Physics

1. Bhora re 0.2-kg, rakasungirirwa kumagumo kwetambo yakatambanudzwa, rinotenderedzwa mudenderedzwa re radius ye 1 mita uye kumhanya kwepamusoro kwebhora i 10 rpm. Hukuru hwebhora hwakaita sei? kukurumidza kwepakati uye hukuru hwesimba rekumanikidzwa?

Zvinozivikanwa:

Misa (m) = 0.2 kg

Nharaunda (r) = 1 m

Angular velocity (ω) = 10 rev/min = 10 rev/60 s = 0.17 rev/s = (0.17) (6.28 rad)/s = 1 rad/s

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

Zvaidiwa: a_s dhani ΣF

Solution:

(a) Hukuru hwekumhanya kwepakati pesimba

(b) Hukuru hwesimba rekumanikidzwa

ΣF = ma

T = ma_s

T = (0.2 kg)(1 m/s²)

T = 0.2 kg m/s²

T = 0.2 N

2. Bhora re 1-kg riri kumagumo kwetambo riri kutenderera zvakaenzana mudenderedzwa rakati sandara re 1 m. Tambo yacho ichatyoka kana kumanikidzwa kuri mairi kwapfuura 100 N. Ndeipi kumhanya kwakanyanya kwaunogona kuita bhora?

Zvinozivikanwa:

Huremu (m) = 1 kg

Nharaunda (r) = mita imwe

Simba rekumanikidzwa (T) = simba repakati (ΣF) = 100 N

Kuda: v yepamusoro

Solution:

[wpdm_package id='499′]

1. Huremu nehuremu
2. simba remazuva ose
3. Mutemo wechipiri wekufamba waNewton
4. Simba rekukakavadzana
5. Kufamba panzvimbo yakatwasuka pasina simba rekukweshana
6. Kufamba kwemiviri miviri ine kumhanyisa kwakafanana pamusoro penzvimbo yakatwasuka ine simba rekukweshana
7. Kufamba mundege yakatsamira pasina simba rekukweshana
8. Kufamba mundege yakakombama nesimba rekukweshana
9. Kufamba muelevator
10. Kufamba kwemiviri kwakabatana netambo nemapulley
11. Miviri miviri ine hukuru hwakafanana hwekukurumidzira
12. Kutenderedza denderedzwa rakati sandara - simba rekufamba kwedenderedzwa
13. Kutenderera curve yakakomberedzwa - simba rekufamba kwedenderedzwa
14. Kufamba kwakafanana mudenderedzwa rakatwasuka
15. Simba repakati nepakati rakafanana mukufamba kwedenderedzwa

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1. Mota yakatenderera curve yakakombama. Ndeipi kona yemugwagwa ine curve yeradius yemamita makumi matanhatu ine kumhanya kwakagadzirwa kwe20 m/s? Ngatitii hapana kukweshera pakati pemotokari nemugwagwa.

mhinduro

N= simba remazuva ose

chivi θ = chikamu chakatambanudzwa chesimba rakajairika

N cos θ = chikamu chakamira chesimba rakajairika

w = mg = iyo uremu yemota

Mugwagwa wacho wakagadzirwa kuti uvharwe nemabhanga kuti usanyanya kuvimba nekukakavadzana.

Simba remambure rakatwasuka, iro chikamu chakatambanudzwa chesimba rakajairika (chivi θ), zvinodiwa kuti mota irambe ichifamba yakatenderedza makona.

Tinosarudza x-axis seyakatambanudzwa uye y-axis seyakamira, kuitira kuti kukurumidza kwepakati,_R, iri munzira yakatwasuka. Munzira yakatwasuka, simba chete ndiro chikamu chakatwasuka chesimba rakajairika (chivi θ), inodiwa kugadzira kukurumidza kwepakatiN sin θ = simba repakati.

Shandisa mutemo waNewton wekufamba munzira yakatwasuka:

Shandisa mutemo waNewton wekufamba munzira yakatwasuka:

Chinzvimbokuisa N muchiyero 1 kuenda kuN muchiyero 2 :

[wpdm_package id='497′]

1. Huremu nehuremu
2. simba remazuva ose
3. Mutemo wechipiri wekufamba waNewton
4. Simba rekukakavadzana
5. Kufamba pamusoro penzvimbo yakatwasuka pasina simba rekukweshana
6. Kufamba kwemiviri miviri ine kumhanyisa kwakafanana pamusoro penzvimbo yakatwasuka ine simba rekukweshana
7. Kufamba mundege yakakotama pasina simba rekukweshana
8. Kufamba mundege yakakombama nesimba rekukweshana
9. Kufamba muelevator
10. Kufamba kwemiviri kwakabatana netambo nemapulley
11. Miviri miviri ine hukuru hwakafanana hwekukurumidzira
12. Kutenderedza denderedzwa rakati sandara - simba rekufamba kwedenderedzwa
13. Kutenderera curve yakakomberedzwa - simba rekufamba kwedenderedzwa
14. Kufamba kwakafanana mudenderedzwa rakatwasuka
15. Simba repakati nepakati rakafanana mukufamba kwedenderedzwa

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1. Mota inorema 2000 kg inotenderera mugwagwa wakatsetseka we radius 150 m. Iyo coefficient ye kukweshana kwemamiriro ezvinhu i0.5. Sarudza kumhanya kwakanyanya kuitira kuti mota itevere curve uye isatsvedzerere. Kuwedzera nekuda kwegiravhiti = 10 m/s².

