = 1 ^o C

Kupisa (Q) = 3900 Joule

Kupisa kwemvura yegungwa (c) = 3.9 x 10 ³ J/ k g°C = 3900 J/Kg°C

Zvinodiwa: Misa (m)

Solution:

Q = mc Δ T

Q = kupisa , m = huremu, c = kupisa kwakananga , Δ T = shanduko yekupisa

m = Q / c Δ T = 3900 / (3900)(1) = 3900 / 3900 = 1 kg

5. Mhangura ye2-kg inonwisa 39,000 J yekupisa pa30°C. Kana kupisa kwemhangura kuri 390 J/kg °C, tembiricha yekupedzisira yemhangura ndeyei…

Zvinozivikanwa:

Huremu (m) = 2 kg

Tembiricha yekutanga (T ₁ ) = 30 ^o C

Kupisa (Q) = 39,000 Joule

Kupisa kwakananga (c) kwemhangura = 390 J/kg ^o C

Zvinodiwa : Tembiricha yekupedzisira ( _T2 )

Solution:

Q = mc ΔT

Q = kupisa , m = huremu, c = kupisa kwakananga , ΔT = shanduko yekupisa

Q = mc ΔT = mc (T ₂ – T ₁ )

39,000 = (2)( 390)(T ₂ - 30)

100 = (2)(1)(T ₂ - 30)

100 = (2)(T ₂ - 30)

50 = T ₂ - 30

T ₂ = 50 + 30

T ₂ = 80 ^o C

[irp]

6. Mvura ine 5 -kg inodziiswa kubva pa15°C kusvika 40°C. Chii chinonzi kupisa kunotorwa nemvura. Kupisa kwemvura chaiyo i4.2 × 10 ³ J/Kg° C.

Zvinozivikanwa:

Huremu (m) = 5 kg

Tembiricha yekutanga (T1 ₎ = 15°C

Kupisa kwekupedzisira (T2 ₎ = 40°C

Kupisa kwemvura chaiyo (c) = 4.2 × 10 ³ J/kg° C

Kudiwa: Kupisa (Q)

Solution:

Q = mc ΔT

Q = (5 kg)( 4.2 × 10 ³ J/kg°C)(40°C – 15°C)

Q = (5)( 4.2 × 10 ³ J)(25)

Q = 525 x 10 ³ J

Q = 525,000 Joule

7. Mvura ine 2 -kg inodziiswa kubva pa24°C kusvika 90°C. Chii chinonzi kupisa kunotorwa nemvura. Kupisa kwemvura chaiyo i4.2 × 10 ³ J/Kg° C.

Zvinozivikanwa:

Huremu (m) = 2 kg

Tembiricha yekutanga (T1 ₎ = 24°C

Kupisa kwekupedzisira (T2 ₎ = 90°C

Kupisa kwemvura chaiyo (c) = 4,200 Joules/kg°C

Kudiwa :: Kupisa (Q)

Solution:

Q = m c ΔT

Q = (2 kg)( 4,200 Joules/kg°C)(90°C – 24°C)

Q = (2 kg)( 4,200 Joules/kg°C)(66°C)

Q = (132)( 4,200 Joules)

Q = 554,400 Joule

[irp]

8. Mvura ine magiramu mashanu inodziiswa kubva pa10°C kusvika 40°C. Chii chinonzi kupisa kunotorwa nemvura. Kupisa kwemvura chaiyo i1 × 10 ³ cal / g r ° C.

Zvinozivikanwa:

Huremu (m) = magiramu makumi maviri

Tembiricha yekutanga (T ₁ ) = 10 ^o C

Kupisa kwekupedzisira (T2 ₎ = 40 ^o C

Kupisa kwemvura chaiyo (c) = 1 c al/ gr°C

Kudiwa : Kupisa

Solution:

Q = mc ΔT

Q = (5 gramu)( 1 cal/ gr°C)(40 ^o C – 10 ^o C)

Q = (5)( 1 c al)(30)

Q = 150 makoriyori

9. Mvura ine 0.2 -kg inonwisa 42,000 Joules yekupisa pa25 ^o C. Kupisa kwemvura chaiyo i4200 J/kg ^o C, chii chinonzi tembiricha yekupedzisira yemvura.

