Matambudziko Akagadziriswa muFizikisi Yekutanga

1. Bhora re 0.2-kg, rakasungirirwa kumagumo kwetambo yakatambanudzwa, rinotenderedzwa mudenderedzwa re radius yemita imwe uye kumhanya kukuru kwebhora i10 rpm. Chii chinonzi kukura kwekumhanya kwepakati uye kukura kwesimba rekumanikidza?

Zvinozivikanwa:

Huremu (m) = 0.2 kg

Nharaunda (r) = 1 m

Kumhanya kweAngular (ω) = 10 rev/min = 10 rev/60 s = 0.17 rev/s = (0.17)(6.28 rad)/s = 1 rad/s

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

Zvaidiwa: a _s uye Σ F

Solution:

(a) Hukuru hwekumhanya kwepakati pesimba

(b) Hukuru hwesimba rekumanikidzwa

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. 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 resimba (T) = simba repakati ( Σ F) = 100 N

Zvinodiwa: v maximum

Solution:

[irp]

[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

Read more

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

N sin θ = chikamu chakatambanuka chesimba rakajairika

N cos θ = chikamu chakamira chesimba rakajairika

w = mg = huremu hwemotokari

Mugwagwa wacho wakagadzirwa kuti uvharwe nemabhanga kuti usanyanya kuvimba nekukakavadzana.

Simba rakatambanudzwa, iro chikamu chakatambanudzwa chesimba rakajairika ( N sin θ) , chinodiwa kuti mota irambe ichifamba yakatenderedza curve.

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:

[irp]

Shandisa mutemo waNewton wekufamba munzira yakatwasuka:

Isa N muequation 1 muN muequation 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

Read more

1. Mota inorema 2000 kg inotenderera curve mumugwagwa wakatsetseka we radius 150 m. Iyo coefficient ye static friction i0.5. Sarudza kumhanya kwakanyanya kuitira kuti mota itevere curve uye isatsvedze. Kumhanya nekuda kwegiravhiti = 10 m/s ².

Zvinozivikanwa:

Huremu (m) = 2000 kg

Nharaunda (r) = 150 mamita

Koefficient yekukweshana kwestatic ( μs ₎ = 0.5

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

Simba rekukwenya kwakamira (F _s ) = μ _s N = μ _s w = (0.7) (20,000 N) = 14,000 N

Aida: v

Solution:

[irp]

[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

Read more

1. Makiro maviri m ₁ = 2 kg uye m ₂ = 5 kg ari panzvimbo yakatsamira uye akabatanidzwa pamwe chete netambo sezvakaratidzwa mumufananidzo. Chiyero chekukakavadzana kwekinetic pakati pe m ₁ nekutsamira i 0.2 uye chiyero chekukakavadzana kwekinetic pakati pe m ₂ nekutsamira i 0.1.

(a) Sarudza kukurumidza kwavo

(b) Sarudza simba rekumanikidza

Zvinozivikanwa:

Huremu 1 (m1 ₎ = 2 kg

Huremu 2 (m2 ₎ = 4 kg

Kukweshana kwekinetic pakati pe m ₁ ne plane yakatsveyama (μ _k1 ) = 0.2

Kukweshana kwekinetic pakati pe m2 _neplane yakatsveyama (μ _k2 ) = 0.1

Kukurumidza kunokonzerwa negiravhiti (g) = 9.8 m/s ²

a) Hukuru uye gwara rekumhanya

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

w _1x = w ₁ chivi 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 = Simba rakajairika pa m ₁ = w _1y = 17 Newtons

F _k1 = Simba rekukweshana kwekinetic pa m ₁ = μ _k1 N ₁ = (0.2)(17 N) = 3.4 Newtons

---

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

w _2x = w ₂ chivi 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 = Simba rakajairika pa m ₂ = w _2y = 19.6 Newtons

F _k2 = Simba rekukweshana kwekinetic pa m ₂ = μ _k2 N ₂ = (0.1)(19.6 N) = 1.96 Newtons

---

Kukura kwekukurumidzira:

∑ F _x = ma _x

w _2x > w _1x saka divi rekumhanyisa rakafanana nedivi re w _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 = (m ₁ + m ₂ ) 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/s ²

