Mavuto Othetsedwa mu Fiziki Yoyambira

1. Mpira wa 0.2-kg, wolumikizidwa kumapeto kwa chingwe chopingasa, umazunguliridwa mu bwalo la radius ya mita imodzi ndipo liwiro lalikulu la mpira ndi 10 rpm. Kodi kukula kwa kuthamanga kwa centripetal ndi kukula kwa mphamvu yokakamiza ndi kotani?

Zodziwika:

Kulemera (m) = 0.2 kg

Ulalo wozungulira (r) = 1 m

Liwiro la angular (ω) = 10 rev/min = 10 rev/60 s = 0.17 rev/s = (0.17)(6.28 rad)/s = 1 rad/s

Liwiro (v) = r ω = (1 m)(1 rad/s) = 1 m/s

Ankafuna: a _s ndi Σ F

Yankho:

(a) Kukula kwa kuthamanga kwa centripetal

(b) Kukula kwa mphamvu ya kukakamira

Σ F = ma

T = ma _s

T = (0.2 kg)(1 m/s ² )

T = 0.2 kg m/s ²

T = 0.2 N

[irp]

2. Mpira wa 1 kg kumapeto kwa chingwe ukuzungulira mofanana mu bwalo lozungulira la radius 1 m. Chingwecho chidzasweka pamene mphamvu yake ikupitirira 100 N. Kodi liwiro lalikulu lomwe mpirawo ungakhale nalo ndi lotani?

Zodziwika:

Kulemera (m) = 1 kg

Ulalo wozungulira (r) = mita imodzi

Mphamvu yamphamvu (T) = mphamvu yapakati ( Σ F) = 100 N

Akufuna: v maximum

Yankho:

[irp]

[wpdm_package id='499′]

1. Kulemera ndi kulemera
2. mphamvu yachibadwa
3. Lamulo lachiwiri la Newton la kayendedwe
4. Mkangano mphamvu
5. Kuyenda pamalo opingasa popanda mphamvu yokangana
6. Kuyenda kwa matupi awiri okhala ndi kuthamanga komweko pamalo opingasa ndi mphamvu yokangana
7. Kuyenda pa ndege yopendekeka popanda mphamvu yokangana
8. Kuyenda pa ndege yokhotakhota ndi mphamvu yokangana
9. Kuyenda mu elevator
10. Kuyenda kwa matupi kumalumikizidwa ndi zingwe ndi ma pulleys
11. Matupi awiri omwe ali ndi kukula kofanana kwa kuthamanga
12. Kuzungulira makona osalala - mphamvu ya kayendedwe kozungulira
13. Kuzungulira mkombero wozungulira - mphamvu ya kuyenda kozungulira
14. Kuyenda kofanana mozungulira mopingasa
15. Mphamvu yapakati yozungulira yofanana

Werengani zambiri

1. Galimoto yozungulira makona ozungulira. Kodi ngodya ya msewu womwe uli ndi makona ozungulira a mamita 60 ndi liwiro lopangidwa la 20 m/s ndi yotani? Tiyerekeze kuti palibe ayambitsenso pakati pa galimoto ndi msewu.

Anakonza

N= mphamvu yachibadwa

N sin θ = gawo lopingasa la mphamvu yachibadwa

N cos θ = gawo loyima la mphamvu yachibadwa

w = mg = kulemera kwa galimoto

Msewuwu wapangidwa kuti ukhale ndi magombe kuti uchepetse kudalira kukangana.

Mphamvu yopingasa yolunjika, gawo lopingasa la mphamvu yachibadwa ( N sin θ) , imafunika kuti galimoto iyende mozungulira mozungulira.

Timasankha x-axis ngati yopingasa ndi y-axis ngati yoyima, kotero kuti kufulumira kwapakati,_R, ili motsatira njira yopingasa. Mu njira yopingasa, mphamvu yokhayo ndi gawo lopingasa la mphamvu yachibadwa (N tchimo θ), yofunikira kuti ipange kuthamanga kwapakatiN sin θ = mphamvu yapakati.

Gwiritsani ntchito lamulo la Newton la kuyenda molunjika mbali imodzi:

[irp]

Gwiritsani ntchito lamulo la Newton la kuyenda molunjika mbali yopingasa:

M'malo mwa N mu equation 1 mu N mu equation 2 :

[wpdm_package id='497′]

1. Kulemera ndi kulemera
2. mphamvu yachibadwa
3. Lamulo lachiwiri la Newton la kayendedwe
4. Mkangano mphamvu
5. Kuyenda pamwamba mopingasa popanda mphamvu yokangana
6. Kuyenda kwa matupi awiri omwe ali ndi kuthamanga komweko pamalo opingasa ndi mphamvu yokangana
7. Kuyenda pa ndege yopendekeka popanda mphamvu yokangana
8. Kuyenda pa ndege yokhotakhota ndi mphamvu yokangana
9. Kuyenda mu elevator
10. Kuyenda kwa matupi kumalumikizidwa ndi zingwe ndi ma pulleys
11. Matupi awiri omwe ali ndi kukula kofanana kwa kuthamanga
12. Kuzungulira makona osalala - mphamvu ya kayendedwe kozungulira
13. Kuzungulira mkombero wozungulira - mphamvu ya kuyenda kozungulira
14. Kuyenda kofanana mozungulira mopingasa
15. Mphamvu yapakati yozungulira yofanana

Werengani zambiri

1. Galimoto yolemera makilogalamu 2000 imazungulira curve pamsewu wathyathyathya wa radius 150 m. Coefficient of static friction ndi 0.5. Dziwani liwiro lalikulu kuti galimotoyo itsatire curve ndipo isagwedezeke. Kuthamanga chifukwa cha mphamvu yokoka = 10 m/s ².