Zvinozivikanwa:

Misa (m) = 2000 kg

Nharaunda (r) = 150 mamita

Kukweshana kwekusagadzikana (coefficient of static friction)μ_s= = 0.5

uremu (w) = mg = (2000 kg)(10 m/s²) = 20,000 kg m/s² = 20,000N

Simba rekukweshana kwakasimba (F)_s) = μ_s N = μ_s w = (0.7)(20,000 N) = 14,000 N

Aida: v

Solution:

[wpdm_package id='496′]

1. Huremu nehuremu
2. simba remazuva ose
3. Mutemo wechipiri wekufamba waNewton
4. Simba rekukakavadzana
5. Kufamba pamusoro penzvimbo yakatwasuka pasina simba rekukweshana
6. Kufamba kwemiviri miviri ine kumhanyisa kwakafanana pamusoro penzvimbo yakatwasuka ine simba rekukweshana
7. Kufamba mundege yakakotama pasina simba rekukweshana
8. Kufamba mundege yakakombama nesimba rekukweshana
9. Kufamba muelevator
10. Kufamba kwemiviri kwakabatana netambo nemapulley
11. Miviri miviri ine hukuru hwakafanana hwekukurumidzira
12. Kutenderedza denderedzwa rakati sandara - simba rekufamba kwedenderedzwa
13. Kutenderera curve yakakomberedzwa - simba rekufamba kwedenderedzwa
14. Kufamba kwakafanana mudenderedzwa rakatwasuka
15. Simba repakati nepakati rakafanana mukufamba kwedenderedzwa

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1. Makiromita maviri m₁ = 2 kg uye m₂ = 5 kg dziri panzvimbo yakakombama uye dzakabatana pamwe chete netambo sezvakaratidzwa mumufananidzo. Chiyero chekukakavadzana kwekinetic pakati pe m₁ uye kutsvedza kuri 0.2 uye coefficient ye kukweshana kwekinetic pakati pe m₂ uye kutsvedza kuri 0.1.

(a) Sarudzai zvavo kukurumidza

(b) Sarudza simba rekumanikidza

Zvinozivikanwa:

Misa 1 (m₁) = 2 kg

Huremu 2 (m₂) = 4 kg

Kukweshana kwekinetic pakati pe m₁ uye ndege yakatsamira (μ_k1) = 0.2

Kukweshana kwekinetic pakati pe m₂ uye ndege yakatsamira (μ_k2) = 0.1

Kuwedzera nekuda kwegiravhiti (g) = 9.8 m/s²

a) Hukuru uye gwara rekumhanya

w₁ = uremu 1 = m₁ g = (2 kg)(9.8 m/s²) = 19.6 Newton

w_1x = w₁ pasina 30^o = (19.6 N)(0.5) = 9.8 Newton

w_1y = w₁ kusvika 30^o = (19.6 N)(0.87) = 17 Newton

N₁ = Iyo simba remazuva ose pa m₁ = w_1y = 17 Newton

F_k1 = Simba rekukweshana kwekinetic pa m₁ = μ_k1 N₁ = (0.2)(17 N) = 3.4 Newton

---

w₂ = huremu 2 = m₂ g = (4 kg)(9.8 m/s²) = 39.2 Newton

w_2x = w₂ pasina 60^o = (39.2 N)(0.87) = 34.1 Newton

w_2y = w₂ kusvika 60^o = (39.2 N)(0.5) = 19.6 Newton

N₂ = Simba rakajairika pa m₂ = w_2y = 19.6 Newton

F_k2 = Simba rekukweshana kwekinetic pa m₂ = μ_k2 N₂ = (0.1)(19.6 N) = 1.96 Newton

---

Kukura kwekukurumidzira:

∑F_x = amai_x

w_2x > w_1x saka divi rekumhanya kwakafanana nedivi raw_2x.

Masimba anonongedzera kumhanyisa akanaka uye masimba ane divi rakasiyana nerekumhanyisa haana kunaka.

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

w_2x - F_k2 - w_1x - F_k1 = (m₁ +m₂ ) a_x

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

18.94 N = (6 kg) a_x

a_x = 18.94 N : 6 kg

a_x = 3.16 m/s²

Hukuru hwekukurumidzira = 3.16 m/s² Kutungamira kwekumhanyisa = kutungamira kwaT₁ = kutungamira kwe w_2x

b) Hukuru hwesimba rekumanikidza

Shandisa mutemo wechipiri waNewton pane chinhu chechipiri:

w_2x - F_k2 - T₂ = m₂ a_x

34.1 N – 1.96 N – T₂ = (4kg)(3.16m/s²)

32.14 N – T₂ = 12.64N

T₂ = 32.14 N – 12.64 N = 19.5 Newtons

Simba rekumanikidza = T = T₁ =T₂ = 19.5 Newton

2. m₁ = 4 kg, m₂ = 2 kg. Sarudza (a) hukuru uye divi rekumhanya (b) Hukuru hwesimba rekumanikidza rinobatanidza m₁ uye m₂ (c) hukuru hwesimba rekumanikidza rinobatanidza pulley nedenga.

mhinduro

w₁ = m₁ g = (4 kg)(9.8 m/s²) = 39.2 Newton

w₂ = m₂ g = (2 kg)(9.8 m/s²) = 19.6 Newton

a) Hukuru uye kutungamira kwekumhanya

∑F_y = amai_y

w₁ > w₂ saka divi rechinhu chacho rakafanana nedivi rehuremu 1 (w₁)Masimba ane divi rakafanana nekukurumidzisa akanaka uye masimba ane divi rakasiyana nekukurumidzisa haana kunaka.