Hukuru hwekukurumidzira = 3.16 m/s ^2. Nzira yekukurumidzira = nzira yeT ₁ = nzira yew _2x

b) Hukuru hwesimba rekumanikidza

Shandisa mutemo wechipiri waNewton pane chinhu chechipiri:

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

Simba rekumanikidzana = T = T ₁ = T ₂ = 19.5 Newtons

[irp]

2. m ₁ = 4 kg, m ₂ = 2 kg. Sarudza (a) hukuru uye divi rekumhanya (b) Hukuru hwesimba rekumanikidza rinobatanidza m ₁ uye m ₂ (c) hukuru hwesimba rekumanikidza rinobatanidza pulley nedenga.

mhinduro

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) Hukuru uye kutungamira kwekumhanya

∑ F _y = may _y

w ₁ > w ₂ saka kutungamira kwechinhu kwakafanana nekutungamira kwehuremu 1 ( w ₁ ) . Masimba ane divi rakafanana nekuwedzera simba akanaka uye masimba ane divi rakapesana nekumhanyisa simba haana kunaka.

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) _pagore

a _y = 19.6 N : 6 kg

a _y = 3.26 m/s ²

Hukuru hwekukurumidzira = 3.26 m/s ^2. Nzira yekukurumidzira = nzira ye w ₁.

b) Hukuru hwesimba rekumanikidzwa rinobatanidza m ₁ ne m ₂

Shandisa mutemo wechipiri waNewton 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

Hukuru hwesimba rekumanikidzana rinobatanidza zvinhu = T = T ₁ = T ₂ = 26.16 Newtons

c) Hukuru hwesimba rekumanikidza rinobatanidza pulley nedenga.

Pulley yazorora:

∑ F _y = may _y —— a _y = 0

∑ F _y = 0

Masimba ari kumusoro akanaka, masimba ari pasi haana kunaka:

T ₃ – T ₁ – T ₂ = 0

T3 = _T1 + _T2

T ₁ naT ₂ zvine hukuru hwakafanana , T ₁ = T ₂ = T = 26.16 N:

T ₃ = 2T = 2(26.16 N) = 52.32 Newtons

[irp]

3. Chivharo 1 (m ₁ = 10 kg) uye chivharo 2 (m ₂ = 15 kg) zvakabatana netambo pamusoro pepulley isina kukweshana. Coefficient yekukweshana kwakagadzika pakati pechivharo 2 chine kukweshana = 0.6. Coefficient yekukweshana kwekinetic pakati pechivharo 2 chine kukweshana = 0.42. Sarudza (a) Hukuru hwesimba diki F rakashandiswa pazvinhu kuitira kuti zvinhu zvikwidziridzwe kumusoro (b) Sarudza hukuru hwesimba rekukweshana.

mhinduro

w ₁ = Huremu hwebhuroko 1 = m ₁ g = (10 kg)(9.8 m/s ² ) = 98 Newtons

w ₂ = Huremu hwebhuroko 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 chivi 30 ^o = (147 N)(0.5) = 73.5 Newtons

N ₂ = Simba rakajairika pabhuroko 2 = w _2y = 127.89 Newtons

F _k2 = Simba rekukweshana kwekinetic pablock 2 = μ _k2 N ₂ = (0.42)(127.89 N) = 53.7 Newtons

F _s2 = Simba rekukweshana kwesimba pabhuroko 2 = μ _s2 N ₂ = (0.6)(127.89 N) = 76.7 Newtons

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

∑ F _x = ma _x —— a _x = 0

∑ F _x = 0

Masimba ekumusoro neakarurama akanaka, masimba epasi neakuruboshwe haana kunaka.