Zodziwika:

Kulemera (m) = 2000 kg

Ulalo wozungulira (r) = mamita 150

Koyefifiti ya kukangana kosasinthasintha ( μs ₎ = 0.5

Kulemera (w) = mg = (2000 kg)(10 m/s ² ) = 20,000 kg m/s ² = 20,000 N

Mphamvu ya kukangana kosasunthika (F _s ) = μ _s N = μ _s w = (0.7) (20,000 N) = 14,000 N

Ankafuna: v

Yankho:

[irp]

[wpdm_package id='496′]

1. Kulemera ndi kulemera
2. mphamvu yachibadwa
3. Lamulo lachiwiri la Newton la kayendedwe
4. Mkangano mphamvu
5. Kuyenda pamwamba mopingasa popanda mphamvu yokangana
6. Kuyenda kwa matupi awiri omwe ali ndi kuthamanga komweko pamalo opingasa ndi mphamvu yokangana
7. Kuyenda pa ndege yopendekeka popanda mphamvu yokangana
8. Kuyenda pa ndege yokhotakhota ndi mphamvu yokangana
9. Kuyenda mu elevator
10. Kuyenda kwa matupi kumalumikizidwa ndi zingwe ndi ma pulleys
11. Matupi awiri omwe ali ndi kukula kofanana kwa kuthamanga
12. Kuzungulira makona osalala - mphamvu ya kayendedwe kozungulira
13. Kuzungulira mkombero wozungulira - mphamvu ya kuyenda kozungulira
14. Kuyenda kofanana mozungulira mopingasa
15. Mphamvu yapakati yozungulira yofanana

Werengani zambiri

1. Zidutswa ziwiri m ₁ = 2 kg ndipo m _{2 = 5 kg} zili pamalo opendekera ndipo zalumikizidwa pamodzi ndi chingwe monga momwe zasonyezedwera pachithunzichi. Chiŵerengero cha chi _...

(a) Dziwani kufulumira kwawo

(b) Dziwani mphamvu ya kukakamira

Zodziwika:

Kulemera 1 (m ₁ ) = 2 kg

Kulemera 2 (m2 ₎ = 4 kg

Koefficient ya kinetic friction pakati pa m ₁ ndi plane yopendekeka (μ _k1 ) = 0.2

Koefficient ya kinetic friction pakati pa m2 _ndi plane yopendekeka (μ _k2 ) = 0.1

Kuthamanga chifukwa cha mphamvu yokoka (g) = 9.8 m/s ²

a) Kukula ndi komwe kumayambira kuthamanga kwa liwiro

w ₁ = kulemera 1 = m ₁ g = (2 kg)(9.8 m/s ² ) = 19.6 Newtons

w _1x = w ₁ sin 30 ^o = (19.6 N)(0.5) = 9.8 Newtons

w _1y = w ₁ cos 30 ^o = (19.6 N)(0.87) = 17 Newtons

N ₁ = Mphamvu yachibadwa pa m ₁ = w _1y = 17 Newtons

F _k1 = Mphamvu ya kukangana kwa kinetic pa m ₁ = μ _k1 N ₁ = (0.2)(17 N) = 3.4 Newtons

---

w ₂ = kulemera 2 = m ₂ g = (4 kg)(9.8 m/s ² ) = 39.2 Newtons

w _2x = w ₂ tchimo 60 ^o = (39.2 N) (0.87) = 34.1 Newtons

w _2y = w ₂ cos 60 ^o = (39.2 N)(0.5) = 19.6 Newtons

N ₂ = Mphamvu yachibadwa pa m ₂ = w _2y = 19.6 Newtons

F _k2 = Mphamvu ya kukangana kwa kinetic pa m ₂ = μ _k2 N ₂ = (0.1)(19.6 N) = 1.96 Newtons

---

Kukula kwa kuthamanga kwa magazi:

∑ F _x = _max

w _2x > w _1x kotero njira yoyendetsera liwiro ndi yofanana ndi njira ya w _2x.

Mphamvu zomwe zimayang'ana pa kuthamanga kwa magazi ndi zabwino ndipo mphamvu zomwe zili ndi mbali yosiyana ndi kuthamanga kwa magazi ndi zoipa.

w_2x - F_k2 - T₂ + T₁ - w_1x - F_k1 = (m₁ +m₂) ndi_x

w _2x – F _k2 – w _1x – F _k1 = (m ₁ + m ₂ ) a _x

34.1 N – 1.96 N – 9.8 N – 3.4 N = (2 kg + 4kg) a _x

18.94 N = (6 kg) a _x

a _x = 18.94 N : 6 kg

a _x = 3.16 m/s ²

Kukula kwa kuthamanga = 3.16 m/s ^2. Kuwongolera kuthamanga = njira ya T ₁ = njira ya w _2x

b) Kukula kwa mphamvu ya kukakamira

Gwiritsani ntchito lamulo lachiwiri la Newton pa chinthu 2:

w _2x – F _k2 – T ₂ = m ₂ a _x

34.1 N – 1.96 N – T ₂ = (4 kg) (3.16 m/s ² )

32.14 N – T ₂ = 12.64 N

T ₂ = 32.14 N – 12.64 N = 19.5 Newtons

Mphamvu ya kukakamira = T = T ₁ = T ₂ = 19.5 Newtons

[irp]

2. m ₁ = 4 kg, m ₂ = 2 kg. Dziwani (a) kukula ndi komwe kumayambira kuthamanga (b) Kukula kwa mphamvu yokakamiza yomwe imalumikiza m ₁ ndi m ₂ (c) kukula kwa mphamvu yokakamiza yomwe imalumikiza pulley ndi denga.

Anakonza

w ₁ = m ₁ g = (4 kg)(9.8 m/s ² ) = 39.2 Newtons

w ₂ = m ₂ g = (2 kg)(9.8 m/s ² ) = 19.6 Newtons

a) Kukula ndi komwe kumayambira kuthamanga kwa liwiro

∑ F _y = may _y

w ₁ > w ₂ kotero kuti njira ya chinthucho ndi yofanana ndi njira ya kulemera 1 ( w ₁ ) . Mphamvu zomwe zili ndi njira yofanana ndi njira yofulumira ndi zabwino ndipo mphamvu zomwe zili ndi njira yosiyana ndi njira yothamangira ndi zoipa.

w ₁ – T ₁ + T ₂ – w ₂ = (m ₁ + m ₂ ) a _y

w ₁ – w ₂ = (m ₁ + m ₂ ) a _y

39.2 N - 19.6 N = (4 kg + 2 kg) a _y

19.6 N = (6 kg) a _y

a _y = 19.6 N : 6 kg

a _y = 3.26 m/s ²

Kukula kwa kuthamanga = 3.26 m/s ^2. Kuwongolera kuthamanga = kulunjika kwa w ₁.

b) Kukula kwa mphamvu ya kukakamira yomwe imagwirizanitsa m ₁ ndi m ₂

Gwiritsani ntchito lamulo lachiwiri la Newton pa _m2 :

∑ F _y = may _y

w ₁ – T ₁ = m ₁ a _y

39.2 N – T ₁ = (4 kg)( 3.26 m/s ² )

39.2 N – T ₁ = 13.04 N

T ₁ = 39.2 N – 13.04 N

T ₁ = 26.16 Newton

Kukula kwa mphamvu yolumikizira zinthu = T = T ₁ = T ₂ = 26.16 Newtons

c) Kukula kwa mphamvu yolumikizira pulley ndi denga.