w₁ - T₁ +T₂ - w₂ = (m₁ +m₂) a_y

w₁ - w₂ = (m₁ +m₂) 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/s²

Hukuru hwekukurumidzira = 3.26 m/s²Nzira yekumhanyisa = nzira ye w₁ .

b) Hukuru hwesimba rekumanikidzwa rinobatanidza m₁ uye m₂

Shandisa Mutemo wechipiri waNewton pa m₂ :

∑F_y = amai_y

w₁ - T₁ = m₁ a_y

39.2 N – T₁ = (4 kg)(3.26 m/s²)

39.2 N – T₁ = 13.04N

T₁ = 39.2 N – 13.04 N

T₁ = 26.16 Newton

Hukuru hwesimba rekumanikidzana rinobatanidza zvinhu = T = T₁ =T₂ = 26.16 Newton

c) Hukuru hwesimba rekumanikidza rinobatanidza pulley nedenga.

Pulley yazorora:

∑F_y = amai_y —— a_y = 0

∑F_y = 0

Masimba ari kumusoro akanaka, masimba ari pasi haana kunaka:

T₃ - T₁ - T₂ = 0

T₃ =T₁ +T₂

T₁ uye T₂ vane hukuru hwakafanana, T₁ =T₂ = T = 26.16 N :

T₃ = 2T = 2(26.16 N) = 52.32 Newtons

3. Bhuroko 1 (m₁ = 10 kg) uye bhokisi 2 (m₂ = 15 kg) yakabatana netambo pamusoro pepulley isina kukweshana. Coefficient yekukweshana kwakagadzika pakati peblock 2 ine inclination = 0.6. Coefficient yekukweshana kwekinetic pakati peblock 2 ine inclination = 0.42. Sarudza (a) Hukuru hwesimba diki F rakashandiswa pazvinhu kuitira kuti zvinhu zvikwidziridzwe kumusoro (b) Sarudza hukuru hwesimba rekukweshana.

mhinduro

w₁ = Huremu hwebhuroko 1 = m₁ g = (10 kg)(9.8 m/s²) = 98 Newton

w₂ = Huremu hwebhuroko 2 = m₂ g = (15 kg)(9.8 m/s²) = 147 Newton

w_2y = w₂ kusvika 30^o = (147 N)(0.87) = 127.89 Newton

w_2x = w₂ pasina 30^o = (147 N)(0.5) = 73.5 Newton

N₂ = Simba rakajairika pabhokisi 2 = w_2y = 127.89 Newton

F_k2 = Simba rekukweshana kwekinetic pablock 2 = μ_k2 N₂ = (0.42)(127.89 N) = 53.7 Newton

F_s2 = Simba rekukweshana kwesimba pabhuroko 2 = μ_s2 N₂ = (0.6)(127.89 N) = 76.7 Newton

a) Hukuru hwesimba diki F rakashandiswa pazvinhu saka zvinhu zvakakurumidza kukwira kumusoro

∑F_x = amai_x —— a_x = 0

∑F_x = 0

Masimba ekumusoro neakarurama akanaka, masimba epasi neakuruboshwe haana kunaka.

F – F_k2 - w_2x - w₁ - T₂ +T₁ = 0

F – F_k2 - w_2x - w₁ = 0

F = F_k2 +w_2x +w₁

F = 53.7 N + 73.5 N + 98 N

F = 225.2 Newton

b) Hukuru hwesimba rekumanikidzwa

Shandisa mutemo waNewton wekufamba pabhokisi 1:

∑F_y = amai_y —— a_y = 0

∑F_y = 0

T₁ - w₁ = 0

T₁ = w₁ = 98 Newton

Shandisa mutemo waNewton wekufamba pabhokisi 2:

F – F_k2 - w_2x - T₂ = 0

T₂ = F – F_k2 - w_2x

T₂ = 225.2 N – 53.7 N – 73.5 N

T₂ = 98 Newton

Hukuru hwesimba rekumanikidza = T₁ =T₂ = T = 98 Newton

4. Bhuroko 1 (m₁ = 16 kg) iri pamusoro penzvimbo yakatambanuka uye bhokisi 2 (m₂ = 12 kg) yakarara panzvimbo yakatsetseka yakakotama, yakabatana netambo inopfuura nepapure diki, isina kukweshana. Bhuroko 3 (m₃ = 5 kg) iri pabhokisi 2. Chiyero chekukakavadzana kwekinetic pakati pebhokisi 2 nepamusoro penzvimbo yakatwasuka i0,4. CoefChikamu chikuru chekukakavadzana kwe static pakati pe block 2 ne block 3 i 0,3.

(A) Kana sisitimu yasunungurwa kubva pakuzorora, bhokisi rechitatu nebhokisi rechipiri zvinoramba zvichitsvedza pamwe chete?

(B) Kana paine bhokisi rechitatu, chii chinonzi kukurumidza kwebhokisi rekutanga nebhokisi rechipiri?