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) Hukuru hwesimba rekumanikidzwa

Shandisa mutemo waNewton wekufamba pabhokisi 1:

∑ F _y = may _y —— a _y = 0

∑ F _y = 0

T ₁ – w ₁ = 0

T ₁ = w ₁ = 98 Newton

Shandisa mutemo waNewton wekufamba pabhokisi 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

Hukuru hwesimba rekumanikidzwa = T ₁ = T ₂ = T = 98 Newtons

[irp]

4. Bhokisi 1 (m ₁ = 16 kg) riri pamusoro penzvimbo yakatambanuka uye bhokisi 2 (m ₂ = 12 kg) riri panzvimbo yakatsetseka, yakabatana netambo inopfuura nepapuri diki, isina kukweshana. Bhokisi 3 (m ₃ = 5 kg) riri pabhokisi 2. Kukweshana kwechinetic pakati pebhokisi 2 nepamusoro payo i0,4. Kukweshana kwekusagadzikana pakati pebhokisi 2 nebhokisi 3 i0,3.

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

(b) Kana paine bhokisi 3, chii chinoita kuti bhokisi 1 nebhokisi 2 zviwedzere?

Solution:

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

w ₁ = Huremu hwebhuroko 1 = m ₁ g = (16 kg)(9.8 m/s ² ) = 156.8 Newtons

w _1x = w ₁ chivi 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 = Simba rakajairika rinoitwa pabhuroko 1 nendege yakakombama = w _1y = 78.4 Newtons

w ₃ = Huremu hwebhuroko 3 = m ₃ g = (5 kg)(9.8 m/s ² ) = 49 Newtons

N ₂₃ = Simba rakajairika rinoitwa pabhokisi 3 nebhokisi 2 = w ₃ = 49 Newtons

N ₃₂ = Simba rakajairika rinoitwa pabhokisi rechipiri nebhokisi 3 = N ₂₃ = w ₃ = 49 Newtons

(N ₂₃ naN ₃₂ imhando mbiri dzezviito- maitiro )

F _s23 = Simba rekukweshana kwakasimba kunoitwa pabhokisi 3 nebhokisi 2 = μ _s N ₂₃ = (0.3)(49 N) = 14.7 Newtons

F _s32 = Simba rekukweshana kwakasimba kunoshandiswa pabhuroko rechipiri nebhuroko rechitatu = F _{s 23} = 14.7 Newtons

₍ F _s23 naF s32 mapaya ekuita-kuita )

w ₂ = Huremu hwebhuroko 2 = m ₂ g = (12 kg)(9.8 m/s ² ) = 117.6 Newtons

N ₂ = Simba rakajairika rinoitwa pachinhu 2 nepamusoro pakatwasuka = ​​w ₂ + N ₃₂ = 117.6 Newtons + 49

Newton = 166.6 Newton

F _k2 = Simba rekukweshana kwekinetic pablock 2 = μ _k N ₂ = (0.4)(166.6 N) = 66.64 Newtons

Shandisa mutemo waNewton wekufamba pabhokisi rechitatu:

∑ F _x = ma _x

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

Kukurumidza kwakanyanya kwebhuroko 3 kuitira kuti bhuroko 3 nebhuroko 2 zvirambe zvichitsvedza pamwe chete i2.94 m/s ².

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

Kutungamira kwebhuroko = nzira yekumhanyisa kwebhuroko = nzira yaT ₂ = nzira yaw _1x.

∑ F _x = ma _x

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

w _1x – F _k2 = (m ₁ + m ₂ + m ₃ ) 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/s ²

a _x iri positive, zvichireva kuti divi rekuchinja kweblock kana divi rekukurumidza rakafanana nedivi raT ₂ kana divi raw _1x.

Hukuru hwekumhanya kwemhepo ndeye 2.11 m/s ² , pasi pe 2.94 m/s ² saka tinogona kugumisa kuti bhokisi rechitatu nebhokisi rechipiri zvichiri kutsvedza pamwe chete mushure mekusunungurwa kubva pakuzorora.

b) Hukuru hwekukurumidzira kwebhokisi 1 nebhokisi 2

∑ F _x = ma _x

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 = (16 kg + 12 kg) 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. 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

Read more

1. Bhokisi re2-kg riri panzvimbo yakakombama pakona 37 ^o kuenda kune yakatwasuka. Sarudza hukuru hwesimba rekunze rinoshandiswa pabhokisi, kuitira kuti bhokisi risatsvedzerere pasi. (sin 37 ^o = 0.6, cos 37 ^o = 0.8, g = 10 ms ^-2 , µ _k = 0.2)