Pulley yapuma:

∑ F _y = may _y —— a _y = 0

∑ F _y = 0

Mphamvu zakukwera ndi zabwino, mphamvu zakutsika ndi zoipa:

T ₃ – T ₁ – T ₂ = 0

T3 = _T1 + _T2

T ₁ ndi T ₂ zili ndi kukula kofanana , T ₁ = T ₂ = T = 26.16 N:

T ₃ = 2T = 2(26.16 N) = 52.32 Newtons

[irp]

3. Block 1 (m ₁ = 10 kg) ndi block 2 (m ₂ = 15 kg) zolumikizidwa ndi chingwe pamwamba pa pulley yopanda kukangana. Coefficient ya kukangana kosasinthasintha pakati pa block 2 yokhala ndi kupendekera = 0.6. Coefficient ya kukangana kwa kinetic pakati pa block 2 yokhala ndi kupendekera = 0.42. Dziwani (a) Kukula kwa mphamvu yocheperako F yomwe imagwiritsidwa ntchito pazinthu kuti zinthuzo zifulumizitse kupita mmwamba (b) Dziwani kukula kwa mphamvu yokangana.

Anakonza

w ₁ = Kulemera kwa chipika 1 = m ₁ g = (10 kg)(9.8 m/s ² ) = 98 Newtons

w ₂ = Kulemera kwa chipika 2 = m ₂ g = (15 kg)(9.8 m/s ² ) = 147 Newtons

w _2y = w ₂ cos 30 ^o = (147 N)(0.87) = 127.89 Newtons

w _2x = w ₂ tchimo 30 ^o = (147 N) (0.5) = 73.5 Newtons

N ₂ = Mphamvu yachibadwa pa boloko 2 = w _2y = 127.89 Newtons

F _k2 = Mphamvu ya kukangana kwa kinetic pa block 2 = μ _k2 N ₂ = (0.42)(127.89 N) = 53.7 Newtons

F _s2 = Mphamvu ya kukangana kosasinthasintha pa chipika 2 = μ _s2 N ₂ = (0.6)(127.89 N) = 76.7 Newtons

a) Kukula kwa mphamvu yochepa kwambiri ya F yomwe imagwiritsidwa ntchito pazinthuzo kotero kuti zinthuzo zidakwera mofulumira

∑ F _x = max _—— a _x = 0

∑ F _x = 0

Mphamvu zakumtunda ndi zakumanja ndi zabwino, mphamvu zakutsika ndi zakumanzere ndi zoipa.

F – F _k2 – w _2x – w ₁ – T ₂ + T ₁ = 0

F – F _k2 – w _2x – w ₁ = 0

F = F _k2 + w _2x + w ₁

F = 53.7 N + 73.5 N + 98 N

F = 225.2 Newton

b) Kukula kwa mphamvu ya kukangana

Gwiritsani ntchito lamulo la Newton la kayendedwe pa block 1:

∑ F _y = may _y —— a _y = 0

∑ F _y = 0

T ₁ – w ₁ = 0

T ₁ = w ₁ = 98 Newton

Gwiritsani ntchito lamulo la Newton la kayendedwe pa block 2:

F – F _k2 – w _2x – T ₂ = 0

T ₂ = F – F _k2 – w _2x

T ₂ = 225.2 N – 53.7 N – 73.5 N

T ₂ = 98 Newton

Kukula kwa mphamvu ya kukakamira = T ₁ = T ₂ = T = 98 Newtons

[irp]

4. Block 1 (m ₁ = 16 kg) ili pamalo opingasa ndipo block 2 (m ₂ = 12 kg) ili pamalo osalala, olumikizidwa ndi chingwe chomwe chimadutsa pa pulley yaying'ono, yopanda kukangana. Block 3 (m ₃ = 5 kg) ili pa block 2. Coefficient ya kinetic friction pakati pa block 2 ndi malo opingasa ndi 0,4. Coefficient ya static friction pakati pa block 2 ndi block 3 ndi 0,3.

(a) Pamene dongosololi latulutsidwa kuchokera pamalo opumulira, chipika 3 ndi chipika 2 zimangoyendabe pamodzi?

(b) Ngati pali chipika 3, kodi kuthamanga kwa chipika 1 ndi chipika 2 ndi kotani?

Yankho:

a) Dongosolo likatulutsidwa kuchokera pamalo opumulira, chipika 3 ndi chipika 2 zimangoyendabe pamodzi?

w ₁ = Kulemera kwa chipika 1 = m ₁ g = (16 kg)(9.8 m/s ² ) = 156.8 Newtons

w _1x = w ₁ sin 60 ^o = (156.8 N)(0.87) = 136.4 Newtons

w _1y = w ₁ cos 60 ^o = (156.8 N)(0.5) = 78.4 Newtons

N ₁ = Mphamvu yachibadwa yomwe imagwiritsidwa ntchito pa block 1 ndi ndege yopendekera = w _1y = 78.4 Newtons

w ₃ = Kulemera kwa chipika 3 = m ₃ g = (5 kg)(9.8 m/s ² ) = 49 Newtons

N ₂₃ = Mphamvu yachibadwa yomwe imagwiritsidwa ntchito pa chipika 3 ndi chipika 2 = w ₃ = 49 Newtons