Solution:

a) Kana sisitimu yasunungurwa kubva pakuzorora, bhokisi rechitatu nebhokisi rechipiri zvinoramba zvichitsvedza pamwe chete?

w₁ = Iyo huremu hwebhuroko 1 = m₁ g = (16 kg)(9.8 m/s²) = 156.8 Newton

w_1x = w₁ pasina 60^o = (156.8 N)(0.87) = 136.4 Newton

w_1y = w₁ kusvika 60^o = (156.8 N)(0.5) = 78.4 Newton

N₁ = Iyo simba rakajairika rinoshandiswa pabhuroko 1 nendege yakakotama = w_1y = 78.4 Newton

w₃ = Iyo huremu hwebhuroko 3 = m₃ g = (5 kg)(9.8 m/s²) = 49 Newton

N₂₃ = Iyo simba rakajairika rinoitwa pabhokisi rechitatu nebhokisi rechipiri = w₃ = 49 Newton

N₃₂ = Iyo nsimba rakajairika rinoitwa pabhokisi rechipiri nebhokisi rechitatu = N₂₃ = w₃ = 49 Newton

(N₂₃ uye N₃₂ mapeya ekuita-kuita)

F_s23 = Iyo simba rekukweshana kwakasimba kunoitwa pabhokisi rechitatu nebhokisi rechipiri = μ_s N₂₃ = (0.3)(49 N) = 14.7 Newton

F_s32 = Iyo simba rekukweshana kwakasimba kunoitwa pablock 2 neblock 3 =F_s23 = 14.7 Newton

(F_s23 uye F_s32 mapeya ekuita-kuita)

w₂ = Iyo huremu hwebhuroko 2 = m₂ g = (12 kg)(9.8 m/s²) = 117.6 Newton

N₂ = Iyo simba rakajairika rinoitwa pachinhu chechipiri nepamusoro pechinhu chakarara = w₂ +N₃₂ = 117.6 Newtons + 49

Newton = 166.6 Newton

F_k2 = Iyo simba rekukweshana kwekinetic pablock 2 = μ_k N₂ = (0.4)(166.6 N) = 66.64 Newton

Shandisa mutemo waNewton wekufamba pabhokisi rechitatu:

∑F_x = amai_x

F_s23 =m₃ a_x

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

μ_s m₃ g = m₃ a_x

μ_s g = a_x

a_x = (0.3)(9.8 m/s²) = 2.94 m/s²

Kumhanya kwakanyanya kwebhuroko rechitatu kuitira kuti bhuroko rechitatu nebhuroko rechipiri zvirambe zvichitsvedza pamwe chete i2.94 m/s².

Iye zvino tava kuverenga kukura kwekumhanya kwesystem mushure mekusunungurwa kubva pakuzorora.

Kutungamira kwebhuroko = nzira yekumhanyisa kwebhuroko = nzira yaT₂ = kutungamira kwe w_1x.

∑F_x = amai_x

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

w_1x - F_k2 = (m₁ +m₂ +m₃ ) a_x

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

69.76 N = (33 kg) a_x

a_x = 2.11 m/s²

a_x zvakanaka, zvinoreva kuti divi rekubviswa kweblock kana divi rekumhanyisa rakafanana nedivi raT₂ kana kuti kutungamira kwe w_1x.

Hukuru hwekukurumidzira huri 2.11 m / s² , lsimba kupfuura 2.94 m / s² saka tinogona kugumisa kuti bhokisi rechitatu nebhokisi rechipiri zvichiri kutsvedza pamwe chete mushure mekusunungurwa kubva pazororo.

b) Kukura kwekumhanya kwebhokisi 1 nebhokisi 2

∑F_x = amai_x

w_1x - F_k2 = (m₁ +m₂) 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 = (16 kg + 12 kg) a_x

89.36 N = (28 kg) a_x

a_x = 89.36 N : 28 kg = 3.19 m/s²

[wpdm_package id='493′]

1. Huremu nehuremu
2. simba remazuva ose
3. Mutemo wechipiri wekufamba waNewton
4. Simba rekukakavadzana
5. Kufamba pamusoro penzvimbo yakatwasuka pasina simba rekukweshana
6. Kufamba kwemiviri miviri ine kumhanyisa kwakafanana pamusoro penzvimbo yakatwasuka ine simba rekukweshana
7. Kufamba mundege yakakotama pasina simba rekukweshana
8. Kufamba mundege yakakombama nesimba rekukweshana
9. Kufamba muelevator
10. Kufamba kwemiviri kwakabatana netambo nemapulley
11. Miviri miviri ine hukuru hwakafanana hwekukurumidzira
12. Kutenderedza denderedzwa rakati sandara - simba rekufamba kwedenderedzwa
13. Kutenderera curve yakakomberedzwa - simba rekufamba kwedenderedzwa
14. Kufamba kwakafanana mudenderedzwa rakatwasuka
15. Simba repakati nepakati rakafanana mukufamba kwedenderedzwa

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1. Bhokisi re2-kg rakarara panzvimbo yakakombama pakona 37^o kusvika panzvimbo yakatwasuka. Sarudza hukuru hwesimba rekunze rinoshandiswa pabhuroko, kuitira kuti bhuroko risatsvedzerere pasi. (syn 37^o = 0.6, cos 37^o = 0.8, g = 10 ms^-2, µ_k = 0.2)

Zvinozivikanwa:

Misa (m) = 2 kg

Kuwedzera nekuda kwegiravhiti (g) = 10 m/s²

Mabhuroko uremu (w) = mg = (2)(10) = 20 Newtons

Pasina makumi matatu nemaviri^o = 0.6

Kos 37^o = 0.8

Koefficient ye kukweshana kwekinetic (µ_k= = 0.2

Chikamu che y chehuremu (w)_y) = w kusvika 37^o = (20)(0.8) = 16 Newton

Chikamu che x chehuremu (w)_x) = w chivi θ = (20)(chivi 37) = (20)(0.6) = 12 Newtons

simba rakajairika (N) = w_y = 16 Newton

Wanted : Simba rekunze (F)

mhinduro :

w_x = 12 Newton

Simba rekukweshana kwekinetic (f)_k) = µ_k N = (0.1)(16) = 1.6 Newtons

Hukuru hwesimba rekunze F rakashandiswa pabhuroko :

F + f_k - w_x = 0

F = w_x - f_k

F = 12 – 1.6

F = 10.4 Newton

Simba rekunze F rakakura kupfuura 10.4 Newtons.