Zvinozivikanwa:

Huremu (m) = 2 kg

Kukurumidza kunokonzerwa negiravhiti (g) = 10 m/s ²

Kurema kwebhuroko (w) = mg = (2)(10) = 20 Newtons

Chivi 37 ^o = 0.6

Cos 37 ^o = 0.8

Kukweshana kwekinetic (µk ₎ = 0.2

Chikamu che y chehuremu (w _y ) = w cos 37 ^o = (20)(0.8) = 16 Newtons

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

simba rakajairika (N) = w _y = 16 maNewton

Zvinodiwa : 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.

[irp]

2. Huremu hwebhuroko = 2 kg, coefficient ye static friction µ _s = 0.4 uye θ = 45 ^o . Tsvaga hukuru hwesimba F kuitira kuti bhuroko ritange kutsvedza.

Zvinozivikanwa:

Chiyero chekukweshana kwesimba (µs ₎ = 0.4

Angle (θ) = 45 ^o

Kukurumidza kunokonzerwa negiravhiti (g) = 10 m/s ²

Huremu hwebhuroko (m) = 2 kg

Huremu hwebhuroko (w) = mg = (2 kg)(10 m/s ² ) = 20 kg m/s ² = 20 Newtons

Chikamu che x chehuremu (w _x ) = w sin 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

Zvinodiwa : 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 kwesimba :

f _s = µ _s N = (0,4)(10√2) = 4√2

Kukura kwesimba F zvekuti bhokisi rinotanga kutsvedza mudenga :

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

Read more

1. Bhokisi rine huremu hwe5 kg riri padenderedzwa rakanamira pakona ye30 ^o . Bhokisi racho rinotsigirwa netambo. Sarudza simba rekumanikidza (T) uye simba rakajairika (N)!

mhinduro

∑F_x = 0

T – w sin 30 ^o = 0

T = w chivi 30 ^o

T = (5 kg)(9.8 m/s ² ) 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

[irp]

2. Zvinhu zviviri zvine huremu m ₁ = m ₂ = 2 kg, zvakabatanidzwa netambo isina huremu pamusoro pepure isina kukweshana. Tsvaga masimba ekukweshana T ₁ naT ₂.

mhinduro

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

Shandisa mutemo wekutanga waNewton pakupikisa 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

Shandisa mutemo wekutanga waNewton pakupikisa 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. Chinhu chinorema w _A = 30 N uye chinhu chinorema w _B = 40 N, zvinosungirirwa netambo yakareruka inopfuura nepapulley isina kukweshana yehukuru hushoma. Sarudza coefficient yekukwirirana kwakanyanya pakati pe w _B nenzvimbo yakatsamira, kana sisitimu iri pakadzikama.

mhinduro

(a) Dhayagiramu yemuviri wakasununguka wechinhu w _A (b) Dhayagiramu yemuviri wakasununguka wechinhu w _B

Shandisa mutemo wekutanga waNewton kuti urambe w _A nenzira yakatwasuka (y):

∑ F _y = 0 (hapana kumhanyisa munzira yakatwasuka)

T – w _A = 0

T = w _A = 30 Newton

Shandisa mutemo wekutanga waNewton kuti urambe w _B nenzira yakatwasuka (y) :

∑ F _y = 0

N – w _B cos 45 ^o = 0

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

Shandisa mutemo wekutanga waNewton kuti urambe w _B munzira yakatwasuka (x):

∑ F _x = 0

F _k + w _B sin 45 ^o – T = 0

μ _s N + w _B chivi 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 nepamusoro penzvimbo yakatsamira = 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

Read more

1. Tsvaga masimba ekumanikidza T ₁ , T ₂ , uye T _3. Usatarisa huremu hwetambo.

mhinduro

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

Shandisa mutemo wekutanga waNewton pane chinhu chacho:

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

Shandisa mutemo wekutanga waNewton patambo:

∑ 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 ———- Equation 1

[irp]