Zvinozivikanwa:

Huremu hwemvura (m) = 0.2 kg

Kupisa (Q) = 42,000 Joule

Kupisa kwemvura chaiyo (c) = 4200 J/kg ^o C

Tembiricha yekutanga (T ₁ ) = 25 ^o C

Zvinodiwa: Tembiricha yekupedzisira ( _T2 )

Solution:

Q = mc ΔT = mc (T ₂ – T ₁ )

Mubvunzo = kupisa, m = huremu, c = kupisa chaiko, ΔT = kuchinja kwekupisa, T₁ = tembiricha yekutanga, T₂ = tembiricha yekupedzisira

Q = mc (T ₂ - T ₁ )

42,000 = (0.2)(4200)(T ₂ - 25)

42,000 = 840 (T ₂ - 25)

42,000 = 840 T ₂ - 21,000

42,000 + 21,000 = 840 T ₂

63,000 = 840 T ₂

T ₂ = 63,000 / 840

T ₂ = 75 ^o C

1. Kuchinja zviyero zvekupisa
2. Linear kuwedzera
3. Kuwedzera kwenzvimbo
4. Kuwedzera inzwi
5. Heat
6. Kuenzana kwekupisa kwemuchina
7. Kupisa kwakananga uye kugona kupisa
8. Kupisa kwakahwanda, kupisa kwekusanganiswa, kupisa kwekupfuta
9. Kuchengetedza simba rekutamisa kupisa

Read more

Kukura kwemutsetse kunongowanikwa nezvinhu zvakasimba chete; kuwedzera kwevhoriyamu kunowanikwa nezvinhu zvese, zvese zvakasimba, zvemvura, uye zvegasi. Kukura kwevhoriyamu kwakafanana nekukura kwemutsetse.

Tsananguro: Vo _o = Vhoriyamu yekutanga, V = Vhoriyamu yekupedzisira, ΔV = V – Vo _o = Kuchinja kwevhoriyamu, To _o = Tembiricha yekutanga, T = Tembiricha yekupedzisira, ΔT = T – To _o = Kuchinja kwetembiricha, β = chiyero chekuwedzera kwevhoriyamu. Zvikamu zve β = ( ^Co ) ^-1

[irp]

Equation yekuwedzera vhoriyamu iri pamusoro apa inoshanda chete kana shanduko muhuwandu hwezvinhu (zvese zvakasimba, zvemvura, uye zvegasi) dziri diki pane vhoriyamu yekutanga yechinhu. Kana shanduko muhuwandu hwechinhu yakakura kupfuura vhoriyamu yekutanga yechinhu, equation yekuwedzera vhoriyamu haipe mhedzisiro chaiyo. Kazhinji, shanduko muhuwandu hunowanikwa nezvinhu zvakasimba hadzisi dzakanyanya kukura. Kune rumwe rutivi, coefficient yekuwedzera vhoriyamu yemvura negasi yakakura. Coefficient yekuwedzera vhoriyamu yezvinhu zvine gasi iri nyorewo kuchinja kana tembiricha ikachinja. Saka fomura iri pamusoro inoshandiswa chete pakuwedzera kwezvinhu zvakasimba.

[irp]

1. Pa30 ^o C, vhoriyamu yesphere yearuminiyamu i30 cm ^3. Iyo coefficient yekuwedzera kwemutsara i24 x 10 ^{-6 o} C ^-1 . Kana vhoriyamu yekupedzisira iri 30.5 cm ³ , tembiricha yekupedzisira yesphere yearuminiyamu ndeyei?

Zvinozivikanwa:

Kuwanda kwekuwedzera kwemutsara ( α ) = 24 x 10 ^{-6 o} C ^-1

Kuwanda kwehuwandu ( β ) = 3 α = 3 x 24 x 10 ^{-6 o} C ^-1 = 72 x 10 ^{-6 o} C ^-1

Tembiricha yekutanga (T1 ₎ = 30 ^o C

Vhoriyamu yekutanga (V ₁ ) = 30 cm ³

Vhoriyamu yekupedzisira (V ₂ ) = 30.5 cm ³

Kuchinja kwevhoriyamu ( Δ V) = 30.5 cm ³ – 30 cm ³ = 0.5 cm ³

Zvinodiwa: Tembiricha yekupedzisira ( _T2 )