2. Huremu hwebhuroko = 2 kg, coefficient yekukweshana kwakagadzika µ_s = 0.4 uye θ = 45^oSarudza hukuru hwesimba F kuitira kuti bhokisi ritange kutsvedza.

Zvinozivikanwa:

Muyero wekukweshana kwakasimba (µ)_s= = 0.4

Angle (θ) = 45^o

Kukurumidza kunokonzerwa negiravhiti (g) = 10 m/s²

Huremu hwebhuroko (m) = 2 kg

Huremu hwebhuroko (w) = mg = (2 kg)(10 m/s²) = 20 kg m/s² = 20 Newton

Chikamu che x chehuremu (w)_x) = w chivi θ = (20)(chivi 45) = (20)(0.5√2) = 10√2 Newtons

Chikamu che y chehuremu (w)_y) = w cos θ = (20)(cos 45) = (20)(0.5√2) = 10√2 Newtons

Wanted : Hukuru hwesimba F

Solution:

Bhokisi rinotanga kutsvedza, kana F ≥ w_x + f_s.

Chikamu che x chehuremu:

w_x = 10√2 Newton

chikamu che y chehuremu :

w_y = 10√2 Newton

Simba rakajairika :

N = w_y = 10√2 Newton

Simba rekukweshana kwakasimba :

f_s = µ_s N = (0,4)(10√2) = 4√2

Kukura kwesimba F zvekuti bhokisi rinotanga kutsvedza :

F ≥ w_x + f_s

F ≥ 10√2 + 4√2

F ≥ 14√2 Newton

[wpdm_package id='492′]

1. Zvidimbu zviri muchiyero chimwe chete
2. Zvidimbu zviri muchimiro chemativi maviri
3. Kuenzana kwemiviri yakabatana netambo nemapulley
4. Kuenzana kwemiviri iri mundege yakakotama

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1. Bhokisi re uremu 5 kg iri mundege yakatsamira pakona 30^oBhokisi racho rinotsigirwa netambo. Sarudza simba rekumanikidza (T) uye simba remazuva ose (N)!

mhinduro

∑F_x = 0

T – w chivi 30^o = 0

T = w chivi 30^o

T = (5 kg)(9.8 m/s²) chivi 30^o

T = (49)(0.5)

T = 24.5 Newton

∑F_y = 0

N – w cos 30^o = 0

N = w cos 30^o

N = (49)(0.87)

N = 43 Newton

2. Zvinhu zviviri zvine huremu m₁ = m₂ = 2 kg, yakabatana netambo isina huremu pamusoro pepure isina kukweshana. Tsvaga simba rekukwesha T₁ uye T₂.

mhinduro

(a) Dhayagiramu yemuviri wakasununguka yechinhu 1 (b) Dhayagiramu yemuviri wakasununguka yechinhu 2

Shandisa mutemo wekutanga waNewton pakupikisa 1:

∑F_y = 0

T₁ - w₁ = 0

T₁ = w₁ = m₁ g = (2 kg)(9.8 m/s²) = 19.6 N

Shandisa Mutemo wekutanga waNewton kuramba 2:

∑F_y = 0

T₂ - w₂ = 0

T₂ = w₂ = m₂ g = (2 kg)(9.8 m/s²) = 19.6 N

T₁ =T₂ = 19.6N.

3. Chinhu che uremu w_A = 30 N uye chinhu chinorema w_B = 40 N, zvinosungirirwa netambo yakareruka inopfuura nepamusoro pepulley isina kukweshana yehukuru husina kukosha. Sarudza coefficient yehukuru hwepamusoro kukweshana kwemamiriro ezvinhu pakati pe w_B uye pamusoro wakakotama, kana hurongwa hwacho hwakamira.

mhinduro

(a) Dhayagiramu yemuviri wakasununguka wechinhu w_A (b) Dhayagiramu yemuviri wakasununguka wechinhu w_B

Shandisa mutemo wekutanga waNewton pakupikisa w_A munzira yakatwasuka (y):

∑F_y = 0 (hapana kukurumidza munzira yakatwasuka)

T – w_A = 0

T = w_A = 30 Newton

Shandisa mutemo wekutanga waNewton pakupikisa w_B munzira yakatwasuka (y) :

∑F_y = 0

N – w_B kusvika 45^o = 0

N = w_B kusvika 45^o = (40)(0.7) = 28 Newton

Shandisa mutemo wekutanga waNewton pakupikisa w_B munzira yakatwasuka (x):

∑F_x = 0

F_k +w_B pasina 45^o -T = 0

μ_s N + w_B pasina 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

Muyero wekukweshana kwakanyanya pakati pe w_B uye pamusoro wakakombama = 0.07.