-

∑ F _y = 0

T _3y + T _2y – T _1y = 0

T ₃ chivi 30 ^o + T ₂ chivi 40 ^o - T ₁ = 0

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

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

Read more

^{1. Huremu hwechinhu, m = 10 kg, chakatsigirwa netambo. Tsvaga kusimba kwetambo!} g = 10 m/s ²

Zvinozivikanwa:

Huremu (m) = 10 kg

Kukurumidza kunokonzerwa negiravhiti (g) = 10 m/s ²

Zvinodiwa: Simba rekumanikidza (T)

Solution:

ΣF _y = 0

T – w = 0

T = w

T = mg

T = (10 kg)(10 m/s ² ) = 100 kg m/s ²

T = 100 Newton

[irp]

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

mhinduro

Zvinozivikanwa:

Huremu (m) = 10 kg

Kukurumidza kunokonzerwa negiravhiti (g) = 10 m/s ².

Zvinodiwa: Simba rekumanikidza (T)

Solution:

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

T ₁ = simba rekumanikidza 1

_{T 1x} = chikamu che x chesimba rekumanikidzwa 1 = T ₁ cos 45 ^o = 0.7 T ₁

_{T 1y} = chikamu che y chesimba rekumanikidzwa 2 = T ₁ sin 45 ^o = 0.7 T ₁

T ₂ = simba rekumanikidza 2

_{T 2x} = chikamu che x chesimba rekumanikidzwa 2 = T ₂ cos 45 ^o = 0.7 T ₂

_{T 2y} = chikamu che y chesimba rekumanikidzwa 2 = T ₂ sin 45 ^o = 0.7 T ₂

Mamiriro ekuenzana ΣF = 0.

y akisi:

ΣF _y = 0

T _1y + T _2y – w = 0

0.7T ₁ + 0.7T ₂ – 100 = 0

0.7T ₁ + 0.7T ₂ = 100 —– muyero 1

akisi 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

Sarudza hukuru hweT 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 saka T ₂ = 71.4 Newtons

[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

Read more

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

mhinduro

Zvinozivikanwa:

Huremu hwebhokisi 1 (m1 ₎ = 2 kg

Huremu hwebhokisi 2 (m2 ₎ = 3 kg

Kukurumidza kunokonzerwa negiravhiti (g) = 10 m/s ²

Kurema kwebhokisi 1 (w ₁ ) = m ₁ g = (2)(10) = 20 Newtons

Kurema kwebhokisi 2 (w ₂ ) = m ₂ g = (3)(10) = 30 Newtons

Solution:

(a) hukuru uye gwara rekumhanya

w ₂ > w ₁ saka bhokisi 2 rinomhanyisa pasi uye bhokisi 1 rinomhanyisa kumusoro.

Masimba ane divi rimwe chete nekukurumidzisa (w ₂ na T ₁ ), chiratidzo chawo chakanaka. Masimba ane divi rakapesana nekukurumidzisa (T ₂ na w ₁ ), chiratidzo chavo chakanaka.

∑ 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

Hukuru hwekumhanya -mhanya i2 m/s ².

(b) Simba rekumanikidza

Bhokisi rechipiri:

Pane masimba maviri anoitwa pabhokisi rechipiri: chekutanga, huremu hwebhokisi rechipiri (w ₂ ), kunongedzera pasi kuitira kuti rive rakanaka. Chechipiri, simba rekumanikidzwa rinoitwa pabhokisi rechipiri (T ₂ ), kunongedzera kumusoro kuitira kuti rive negative. Shandisa mutemo wechipiri waNewton wekufamba.

∑ 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

Bhokisi 1:

Pane masimba maviri anoitwa pabhokisi 1. Chekutanga , huremu hwebhokisi 1 (w ₁ ), hunonongedza pasi saka huri negative. Chechipiri , simba rekumanikidzwa riri pabhokisi 1 (T ₁ ) rinonongedza kumusoro saka riri negative. Shandisa mutemo wechipiri waNewton wekufamba:

∑ 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

Hukuru hwesimba rekumanikidzwa = T ₁ = T ₂ = T = 24 Newtons

[irp]