N ₃₂ = Mphamvu yachibadwa yomwe imagwiritsidwa ntchito pa chipika 2 pafupi ndi chipika 3 = N ₂₃ = w ₃ = 49 Newtons

(N ₂₃ ndi N ₃₂ ndi awiri a zochita-zochita )

F _s23 = Mphamvu ya kukangana kosasinthasintha komwe kumachitika pa chipika 3 ndi chipika 2 = μ _s N ₂₃ = (0.3)(49 N) = 14.7 Newtons

F _s32 = Mphamvu ya kukangana kosasinthasintha komwe kumachitika pa chipika chachiwiri ndi chipika chachitatu = F _{s 23} = 14.7 Newtons

(F _s23 ndi F _s32 ndi awiri a zochita-zochita )

w ₂ = Kulemera kwa chipika 2 = m ₂ g = (12 kg)(9.8 m/s ² ) = 117.6 Newtons

N ₂ = Mphamvu yachibadwa yomwe imagwiritsidwa ntchito pa chinthu 2 ndi malo opingasa = w ₂ + N ₃₂ = 117.6 Newtons + 49

Newton = 166.6 Newton

F _k2 = Mphamvu ya kukangana kwa kinetic pa block 2 = μ _k N ₂ = (0.4)(166.6 N) = 66.64 Newtons

Gwiritsani ntchito lamulo la Newton la kayendetsedwe ka zinthu pa bolodi 3:

∑ F _x = _max

F _s23 = m ₃ a _x

—–> F_s23 = μ_s N₂₃ = μ_s w₃ = μ_s m₃ g

μ _s m ₃ g = m ₃ a _x

μ _s g = a _x

a _x = (0.3)(9.8 m/s ² ) = 2.94 m/s ²

Kuthamanga kwakukulu kwa chipika 3 kuti chipika 3 ndi chipika 2 zipitirire kutsetsereka pamodzi ndi 2.94 m/s ².

Tsopano tikuwerengera kukula kwa kuthamanga kwa dongosololi pambuyo poti latulutsidwa kuchoka pamalo opumulira.

Kulunjika kwa kusuntha kwa block = njira ya kufulumira kwa block = njira ya T ₂ = njira ya w _1x.

∑ F _x = _max

w_1x - T₁ + T₂ - F_k2 - F_s32 +F_s23 = (m₁ +m₂ +m₃) ndi_x

w _1x – F _k2 = (m ₁ + m ₂ + m ₃ ) a _x

136.4 N – 66.64 N = (16kg + 12kg + 5kg) a _x

69.76 N = (33 kg) a _x

a _x = 2.11 m/s ²

a _x ndi yabwino, kutanthauza kuti njira yolowera kusuntha kwa block kapena njira yolowera kufulumira ndi yofanana ndi njira ya T ₂ kapena njira ya w _1x.

Kukula kwa kuthamanga kwa mpweya ndi 2.11 m/s ² , kochepera 2.94 m/s ² kotero titha kunena kuti chipika 3 ndi chipika 2 zimangoyenda pamodzi zitatulutsidwa pamalo opumulira.

b) Kukula kwa kuthamanga kwa chipika 1 ndi chipika 2

∑ F _x = _max

w _1x – F _k2 = (m ₁ + m ₂ ) a _x

—–> F_k2 = μ_k N₂ = μ_k w₂ = μ_k m₂ g = (0.4)(12 kg)(9.8 m/s²) = 47.04 Newton

136.4 N – 47.04 N = (16kg + 12kg) a _x

89.36 N = (28 kg) a _x

a _x = 89.36 N : 28 kg = 3.19 m/s ²

[wpdm_package id='493′]

1. Kulemera ndi kulemera
2. mphamvu yachibadwa
3. Lamulo lachiwiri la Newton la kayendedwe
4. Mkangano mphamvu
5. Kuyenda pamwamba mopingasa popanda mphamvu yokangana
6. Kuyenda kwa matupi awiri omwe ali ndi kuthamanga komweko pamalo opingasa ndi mphamvu yokangana
7. Kuyenda pa ndege yopendekeka popanda mphamvu yokangana
8. Kuyenda pa ndege yokhotakhota ndi mphamvu yokangana
9. Kuyenda mu elevator
10. Kuyenda kwa matupi kumalumikizidwa ndi zingwe ndi ma pulleys
11. Matupi awiri omwe ali ndi kukula kofanana kwa kuthamanga
12. Kuzungulira makona osalala - mphamvu ya kayendedwe kozungulira
13. Kuzungulira mkombero wozungulira - mphamvu ya kuyenda kozungulira
14. Kuyenda kofanana mozungulira mopingasa
15. Mphamvu yapakati yozungulira yofanana

Werengani zambiri

1. Chipolopolo cha makilogalamu awiri chili pamalo otsetsereka mozungulira pa ngodya ya 37 ^o kupita mopingasa. Dziwani kukula kwa mphamvu yakunja yomwe imagwiritsidwa ntchito pa chipolopolocho, kuti chipolopolocho chisagwedezeke pansi. (sin 37 ^o = 0.6, cos 37 ^o = 0.8, g = 10 ms ^-2 , µ _k = 0.2)

Zodziwika:

Kulemera (m) = 2 kg

Kuthamanga chifukwa cha mphamvu yokoka (g) = 10 m/s ²

Kulemera kwa chipika (w) = mg = (2)(10) = 20 Newtons

Tchimo 37 ^o = 0.6

Cos 37 ^o = 0.8

Koyefifiti ya kukangana kwa kinetic (µ _k ) = 0.2

Gawo la y la kulemera (w _y ) = w cos 37 ^o = (20)(0.8) = 16 Newtons

Chigawo cha x cha kulemera (w _x ) = w sin θ = (20)(sin 37) = (20)(0.6) = 12 Newtons

mphamvu yachibadwa (N) = w _y = 16 Newtons

Kufunidwa : Mphamvu yakunja (F)

Yankho :

w_x = 12 Newton

Mphamvu ya kukangana kwa kinetic (f _k ) = µ _k N = (0.1)(16) = 1.6 Newtons

Kukula kwa mphamvu yakunja F yomwe idagwiritsidwa ntchito pa block :

F + f _k – w _x = 0

F = w _x – f _k

F = 12 – 1.6

F = 10.4 Newton

Mphamvu yakunja ya F ndi yaikulu kuposa 10.4 Newtons.