[wpdm_package id='490′]

1. Zvidimbu zviri muchiyero chimwe chete
2. Zvidimbu zviri muchimiro chemativi maviri
3. Kuenzana kwemiviri yakabatana netambo nemapulley
4. Kuenzana kwemiviri iri mudenga rakarerekera

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1. Tsvaga simba rekumanikidza T₁, T₂, uye T₃Usateerera tambo uremu.

mhinduro

(a) Dhayagiramu yemuviri wakasununguka wechinhu (b) Dhayagiramu yemuviri wakasununguka wetambo

Nyorera Mutemo wekutanga waNewton pachinhu chacho:

ΣF_y = 0

T₁ – w = 0

T₁ = w = mg

T₁ = (5kg)(9.8m/s²)

T₁ = 49 kg m/s²

T₁ = 49N

Shandisa mutemo wekutanga waNewton patambo:

∑F_x = 0

T_3x - T _2x = 0

T₃ kusvika 30^o - T₂ kusvika 40^o = 0

0.87 T₃ – 0.77 T₂ = 0

0.87 T₃ = 0.77 T₂

T₂ = 0.87 T₃ / 0.77 = 1.1 T₃ ———- Equation 1

-

∑F_y = 0

T_3y +T_2y - T_1y = 0

T₃ pasina 30^o +T₂ pasina 40^o - T₁ = 0

0.5 T₃ + 0.64 T₂ – 49 N = 0 ———- Equation 2

Kutsiva T₂ muequation 2 muequation 2:

0.5 T₃ + 0.64 (1.1 T)₃) – 49 N = 0

0.5 T₃ + 0.70 T₃ - 49 = 0

1.2 T₃ - 49 = 0

1.2 T₃ = 49

T₃ = 49/1.2

T₃ = 41N

---

T₂ = 1.1 T₃

T₂ = (1.1)(40.8 N)

T₂ = 45N

[wpdm_package id='488′]

1. Zvidimbu zviri muchiyero chimwe chete
2. Zvidimbu zviri muchimiro chemativi maviri
3. Kuenzana kwemiviri yakabatana netambo nemapulley
4. Kuenzana kwemiviri iri mudenga rakarerekera

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^{1. Misa yechinhu, m = 10 kg, chakatsigirwa netambo. Tsvaga kusimba kuri mutambo!} g = 10 m/s²

Zvinozivikanwa:

Huremu (m) = 10 kg

Kuwedzera nekuda kwegiravhiti (g) = 10 m/s²

Zvaidiwa: Simba rekumanikidza (T)

Solution:

ΣF_y = 0

T – w = 0

T = w

T = mg

T = (10 kg)(10 m/s²) = 100 kg m/s²

T = 100 Newton

2. Huremu hwechinhu chacho i10 kg. Tsvaga kumanikidzwa kuri mutambo….. Kukurumidza kunokonzerwa negiravhiti = 10 m/s².

mhinduro

Zvinozivikanwa:

Huremu (m) = 10 kg

Kukurumidza kunokonzerwa negiravhiti (g) = 10 m/s².

Zvaidiwa: Simba rekumanikidza (T)

Solution:

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

T₁ = simba rekumanikidza 1

_T1x = chikamu che x chesimba rekumanikidza 1 = T₁ kusvika 45^o = 0.7 T₁

_T1y = chikamu che y chesimba rekumanikidzwa 2 = T₁ pasina 45^o = 0.7 T₁

T₂ = simba rekumanikidza 2

_T2x = chikamu che x chesimba rekumanikidza 2 = T₂ kusvika 45^o = 0.7 T₂

_T2y = chikamu che y chesimba rekumanikidzwa 2 = T₂ pasina 45^o = 0.7 T₂

Mamiriro ekuenzana ΣF = 0.

y akisi:

ΣF_y = 0

T_1y +T_2y – w = 0

0.7T₁ + 0.7T₂ - 100 = 0

0.7T₁ + 0.7T₂ = 100 —– muyero 1

akisi x:

ΣF_x = 0

T_2x - T_1x = 0

0.7T₂ – 0.7T₁ = 0

0.7T₂ = 0.7T₁

T₂ =T₁ —– muyero wechipiri

Sarudza hukuru hweT₁ :

0.7T₁ + 0.7T₁ = 100

1.4T₁ = 100

T₁ = 100/1.4

T₁ = 71.4 Newton

T₁ =T₂ saka T₂ = 71.4 Newton

[wpdm_package id='486′]

1. Zvidimbu zviri muchiyero chimwe chete
2. Zvidimbu zviri muchimiro chemativi maviri
3. Kuenzana kwemiviri yakabatana netambo nemapulley
4. Kuenzana kwemiviri iri mudenga rakarerekera

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1. Mabhokisi maviri akabatanidzwa netambo inomhanya pamusoro pepulley. Usafuratira huremu hwetambo nepulley uye chero kukweshana kuri mupulley. Misa yebhokisi 1 = 2 kg, huremu hwebhokisi 2 = 3 kg, kukurumidza nekuda kwegiravhiti = 10 m/s². Tsvaga (a) Kukurumidza kwehurongwa (b) Kumanikidzwa kwetambo!

mhinduro

Zvinozivikanwa:

Huremu hwebhokisi 1 (m₁) = 2 kg

Huremu hwebhokisi 2 (m₂) = 3 kg

Kukurumidza kunokonzerwa negiravhiti (g) = 10 m/s²

uremu yebhokisi 1 (w₁) = m₁ g = (2)(10) = 20 Newton

Kurema kwebhokisi 2 (w)₂) = m₂ g = (3)(10) = 30 Newton

Solution:

(a) hukuru uye gwara rekumhanya

w₂ > w₁ saka the bhokisi rechipiri rinokwidza nekukurumidza pasi uye bhokisi rekutanga rinokwidza nekukurumidza kumusoro.

Masimba ane divi rimwe chete nekukurumidzisa (w₂ uye T₁), chiratidzo chayo chakanaka. Masimba ane divi rakasiyana nerekumhanya (T)₂ uye w₁), chiratidzo chayo ndechekuti hapana.