2. Chinhu chiri panzvimbo yakatsetseka yakatwasuka. Huremu hwechinhu 1 = 2 kg, huremu hwechinhu 2 = 4 kg, kukurumidza nekuda kwegiravhiti = 10 m/s ² , kuenzana kwekukweshana kwakasimba = 0.4, kuenzana kwekukweshana kwekinetic = 0.3. Sisitimu yacho yakamira kana kuti yakakurumidza? Kana sisitimu yakakurumidza, tsvaga hukuru negwara rekukwidza kwesisitimu!

mhinduro

Zvinozivikanwa:

Huremu hwechinhu 1 (m1 ₎ = 2 kg

Huremu hwechinhu 2 (m2 ₎ = 4 kg

Kukurumidza kunokonzerwa negiravhiti (g) = 10 m/s ²

Koefficient yekukweshana kwesimba ( μs ₎ = 0.4

Chiyero chekukweshana kwekinetic ( μk ₎ = 0.3

Kurema kwechinhu 1 (w ₁ ) = m ₁ g = (2)(10) = 20 Newtons

Kurema kwechinhu 2 (w ₂ ) = m ₂ g = (4)(10) = 40 Newtons

Simba rakajairika rinoshandiswa pachinhu 1 (N) = w ₁ = 20 Newtons

Simba rekukweshana kwakasimba kunoitwa pachinhu 1 (fs ₎ = μ _s N = (0.4)(20) = 8 Newtons

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

Zvinodiwa: kukurumidza (a)

Solution:

w ₂ > fs ₍ 40 Newton > 8 Newton) saka chinhu 2 chinokurumidziswa chakadzika pasi uye chinhu 1 chinokurumidziswa chakatwasuka chakananga kurudyi. Simba rekukweshana rinoita basa pazvinhu 1 isimba rekukweshana kwechinetic (f _k ). Shandisa mutemo wechipiri waNewton wekufamba:

∑ F = ma

w ₂ – iyo = (m ₁ + m ₂ ) a

40 – 6 = (2 + 4) a

34 = 6 a

a = 34 / 6 = 17 / 3

a = 5.7 m/s ²

Hukuru hwekukurumidzira = 5.7 m/s ²

[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

Read more

1. Munhu anorema 50 kg ari muelevator. Kukurumidza kunokonzerwa negiravhiti = 10 m/s ² . Tsvaga simba rakajairika rinoitwa pachinhu chiri muelevator, kana:

(a) lifti iri pazororo

(b) elevator iri kufamba ichidzika pasi nespeed isingachinji

(c) elevator inokwidziridzwa kumusoro nekumhanya kwakasimba 5 / s ²

(d) elevator inodzikira pasi ne 5 m/s ²

(e) elevator panguva yekudonha kwakasununguka

mhinduro

Zvinozivikanwa:

Huremu hwemunhu (m) = 50 kg

Kukurumidza kunokonzerwa negiravhiti (g) = 10 m/s ²

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

Zvinodiwa: 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.

Σ F = ma

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.

Σ F = ma

N – w = 0

N = w

N = 500 Newton

(c) elevator inokwidzwa kumusoro ne5 m/s ²

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 ne 5 m/s ²

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/s ² , divi rayo riri pasi richienda pakati peNyika. Kumhanya kunowedzera mumutsara nenguva ne9,8 m/s mukati mesekondi yega yega.

Kutungamira kwekumhanya kuri pasi, saka tinosarudza nzira yakanaka sekudzikira.

w – N = ma

N = w – ma

N = 500 – (50)(10)

N = 500 – 500

N = 0

[irp]

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

(a) lifti iri pazororo

(b) elevator inodzikira pasi ne5 m/s ²

(c) elevator inokwidzwa kumusoro ne5 m/s ²

(d) elevator pakudonha kwakasununguka

Kukurumidza kunokonzerwa negiravhiti (g) = 10 m/s ²

mhinduro

Zvinozivikanwa:

Huremu hweelevator (m) = 2000 kg

Kukurumidza kwegiravhiti (g) = 10 m/s ²

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

Zvinodiwa: Simba rekumanikidza (T)

Solution:

(a) lifti iri pazororo

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

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

Σ F = ma

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 ²

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 ne 5 m/s ²

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

Read more