Solution:

Δ V = β (V ₁ )( ΔT )

Δ V = β (V ₁ )(T ₂ – T ₁ )

0.5 masendimita³ = (72 X 10^{-6 o}C^-1)(30 cm³)(T)₂ - 30^oC)

0.5 = (2160 x 10 ^-6 ) (T ₂ – 30 )

0.5 = (2.160 x 10 ^-3 ) (T 2 – 30 )

0.5 = (2.160 x 10 ^-3 ) (T ₂ – 30 )

0.5 / (2.160 x 10 ^-3 ) = T ₂ – 30

0.23 x 10 ³ = T ₂ – 30

0.23 x 1000 = T ₂ – 30

230 = T ₂ - 30

230 + 30 = T ₂

T ₂ = 260 ^o C

[irp]

2. Kuwanda kwekuwedzera kwesimbi mumutsara wemutsara i9 x 10 ^{-6 o} C ^-1 . Dhayamita yemukati yesimbi mu20 ^o C i2.2 cm. Kana dhayamita yekupedzisira iri 2.8 cm, tembiricha yekupedzisira ndeyei!

Zvinozivikanwa:

Kuwanda kwekuwedzera kwemutsara ( α ) = 9 x 10 ^{-6 o} C ^-1

Kuwanda kwehuwandu ( β) = 3 α = 3 x 9 x 10 ^{-6 o} C ^-1 = 27 x 10 ^{-6 o} C ^-1

Tembiricha yekutanga (T1 ₎ = 20 ^o C

Dhayamita yekutanga (D ₁ ) = 2.2 cm

Dhayamita yekupedzisira (D ₂ ) = 2.8 cm

Radiyo yekutanga (r ₁ ) = D ₁ / 2 = 2.2 cm ³ / 2 = 1.1 cm ³

Radiyo yekupedzisira (r ₂ ) = D ₂ / 2 = 2.8 cm ³ / 2 = 1.4 cm ³

Vhoriyamu yekutanga (V ₁ ) = 4/3 π r ₁ ³ = (4/3)(3.14)(1.1 cm) ³ = (4/3)(3.14)(1.331 cm ³ ) = 5.57 cm ³

Vhoriyamu yekupedzisira (V ₂ ) = 4/3 π r ₂ ³ = (4/3)(3.14)(1.4 cm) ³ = (4/3)(3.14)(2.744 cm ³ ) = 11.48 cm ³

Kuchinja kwevhoriyamu ( Δ V) = 11.48 cm ³ – 5.57 cm ³ = 5.91 cm ³

Zvinodiwa: Tembiricha _{yekupedzisira} ( T2 )

Solution:

Δ V = β (V ₁ )( ΔT )

5.91 masendimita³ = (27 X 10^{-6 o}C^-1)(5.57 masendimita³)(T)₂ - 20^oC)

5.91 = (150.39 x 10 ^-6 ) (T ₂ - 20)

5.91 / 150.39 x 10 ^-6 = T ₂ – 20

0.039 x 10 ⁶ = T ₂ – 20

39 x 10 ³ = T ₂ – 20

39,000 = T ₂ - 20

39,000 + 20 = T ₂

T ₂ = 39,020 ^o C

3. A 2000-cm³ aluminium mudziyo, yakazadzwa nemvura pa 0^oC. Uye wobva wadziisa kusvika pa90^oC. Kana chiyero chekuwedzera kwearuminiyamu chiri 24 x 10^-6 (^oC)^-1 uye chiyero chekuwedzera kwehuwandu hwemvura i6.3 x 10^-4 (^oC)^-1, tarisa huwandu hwemvura yadeuka.