∑F = ma

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

w₂ – T + T – w₁ = (m₁ +m₂) a

w₂ - w₁ = (m₁ +m₂) a

30 – 20 = (2 + 3) a

10 = 5 a

a = 10 / 5

a = 2 m/s²

Hukuru hwe kukurumidza iri 2 m/s².

(b) Simba rekumanikidza

Bhokisi rechipiri:

Pane masimba maviri anoitwa pabhokisi rechipiri: chekutanga, huremu hwebhokisi rechipiri (w₂), inonongedzera pasi saka zvakanaka. Chechipiri, simba rekumanikidza rakaiswa pabhokisi rechipiri (T)₂), inonongedzera kumusoro saka haina kunaka. Isa Mutemo wechipiri waNewton yekufamba.

∑F = ma

w₂ - T₂ = m₂ a

30 - T₂ = (3)(2)

30 - T₂ = 6

T₂ = 30 - 6

T₂ = 24 Newton

Bhokisi 1:

Pane zviito zviviri zvemasimba pabhokisi 1. Chekutanga, huremu hwebhokisi 1 (w₁), inonongedzera pasi saka haina kunaka. Chepiri, simba rekumanikidza rakashandiswa pabhokisi 1 (T₁) inonongedzera kumusoro saka zvakanaka. Shandisa mutemo wechipiri waNewton wekufamba:

∑F = ma

T₁ - w₁ = m₁ a

T₁ – 20 = (2)(2)

T₁ - 20 = 4

T₁ = 20 + 4

T₁ = 24 Newton

Hukuru hwesimba rekumanikidza = T₁ =T₂ = T = 24 Newton

2. Chinhu chiri panzvimbo yakamanikana yakatwasuka. Huremu hwechinhu 1 = 2 kg, huremu hwechinhu 2 = 4 kg, kumhanyisa nekuda kwegiravhiti = 10 m/s², coefficient ye static friction = 0.4, coefficient ye kinetic friction = 0.3. Sisitimu yacho yakamira kana kuti yakakurumidza? Kana sisitimu yakakurumidza, tsvaga hukuru uye gwara rekumhanya kwesisitimu!

mhinduro

Zvinozivikanwa:

Huremu hwechinhu 1 (m₁) = 2 kg

Huremu hwechinhu 2 (m₂) = 4 kg

Kukurumidza kunokonzerwa negiravhiti (g) = 10 m/s²

Koefficient ye kukweshana kwemamiriro ezvinhu (μ_s= = 0.4

Kukwana kwekukweshana kwekinetic (μ_k) = 0.3

Kurema kwechinhu 1 (w)₁) = m₁ g = (2)(10) = 20 Newton

Kurema kwechinhu 2 (w)₂) = m₂ g = (4)(10) = 40 Newton

simba remazuva ose yakaitwa pachinhu 1 (N) = w₁ = 20 Newton

Simba rekukweshana kwakasimba kunoitwa pachinhu 1 (f)_s) = μ_s N = (0.4)(20) = 8 Newtons

Simba rekukweshana kwekinetic rinoitwa pachinhu 1 (f)_k) = μ_k N = (0.3)(20) = 6 Newtons

Kuda: kukurumidza (a)

Solution:

w₂ > f_s (40 Newton > 8 Newton) saka chinhu 2 chinokurumidziswa chakadzika pasi uye chinhu 1 chinokurumidziswa chakatwasuka chakananga kurudyi. Simba rekukweshana rinoita basa pachinhu 1 isimba rekukweshana kwechinetike (f)._kShandisa mutemo wechipiri waNewton wekufamba:

∑F = ma

w₂ - the = (m₁ +m₂) a

40 – 6 = (2 + 4) a

34 = 6 a

a = 34 / 6 = 17 / 3

a = 5.7 m/s²

Hukuru hwekukurumidzira = 5.7 m/s²

[wpdm_package id='484′]

1. Huremu nehuremu
2. simba remazuva ose
3. Mutemo wechipiri wekufamba waNewton
4. Simba rekukakavadzana
5. Kufamba pamusoro penzvimbo yakatwasuka pasina simba rekukweshana
6. Kufamba kwemiviri miviri ine kumhanyisa kwakafanana pamusoro penzvimbo yakatwasuka ine simba rekukweshana
7. Kufamba mundege yakakotama pasina simba rekukweshana
8. Kufamba mundege yakakombama nesimba rekukweshana
9. Kufamba muelevator
10. Kufamba kwemiviri kwakabatana netambo nemapulley
11. Miviri miviri ine hukuru hwakafanana hwekukurumidzira
12. Kutenderedza denderedzwa rakati sandara - simba rekufamba kwedenderedzwa
13. Kutenderera curve yakakomberedzwa - simba rekufamba kwedenderedzwa
14. Kufamba kwakafanana mudenderedzwa rakatwasuka
15. Simba repakati nepakati rakafanana mukufamba kwedenderedzwa

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1. Munhu anorema 50 kg ari muelevator. Kuwedzera nekuda kwegiravhiti = 10 m/s²Sarudza kuti simba remazuva ose zvakaiswa pachinhu chiri pedyo neelevator, kana:

(a) lifti iri pazororo

(b) elevator iri kufamba ichidzika pasi pa kumhanya kunogara kuripo

(c) elevator inokwidzwa kumusoro pa kukurumidza nguva dzose 5 /s²

(d) elevator inodzikira pasi ne5 m/s isingachinji²

(e) elevator iri mu free-fall

mhinduro

Zvinozivikanwa:

Zvemunhu uremu (m) = 50 kg

Kukurumidza kunokonzerwa negiravhiti (g) = 10 m/s²

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

Kuda: Simba rakajairika (N)

Solution:

(a) lifti iri pazororo

Elevator iri panzvimbo yakanyarara saka hapana kumhanyisa (a = 0)

Tinosarudza nzira yekuenda kumusoro nenzira yakanaka uye nzira yekuenda pasi nenzira yakaipa.