[irp]

2. Kulemera kwa chipika = 2 kg, coefficient of static friction µ _s = 0.4 ndi θ = 45 ^o . Dziwani kukula kwa mphamvu F kuti chipikacho chiyambe kutsetsereka mmwamba.

Zodziwika:

Chiŵerengero cha kukangana kosasinthasintha (µs ₎ = 0.4

Ngodya (θ) = 45 ^o

Kuthamanga chifukwa cha mphamvu yokoka (g) = 10 m/s ²

Kulemera kwa Block (m) = 2 kilogalamu

Kulemera kwa chipika (w) = mg = (2 kg)(10 m/s ² ) = 20 kg m/s ² = 20 Newtons

Chigawo cha x cha kulemera (w _x ) = w sin θ = (20)(sin 45) = (20)(0.5√2) = 10√2 Newtons

Gawo la y la kulemera (w _y ) = w cos θ = (20)(cos 45) = (20)(0.5√2) = 10√2 Ma Newton

Kufunidwa : Kukula kwa mphamvu F

Yankho:

Block imayamba kutsetsereka, ngati F ≥ w_x + f_s.

Chigawo cha x cha kulemera:

w _x = 10√2 Newton

gawo la y la kulemera :

w _y = 10√2 Newton

Mphamvu yachibadwa :

N = w _y = 10√2 Newton

Mphamvu ya kukangana kosasinthasintha :

f _s = µ _s N = (0,4) (10√2) = 4√2

Kukula kwa mphamvu F kotero kuti chipikacho chimayamba kutsetsereka mmwamba :

F ≥ w _x + f _s

F ≥ 10√2 + 4 √2

F ≥ 14√2 Newton

[wpdm_package id='492′]

1. Tinthu tating'onoting'ono tofanana
2. Tinthu tating'onoting'ono tofanana mbali ziwiri
3. Kufanana kwa matupi olumikizidwa ndi zingwe ndi ma pulley
4. Kufanana kwa matupi omwe ali pamtunda wopendekeka

Werengani zambiri

1. Bokosi lolemera makilogalamu 5 lili pamalo opendekeka pa ngodya ya 30 ^o . Bokosilo limathandizidwa ndi chingwe. Dziwani mphamvu ya kukakamira (T) ndi mphamvu yachibadwa (N)!

Anakonza

∑F_x = 0

T – w sin 30 ^o = 0

T = w sin 30 ^o

T = (5 kg)(9.8 m/s ² ) sin 30 ^o

T = (49)(0.5)

T = 24.5 Newtons

∑ F _y = 0

N – w cos 30 ^o = 0

N = w cos 30 ^o

N = (49)(0.87)

N = 43 Newton

[irp]

2. Zinthu ziwiri zolemera m ₁ = m ₂ = 2 kg, zolumikizidwa ndi chingwe chopanda kulemera pamwamba pa pulley yopanda kukangana. Pezani mphamvu zokakamiza T ₁ ndi T ₂.

Anakonza

(a) Chithunzi cha thupi lopanda kanthu pa chinthu 1 (b) Chithunzi cha thupi lopanda kanthu pa chinthu 2

Gwiritsani ntchito lamulo loyamba la Newton potsutsa 1:

∑ F _y = 0

T ₁ – w ₁ = 0

T ₁ = w ₁ = m ₁ g = (2 kg)(9.8 m/s ² ) = 19.6 N

Gwiritsani ntchito lamulo loyamba la Newton potsutsa 2:

∑ F _y = 0

T ₂ – w ₂ = 0

T ₂ = w ₂ = m ₂ g = (2 kg)(9.8 m/s ² ) = 19.6 N

T ₁ = T ₂ = 19.6 N.

[irp]

3. Chinthu cholemera w _A = 30 N ndi chinthu cholemera w _B = 40 N, zimamangiriridwa ndi chingwe chopepuka chomwe chimadutsa pa pulley yopanda kukangana ya kulemera kochepa. Dziwani kuchuluka kwa kukangana kwakukulu pakati pa w _B ndi malo opendekera, ngati dongosolo lili pamalo opumulira.

Anakonza

(a) Chithunzi cha thupi lomasuka cha chinthu w _A (b) Chithunzi cha thupi lomasuka cha chinthu w _B

Gwiritsani ntchito lamulo loyamba la Newton potsutsa w _A molunjika molunjika (y):

∑ F _y = 0 (palibe kufulumira kolunjika molunjika)

T – w _A = 0

T = w _A = 30 Newton

Gwiritsani ntchito lamulo loyamba la Newton potsutsa w _B molunjika molunjika (y) :

∑ F _y = 0

N – w _B cos 45 ^o = 0

N = w _B cos 45 ^o = (40)(0.7) = 28 Newtons

Gwiritsani ntchito lamulo loyamba la Newton potsutsa w _B molunjika mopingasa (x):

∑ F _x = 0

F _k + w _B sin 45 ^o – T = 0

μ _s N + w _B tchimo 45 ^o – T = 0

μ _s (28) + (40) (0.7) – 30 = 0

μ _s (28) + 28 – 30 = 0

μ _s (28) = 30 – 28

μ _s (28) = 2

μ _s = 2 / 28

μ _s = 0.07

Chiŵerengero cha kukangana kwakukulu kosasunthika pakati pa w _B ndi malo opendekera = 0.07.