Zvinozivikanwa:

Vhoriyamu yekutanga yemudziyo wearuminiyamu nemvura (Vo ₎ = 2000 cm ³ = 2 x 10 ³ cm ³

Kupisa kwekutanga kwemudziyo wearuminiyamu nemvura (T1 ₎ = 0 ^o C

Kupisa kwekupedzisira kwemudziyo wearuminiyamu nemvura (T2 ₎ = 90 ^o C

Kuwanda kwekuwedzera kwearuminiyamu (α) = 24 x 10 ^-6 ( ^o C ) ^-1

Kuwedzerwa kwehuwandu hwearuminiyamu (γ) = 3α = 3 (24 x 10 ^-6 ( ^o C ) ^-1 ) = 72 x 10 ^{-6 o} C ^-1

Kuwanda kwehuwandu hwemvura (γ) = 6.3 x 10 ^-4 ( ^o C ) ^-1

Zvinodiwa: Huwandu hwemvura yakadururwa

Solution:

Kuenzanisa kwekuwedzera kwevhoriyamu:

V = Vo _o + γ Vo _o ΔT

V – Vo _o = γ Vo _o ΔT

ΔV = γ V _o ΔT

V = vhoriyamu yekupedzisira, Vo ₌ vhoriyamu yekutanga, ΔV = shanduko muvhoriyamu, γ = chiyero chekuwedzera kwevhoriyamu, ΔT = shanduko mukupisa

Verenga shanduko yehuwandu hwechirongo chearuminiyamu:

ΔV = γ Vo _o ΔT = (72 x 10 ^-6 )(2 x 10 ³ )(90) = 12960 x 10 ^-3 = 12.960 cm ³

Verenga shanduko muhuwandu hwemvura:

ΔV = γ Vo _o ΔT = (6. 3 x 10 ^-4 )(2 x 10 ³ )(90) = 1134 x 10 ^-1 = 113.4 cm ³

Kuchinja kwehuwandu hwemvura kwakakura kupfuura mudziyo wearuminiyamu zvekuti mvura inodururwa.

Verenga huwandu hwemvura yakadururwa:

113.4 cm ³ – 12.960 cm ³ = 100.44 cm ³

[wpdm_package id='702′]

1. Kuchinja zviyero zvekupisa
2. Linear kuwedzera
3. Kuwedzera kwenzvimbo
4. Kuwedzera inzwi
5. Heat
6. Kuenzana kwekupisa kwemuchina
7. Kupisa kwakananga uye kugona kupisa
8. Kupisa kwakahwanda, kupisa kwekusanganiswa, kupisa kwekupfuta
9. Kuchengetedza simba rekutamisa kupisa

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1. Pa 20 ^o C, kureba kwepepa resimbi i50 cm uye upamhi i30 cm. Kana coefficient yekuwedzera kwemutsara wesimbi iri 10 ^{-5 o} C ^-1 , sarudza shanduko munzvimbo nenzvimbo yekupedzisira pa60 ^o C.

Zvinozivikanwa:

Tembiricha yekutanga (T1 ₎ = 20 ^o C

Tembiricha yekupedzisira (T2 ₎ = 60 ^o C

Kuchinja kwetembiricha ( ΔT ) = 60 ^o C – 20 ^o C = 40 ^o C

Nzvimbo yekutanga (A ₁ ) = kureba x upamhi = 50 cm x 30 cm = 1500 cm ²

Kuwanda kwekuwedzera kwesimbi ( α) = 10 ^{-5 o} C ^-1

Chikamu chekuwedzera kwenzvimbo yesimbi ( β) = 2α = 2 x 10 ^{-5 o} C ^-1

Zvinodiwa: Kuchinja kwenzvimbo ( ΔA )

Solution:

Kuchinja kwenzvimbo ( ΔA ):

ΔA = β A ₁ ΔT

ΔA = ( 2 x 10 ^{-5 o} C ^-1 )(1500 cm ² )(40 ^o C)

ΔA = (80 x 10 ^-5 )(1500 cm ² )

ΔA = 1 20,000 x 10 ^-5 cm ²

ΔA = 1. 2 x 10 ⁵ x 10 ^-5 masendimita ²

ΔA = 1.2 cm ²

Nzvimbo yekupedzisira ( _A2 ) :

A ₂ = A ₁ + ΔA

A ₂ = 1500 cm ² + 1. 2 cm ²

A ₂ = 1501 . 2 cm ²

[irp]

2. Pa30 ^o C, nzvimbo yepepa rearuminiyamu i40 cm ² uye coefficient yekuwedzera kwemutsara i24 x 10 ^-6 / ^o C. Sarudza tembiricha yekupedzisira kana nzvimbo yekupedzisira iri 40.2 cm ².