ΣF = amai

N – w = 0

N = w

N = 500 Newton

(b) elevator iri kufamba ichidzika pasi nespeed isingachinji

Kumhanya kunogara kuripo saka hapana kukurumidza (a = 0)

Tinosarudza nzira yekuenda kumusoro nenzira yakanaka uye nzira yekuenda pasi nenzira yakaipa.

ΣF = amai

N – w = 0

N = w

N = 500 Newton

(c) elevator inokwidzwa kumusoro ne5 m/s isingachinji²

Kutungamira kwekumhanyisa kuri kumusoro, saka tinosarudza nzira yakanaka seyakakwira.

N – w = ma

N = w + ma

N = 500 + (50)(5)

N = 500 + 250

N = 750 Newton

Munhu wacho anonzwa pasi richisunda zvakanyanya kupfuura kana elevator yakamira kana kuti ichifamba nekumhanya kwakasimba.

Kana munhu akamira pachikero, chikero chinoverenga hukuru hwesimba rinodzika rinoitwa nemunhu ari pachikero. Nemutemo wechitatu waNewton, izvi zvakaenzana nehukuru hwesimba rinokwira rinoitwa nechikero pamunhu.

(d) elevator inodzikira pasi ne5 m/s isingachinji²

Kutungamira kwekumhanya kuri pasi, saka tinosarudza nzira yakanaka sekudzikira.

w – N = ma

N = w – ma

N = 500 – (50)(5)

N = 500 – 250

N = 250 Newton

Huremu hwemunhu i250 N, hushoma pane huremu chaihwo w = 500 N.

(e) elevator panguva yekudonha kwakasununguka

Kudonha kwakasununguka zvinoreva kuti kukwira kweelevator kwakafanana nekukwira kwesimba rinokwevera pasi. Hukuru hwekukwira kwesimba rinokwevera pasi i9,8 m/s², kwainoenda pasi ichienda pakati peNyika. Kumhanya kwacho kunowedzera mumutsara nenguva ne9,8 m/s panguva yesekondi.

Kutungamira kwekumhanya kuri pasi, saka tinosarudza nzira yakanaka sekudzikira.

w – N = ma

N = w – ma

N = 500 – (50)(10)

N = 500 – 500

N = 0

2. Tarisa kusimba kwetambo yeelevator. Huremu hweelevator = 2000 kg.

(a) lifti iri pazororo

(B) elevator yakakurumidza kudzika pasi ne5 m/s²

(C) Elevator yakakwira kumusoro ne5 m/s isingachinji²

(d) elevator pakudonha kwakasununguka

Kukurumidza kunokonzerwa negiravhiti (g) = 10 m/s²

mhinduro

Zvinozivikanwa:

Huremu hweelevator (m) = 2000 kg

Kukurumidza kwegiravhiti (g) = 10 m/s²

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

Zvaidiwa: Simba rekumanikidza (T)

Solution:

(a) lifti iri pazororo

chikepe iri pakuzorora saka hapana kukurumidza (a = 0)

Tinosarudza nzira yekumusoro senzira yakanaka uye nzira yekudzikira senzira isina kunaka.

ΣF = amai

T – w = 0

T = w

T = 20,000 Newton

Kushushikana kwetambo (T) = huremu hweelevator (w) = 20,000 Newtons

(b) elevator inodzikira pasi ne5 m/s isingachinji²

Kutungamira kwekumhanya kuri pasi, saka tinosarudza nzira yakanaka sekudzikira.

w – T = ma

T = w – ma

T = 20,000 – (2000)(5)

T = 20,000 - 10,000

T = 10,000 Newton

c) elevator inokwidzwa kumusoro ne5 m/s isingachinji²

Kutungamira kwekumhanya kuri pasi, saka tinosarudza nzira yakanaka seyakakwira.

T – w = ma

T = w + ma

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

T = 20,000 + 10,000

T = 30,000 Newton

(d) elevator pakudonha kwakasununguka

Kutungamira kwekumhanya kuri pasi, saka tinosarudza nzira yakanaka sekudzikira.

w – T = ma

T = w – ma

T = 20,000 – (2000)(10)

T = 20,000 - 20,000

T = 0

[wpdm_package id='482′]

1. Huremu nehuremu
2. simba remazuva ose
3. Mutemo wechipiri wekufamba waNewton
4. Simba rekukakavadzana
5. Kufamba pamusoro penzvimbo yakatwasuka pasina simba rekukweshana
6. Kufamba kwemiviri miviri ine kumhanyisa kwakafanana pamusoro penzvimbo yakatwasuka ine simba rekukweshana
7. Kufamba mundege yakakotama pasina simba rekukweshana
8. Kufamba mundege yakakombama nesimba rekukweshana
9. Kufamba muelevator
10. Kufamba kwemiviri kwakabatana netambo nemapulley
11. Miviri miviri ine hukuru hwakafanana hwekukurumidzira
12. Kutenderedza denderedzwa rakati sandara - simba rekufamba kwedenderedzwa
13. Kutenderera curve yakakomberedzwa - simba rekufamba kwedenderedzwa
14. Kufamba kwakafanana mudenderedzwa rakatwasuka
15. Simba repakati nepakati rakafanana mukufamba kwedenderedzwa

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