[wpdm_package id='490′]

1. Tinthu tating'onoting'ono tofanana
2. Tinthu tating'onoting'ono tofanana mbali ziwiri
3. Kufanana kwa matupi olumikizidwa ndi zingwe ndi ma pulley
4. Kufanana kwa matupi omwe ali pamtunda wopendekeka

Werengani zambiri

1. Pezani mphamvu zolimbitsa T ₁ , T ₂ , ndi T _{3. Musanyalanyaze} kulemera kwa chingwe.

Anakonza

(a) Chithunzi cha thupi lopanda kanthu (b) Chithunzi cha thupi lopanda kanthu cha chingwe

Gwiritsani ntchito lamulo loyamba la Newton pa chinthucho:

ΣF _y = 0

T ₁ – w = 0

T ₁ = w = mg

T ₁ = (5 kg)(9.8 m/s ² )

T ₁ = 49 kg m/s ²

T ₁ = 49 N

Gwiritsani ntchito lamulo loyamba la Newton pa chingwe:

∑ F _x = 0

T _3x – T _2x = 0

T ₃ cos 30 ^o – T ₂ cos 40 ^o = 0

0.87 T ₃ – 0.77 T ₂ = 0

0.87 T ₃ = 0.77 T ₂

T ₂ = 0.87 T ₃ / 0.77 = 1.1 T ₃ ———- Chiyerekezo 1

[irp]

-

∑ F _y = 0

T _3y + T _2y – T _1y = 0

T ₃ tchimo 30 ^o + T ₂ tchimo 40 ^o – T ₁ = 0

0.5 T ₃ + 0.64 T ₂ – 49 N = 0 ———- Chiyerekezo 2

Kuyika T ₂ mu equation 2 m'malo mwa equation 2:

0.5 T ₃ + 0.64 (1.1 T ₃ ) – 49 N = 0

0.5 T ₃ + 0.70 T ₃ – 49 = 0

1.2 T ₃ – 49 = 0

1.2 T ₃ = 49

T ₃ = 49 / 1.2

T ₃ = 41 N

---

T ₂ = 1.1 T ₃

T ₂ = (1.1)(40.8 N)

T ₂ = 45 N

[wpdm_package id='488′]

1. Tinthu tating'onoting'ono tofanana
2. Tinthu tating'onoting'ono tofanana mbali ziwiri
3. Kufanana kwa matupi olumikizidwa ndi zingwe ndi ma pulley
4. Kufanana kwa matupi omwe ali pamtunda wopendekeka

Werengani zambiri

^{1. Kulemera kwa chinthu, m = 10 kg, chothandizidwa ndi chingwe. Pezani mphamvu mu chingwe!} g = 10 m/s ²

Zodziwika:

Kulemera (m) = 10 kg

Kuthamanga chifukwa cha mphamvu yokoka (g) = 10 m/s ²

Kufunidwa: Mphamvu ya kukakamira (T)

Yankho:

ΣF _y = 0

T – w = 0

T = w

T = mg

T = (10 kg)(10 m/s ² ) = 100 kg m/s ²

T = 100 Newtons

[irp]

2. Kulemera kwa chinthucho ndi 10 kg. Pezani mphamvu mu chingwe….. Kuthamanga chifukwa cha mphamvu yokoka = 10 m/s ².

Anakonza

Zodziwika:

Kulemera (m) = 10 kg

Kuthamanga chifukwa cha mphamvu yokoka (g) = 10 m/s ².

Kufunidwa: Mphamvu ya kukakamira (T)

Yankho:

^{w = kulemera = mg = (10 kg)(10 m/s2}) = 100 kg m/s²

T ₁ = mphamvu ya kukanikizana 1

_{T 1x} = x-chigawo cha mphamvu yokakamiza 1 = T ₁ cos 45 ^o = 0.7 T ₁

_{T 1y} = gawo la y la mphamvu yokakamiza 2 = T ₁ sin 45 ^o = 0.7 T ₁

T ₂ = mphamvu ya kukanikizana 2

_{T 2x} = x-chigawo cha mphamvu yokakamiza 2 = T ₂ cos 45 ^o = 0.7 T ₂

_{T 2y} = gawo la y la mphamvu yokakamiza 2 = T ₂ sin 45 ^o = 0.7 T ₂

Mkhalidwe wofanana ΣF = 0.

mzere wa y:

ΣF _y = 0

T _1y + T _2y – w = 0

0.7T ₁ + 0.7T ₂ – 100 = 0

0.7T ₁ + 0.7T ₂ = 100 —– equation 1

mzere wa x:

ΣF _x = 0

T _2x – T _1x = 0

0.7T ₂ – 0.7T ₁ = 0

0.7T ₂ = 0.7T ₁

T ₂ = T ₁ —– equation 2

Dziwani kukula kwa T ₁ :

0.7T ₁ + 0.7T ₁ = 100

1.4T ₁ = 100

T ₁ = 100 / 1.4

T ₁ = 71.4 Newton

T ₁ = T ₂ kotero T ₂ = 71.4 Newtons

[wpdm_package id='486′]

1. Tinthu tating'onoting'ono tofanana
2. Tinthu tating'onoting'ono tofanana mbali ziwiri
3. Kufanana kwa matupi olumikizidwa ndi zingwe ndi ma pulley
4. Kufanana kwa matupi omwe ali pamtunda wopendekeka

Werengani zambiri

1. Mabokosi awiri amalumikizidwa ndi chingwe chomwe chikuyenda pamwamba pa pulley. Musanyalanyaze kulemera kwa chingwe ndi pulley ndi kukangana kulikonse mu pulley. Kulemera kwa bokosi 1 = 2 kg, kulemera kwa bokosi 2 = 3 kg, kuthamanga chifukwa cha mphamvu yokoka = 10 m/s ² . Pezani (a) Kuthamanga kwa dongosolo (b) Kukanika kwa chingwe!

Anakonza

Zodziwika:

Kulemera kwa bokosi 1 (m1 ₎ = 2 kg

Kulemera kwa bokosi 2 (m2 ₎ = 3 kg

Kuthamanga chifukwa cha mphamvu yokoka (g) = 10 m/s ²

Kulemera kwa bokosi 1 (w ₁ ) = m ₁ g = (2)(10) = 20 Newtons

Kulemera kwa bokosi 2 (w ₂ ) = m ₂ g = (3)(10) = 30 Newtons

Yankho:

(a) kukula ndi njira ya kuthamanga kwa liwiro

w ₂ > w ₁ kotero bokosi 2 limathamanga pansi ndipo bokosi 1 limathamanga mmwamba.

Mphamvu zomwe zili ndi mbali imodzi ndi kuthamanga (w ₂ ndi T ₁ ), chizindikiro chawo ndi chabwino. Mphamvu zomwe zili ndi mbali yosiyana ndi kuthamanga (T ₂ ndi w ₁ ), chizindikiro chawo ndi choipa.