Zvinozivikanwa:

Tembiricha yekutanga (T1 ₎ = 30 ^o C

Kuwanda kwekuwedzera kwemutsara ( α) = 24 x 10 ^{-6 o} C ^-1

Chikamu chekuwedzera kwenzvimbo ( β) = 2a = 2 x 24 x 10 ^{-6 o} C ^-1 = 48 x 10 ^{-6 o} C ^-1

Nzvimbo yekutanga (A ₁ ) = 40 cm ²

Nzvimbo yekupedzisira (A ₂ ) = 40.2 cm ²

Kuchinja kwenzvimbo ( ΔA) = 40.2 cm ² – 40 cm ² = 0.2 cm ²

Zvinodiwa: Tsvaga tembiricha yekupedzisira (T ₂ )

Solution:

Fomura yekuchinja kwenzvimbo ( ΔA) :

ΔA = β A ₁ Δ T

Tembiricha yekupedzisira (T2 ₎ :

ΔA = β A ₁ (T ₂ – T ₁ )

0.2 masendimita² = (48 x 10^{-6 o}C^-1)(40 cm)²)(T₂ - 30^oC)

0.2 = (1920 x 10 ^-6 ) (T ₂ - 30 )

0.2 = (1.920 x 10 ^-3 ) (T ₂ - 30)

0.2 = (2 x 10 ^-3 ) (T ₂ - 30)

0.2 / (2 x 10 ^-3 ) = T ₂ – 30

0.1 x 10 ³ = T ₂ – 30

1 x 10 ² = T ₂ – 30

100 = T ₂ - 30

100 + 30 = T ₂

T ₂ = 130

Tembiricha yekupedzisira = 130 ^o C

[irp]

3. Radiyumu yerin'i pa20 ^o C iri 20 cm. Kana radiyumu yekupedzisira pa100 ^o C iri 20.5 cm, sarudza coefficient yekuwedzera kwenzvimbo uye coefficient yekuwedzera kwemutsara…

Zvinozivikanwa:

Tembiricha yekutanga (T1 ₎ = 30 ^o C

Tembiricha yekupedzisira (T2 ₎ = 100 ^o C

Kuchinja kwetembiricha ( ΔT ) = 100 ^o C – 30 ^o C = 70 ^o C

Radiyo yekutanga (r ₁ ) = 20 cm

Radiyo yekupedzisira (r ₂ ) = 20.5 cm

Zvinodiwa: Chiyero chekuwedzera kwenzvimbo ( β )

Solution:

Nzvimbo yekutanga (A ₁ ) = π r ₁ ² = (3.14)(20 cm) ² = (3.14)(400 cm ² ) = 1256 cm ²

Nzvimbo yekupedzisira (A ₂ ) = π r ₂ ² = (3.14)(20.5 cm) ² = (3.14)(420.25 cm ² ) = 1319.585 cm ²

Kuchinja kwenzvimbo ( ΔA) = 1319.585 cm ² – 1256 cm ² = 63.585 cm ²

Fomura yekuchinja kwenzvimbo ( ΔA) :

ΔA = β A ₁ ΔT

Kuwanda kwenzvimbo:

ΔA = β A ₁ ΔT

63.585 cm ² = b (1 256 cm ² )(70 ^o C)

63.585 = b ( 87,920 ^o C)

β = 63.585 / 87,920 ^o C

β = 0.00072 / ^o C

β = 7.2 x 1 0 ^-4 / ^o C

β = 7.2 x 1 0 ^{-4 o} C ^-1

Kuwanda kwekuwedzera kwemutsara ( α ):

β = 2 α

α = β / 2

α = (7.2 x 1 0 ^-4 ) / 2

α = 3.6 x 1 0 ^{-4 o} C ^-1

[wpdm_package id='698′]

1. Kuchinja zviyero zvekupisa
2. Linear kuwedzera
3. Kuwedzera kwenzvimbo
4. Kuwedzera inzwi
5. Heat
6. Kuenzana kwekupisa kwemuchina
7. Kupisa kwakananga uye kugona kupisa
8. Kupisa kwakahwanda, kupisa kwekusanganiswa, kupisa kwekupfuta
9. Kuchengetedza simba rekutamisa kupisa

Read more