∑ F = ma

w₂ - T₂ + T₁ - w₁ = (m₁ +m₂) a ——-> T₁ = T₂ = T

w ₂ – T + T – w ₁ = (m ₁ + m ₂ ) a

w ₂ – w ₁ = (m ₁ + m ₂ ) a

30 – 20 = (2 + 3) a

10 = 5 a

a = 10 / 5

a = 2 m/s ²

Kukula kwa kuthamanga kwa liwiro ndi 2 m/s ².

(b) Mphamvu ya kukakamira

Bokosi 2:

Pali mphamvu ziwiri zomwe zimachitika pa bokosi 2: choyamba, kulemera kwa bokosi 2 (w ₂ ), malongosolera pansi kotero kuti ndi zabwino. Chachiwiri, mphamvu yogwira ntchito pa bokosi 2 (T ₂ ), malongosolera mmwamba kotero kuti ndi zoipa. Gwiritsani ntchito lamulo lachiwiri la Newton la kuyenda.

∑ F = ma

w ₂ – T ₂ = m ₂ a

30 – T ₂ = (3)(2)

30 – T ₂ = 6

T ₂ = 30 – 6

T ₂ = 24 Newton

Bokosi 1:

Pali mphamvu ziwiri zomwe zimachitika pa bokosi 1. Choyamba , kulemera kwa bokosi 1 (w ₁ ), kumaloza pansi kotero kuti ndi koipa. Chachiwiri , mphamvu yokakamiza yomwe imagwiritsidwa ntchito pa bokosi 1 (T ₁ ) imaloza mmwamba kotero kuti ndi koipa. Gwiritsani ntchito lamulo lachiwiri la Newton la kuyenda:

∑ F = ma

T ₁ – w ₁ = m ₁ a

T ₁ – 20 = (2)(2)

T ₁ – 20 = 4

T ₁ = 20 + 4

T ₁ = 24 Newton

Kukula kwa mphamvu ya kukakamira = T ₁ = T ₂ = T = 24 Newtons

[irp]

2. Chinthu chomwe chili pamalo opingasa. Kulemera kwa chinthucho 1 = 2 kg, kulemera kwa chinthucho 2 = 4 kg, kuthamanga chifukwa cha mphamvu yokoka = 10 m/s ² , kuchuluka kwa kukangana kosasunthika = 0.4, kuchuluka kwa kukangana kozungulira = 0.3. Dongosolo lili pamalo opumira kapena lofulumira? Ngati dongosololi lafulumira, pezani kukula ndi komwe dongosololi lathamangira!

Anakonza

Zodziwika:

Kulemera kwa chinthu 1 (m1 ₎ = 2 kg

Kulemera kwa chinthu 2 (m2 ₎ = 4 kg

Kuthamanga chifukwa cha mphamvu yokoka (g) = 10 m/s ²

Koyefifiti ya kukangana kosasinthasintha ( μs ₎ = 0.4

Chiŵerengero cha kupsinjika kwa kinetic ( μk ₎ = 0.3

Kulemera kwa chinthu 1 (w ₁ ) = m ₁ g = (2)(10) = 20 Newtons

Kulemera kwa chinthu 2 (w ₂ ) = m ₂ g = (4)(10) = 40 Newtons

Mphamvu yachibadwa yomwe imagwiritsidwa ntchito pa chinthu 1 (N) = w ₁ = 20 Newtons

Mphamvu ya kukangana kosasinthasintha komwe kumachitika pa chinthu 1 (fs ₎ = μ _s N = (0.4)(20) = 8 Newtons

Mphamvu ya kupsinjika kwa kinetic komwe kumachitika pa chinthu 1 (f _k ) = μ _k N = (0.3)(20) = 6 Newtons

Kufunidwa: kufulumizitsa (a)

Yankho:

w ₂ > _fs (40 Newton > 8 Newton) kotero chinthu 2 chimafulumizitsidwa molunjika pansi ndipo chinthu 1 chimafulumizitsidwa mopingasa kumanja. Mphamvu yokangana yomwe imagwira ntchito pa zinthu 1 ndi mphamvu ya kukangana kwa kinetic (f _k ). Gwiritsani ntchito lamulo lachiwiri la Newton la kuyenda:

∑ F = ma

w ₂ – a = (m ₁ + m ₂ ) a

40 – 6 = (2 + 4) a

34 = 6 a

a = 34 / 6 = 17 / 3

a = 5.7 m/s ²

Kukula kwa kuthamanga = 5.7 m/s ²

[wpdm_package id='484′]

1. Kulemera ndi kulemera
2. mphamvu yachibadwa
3. Lamulo lachiwiri la Newton la kayendedwe
4. Mkangano mphamvu
5. Kuyenda pamalo opingasa popanda mphamvu yokangana
6. Kuyenda kwa matupi awiri omwe ali ndi kuthamanga komweko pamalo opingasa ndi mphamvu yokangana
7. Kuyenda pa ndege yopendekeka popanda mphamvu yokangana
8. Kuyenda pa ndege yokhotakhota ndi mphamvu yokangana
9. Kuyenda mu elevator
10. Kuyenda kwa matupi kumalumikizidwa ndi zingwe ndi ma pulleys
11. Matupi awiri omwe ali ndi kukula kofanana kwa kuthamanga
12. Kuzungulira makona osalala - mphamvu ya kayendedwe kozungulira
13. Kuzungulira mkombero wozungulira - mphamvu ya kuyenda kozungulira
14. Kuyenda kofanana mozungulira mopingasa
15. Mphamvu yapakati yozungulira yofanana

Werengani zambiri

1. Munthu wolemera makilogalamu 50 mu elevator. Kuthamanga chifukwa cha mphamvu yokoka = 10 m/s ² . Dziwani mphamvu yachibadwa yomwe imagwiritsidwa ntchito pa chinthucho ndi elevator, ngati:

(a) elevator ili pamalo opumulira

(b) chikepe chikuyenda pansi pa liwiro losasintha

(c) chikepe chokwera mmwamba pa liwiro losalekeza 5 / s ²

(d) chikepe chotsika mofulumira pa 5 m/s ²

(e) chikepe mu kugwa kwaulere

Anakonza

Zodziwika:

Kulemera kwa munthu (m) = 50 kg

Kuthamanga chifukwa cha mphamvu yokoka (g) = 10 m/s ²

Kulemera (w) = mg = (50)(10) = 500 Newtons

Kufunidwa: Mphamvu yachibadwa (N)

Yankho:

(a) elevator ili pamalo opumulira

Chikepe chili pamalo opumulirako kotero palibe kuthamanga (a = 0)

Timasankha njira yopita mmwamba m'njira yabwino ndi njira yopita pansi m'njira yoipa.

Σ F = ma

N – w = 0

N = w

N = 500 Newton

(b) chikepe chikuyenda pansi pa liwiro losasintha

Liwiro lokhazikika kotero palibe kufulumira (a = 0)

Timasankha njira yopita mmwamba m'njira yabwino ndi njira yopita pansi m'njira yoipa.

Σ F = ma

N – w = 0

N = w

N = 500 Newton

(c) chikepe chokwera mmwamba pa liwiro losasintha la 5 m/s ²

Njira yopititsira patsogolo liwiro ndi yokwera, kotero timasankha njira yabwino ngati mmwamba.

N – w = ma

N = w + ma

N = 500 + (50)(5)

N = 500 + 250

N = 750 Newton

Munthuyo amamva pansi likukwera mmwamba kwambiri kuposa pamene elevator ili pamalo amodzi kapena ikuyenda ndi liwiro losalekeza.

Ngati munthuyo aima pa sikelo, sikeloyo imawerenga kukula kwa mphamvu yotsika yomwe munthuyo ali pa sikeloyo amagwiritsa ntchito. Malinga ndi lamulo lachitatu la Newton, izi zikufanana ndi kukula kwa mphamvu yokwera yomwe munthuyo ali nayo pa sikeloyo.

(d) chikepe chotsika mofulumira pa 5 m/s ²

Njira yopititsira patsogolo liwiro ndi yotsika, kotero timasankha njira yabwino ngati yotsika.

w – N = ma

N = w – ma

N = 500 – (50)(5)

N = 500 - 250

N = 250 Newton

Kulemera kwa munthuyo ndi 250 N, komwe ndi kochepa kuposa kulemera kwenikweni w = 500 N.

(e) chikepe mu kugwa kwaulere

Kugwa kwaulere kumatanthauza kuti kuthamanga kwa elevator kuli kofanana ndi kuthamanga chifukwa cha mphamvu yokoka. Kukula kwa kuthamanga chifukwa cha mphamvu yokoka ndi 9,8 m/s ² , komwe ikupita pansi kupita pakati pa Dziko Lapansi. Liwiro limawonjezeka molunjika munthawi ndi 9,8 m/s pa sekondi iliyonse.

Njira yopititsira patsogolo liwiro ndi yotsika, kotero timasankha njira yabwino ngati yotsika.

w – N = ma

N = w – ma

N = 500 – (50)(10)

N = 500 - 500

N = 0

[irp]

2. Dziwani mphamvu ya chingwe cha elevator. Kulemera kwa elevator = 2000 kg.

(a) elevator ili pamalo opumulira

(b) chikepe chotsika mofulumira pa 5 m/s nthawi zonse ²

(c) chikepe chokwera mmwamba pa liwiro losasintha la 5 m/s ²

(d) chikepe mu kugwa kwaulere

Kuthamanga chifukwa cha mphamvu yokoka (g) = 10 m/s ²

Anakonza

Zodziwika:

Kulemera kwa elevator (m) = 2000 kg

Kuthamanga kwa mphamvu yokoka (g) = 10 m/s ²

kulemera (w) = mg = (2000)(10) = 20,000 Newtons

Kufunidwa: Mphamvu ya kukakamira (T)

Yankho:

(a) elevator ili pamalo opumulira

elevator ili pamalo opumulirako kotero palibe kuthamanga (a = 0)

Timasankha njira yopita mmwamba ngati njira yabwino ndi njira yopita pansi ngati njira yoipa.

Σ F = ma

T – w = 0

T = w

T = 20,000 Newtons

Kupsinjika kwa chingwe (T) = kulemera kwa elevator (w) = 20,000 Newtons

(b) chikepe chotsika mofulumira pa 5 m/s nthawi zonse ²

Njira yopititsira patsogolo liwiro ndi yotsika, kotero timasankha njira yabwino ngati yotsika.

w – T = ma

T = w – ma

T = 20,000 – (2000)(5)

T = 20,000 – 10,000

T = 10,000 Newtons

c) chikepe chokwera mmwamba pa liwiro losasintha la 5 m/s ²

Njira yopititsira patsogolo liwiro ndi yotsika, kotero timasankha njira yabwino ngati mmwamba.

T – w = ma

T = w + ma

T = 20,000 + (2000)(5)

T = 20,000 + 10,000

T = 30,000 Newtons

(d) chikepe mu kugwa kwaulere

Njira yopititsira patsogolo liwiro ndi yotsika, kotero timasankha njira yabwino ngati yotsika.

w – T = ma

T = w – ma

T = 20,000 – (2000)(10)

T = 20,000 – 20,000

T = 0

[wpdm_package id='482′]

1. Kulemera ndi kulemera
2. mphamvu yachibadwa
3. Lamulo lachiwiri la Newton la kayendedwe
4. Mkangano mphamvu
5. Kuyenda pamwamba mopingasa popanda mphamvu yokangana
6. Kuyenda kwa matupi awiri ndi kuthamanga komweko pamalo opingasa ozungulira ndi mphamvu yokangana
7. Kuyenda pa ndege yopendekeka popanda mphamvu yokangana
8. Kuyenda pa ndege yokhotakhota ndi mphamvu yokangana
9. Kuyenda mu elevator
10. Kuyenda kwa matupi kumalumikizidwa ndi zingwe ndi ma pulleys
11. Matupi awiri omwe ali ndi kukula kofanana kwa kuthamanga
12. Kuzungulira makona osalala - mphamvu ya kayendedwe kozungulira
13. Kuzungulira mkombero wozungulira - mphamvu ya kuyenda kozungulira
14. Kuyenda kofanana mozungulira mopingasa
15. Mphamvu yapakati yozungulira yofanana

Werengani zambiri