Mfundo yaikulu ya mphamvu ya ntchito ndi makina - mavuto ndi mayankho

1. Bokosi la 2-kg limatsika kuchoka pa 10 m/s kupita ku mpumulo. Coefficient ya kinetic friction ndi 0.2. Kuthamanga chifukwa cha mphamvu yokoka ndi 10 m/s ^2. Kodi kukula kwa displacement ndi kotani?

Wodziwika;

Kulemera (m) = 2 kg

Liwiro loyambirira (v _o ) = 10 m/s

Liwiro lomaliza (v _t ) = 0 m/s

Chiŵerengero cha kupsinjika kwa kinetic ( _μk ) = 0.2

Kulemera (w) = mg = (1 kg)(10 m/s ² ) = 10 kg m/s ² = 10 N

Kufunidwa: Kukula kwa kusamuka (d)

Yankho:

Mfundo yaikulu ya mphamvu ya ntchito ndi makina :

W _nc = ΔEM

W _nc = ΔEK + ΔEP

W _nc = ½ m (v _t ² – vo ₂ ⁾ + mgh

W _nc = ntchito yochitidwa ndi mphamvu yosasunga malamulo yogwira ntchito pa chinthucho

ΔEK = kusintha kwa mphamvu ya kinetic

ΔEP = kusintha kwa mphamvu zomwe zingatheke

m = kulemera

v = liwiro

g = kuthamanga chifukwa cha mphamvu yokoka

h = kusintha kwa kutalika

Kusintha kwa kutalika h = 0 kotero ΔEP = 0

W _nc = ΔEK

Ntchito yochitidwa ndi mphamvu yosasintha:

W _nc = -F _c d = – μ _k N d = – μ _k wd = – μ _k mgd

W _nc = -(0.2)(2)(10)(s)

W _nc = – (4)(2)

Chizindikiro cha minus chimasonyeza kuti njira ya mphamvu ya kinetic friction ndi yosiyana ndi njira yosunthika.

Kusintha kwa mphamvu ya kinetic:

ΔEK = ½ m (v _t ² – v _o ² ) = ½ (2) (0 – 10 ² ) = 0 – 100 = -100

Kukula kwa kusamuka:

W _nc = ΔEK

– masekondi 4 = – 100

s = -100/-4

s = 25 m

[irp]

2. Chipika chimatsika pansi pa malo opendekeka. Chiŵerengero cha kugwedezeka kwa kinetic ndi 0.4. Kuthamanga chifukwa cha mphamvu yokoka ndi g = 10 ms ^-2 . Dziwani liwiro lomaliza pamene chipikacho chikugunda pansi.

Zodziwika:

Kutalika koyambirira (h _o ) = 6 m

Kutalika komaliza (h _t ) = 0 m

Liwiro loyambirira (v _o ) = 0

Chiŵerengero cha kupsinjika kwa kinetic ( _μk ) = 0.4

Kuthamanga chifukwa cha mphamvu yokoka (g) = 10 ms ^-2

cos θ = 8/10

Gawo loyima la kulemera = w _y = w cos θ = mg cos θ = m (10) (8/10) = m (10)(4/5) = m (40/5) = 8 m

Mphamvu yachibadwa = N = w _y = 8 m

Mphamvu ya kukangana kwa kinetic = f _k = μ _k N = μ _k w _y = (0.4)(8 m) = 3.2 m

Kufunidwa: Liwiro lomaliza (v _t )

Yankho:

Mfundo yaikulu ya mphamvu ya ntchito ndi makina:

W _nc = Δ EM

W _nc = Δ EK + Δ EP

Kusintha kwa mphamvu ya kinetic:

ΔEK = 1/2 m (v_t² -v_o²) = 1/2 m (v_t² - 0) = 1/2 mv_t²

Kusintha kwa mphamvu zomwe zingatheke:

Δ EP = mg (h _t – ho ₎ = m (10)(0-6) = m (10)(-6) = – 60 m

Ntchito yochitidwa ndi mphamvu ya kinetic friction:

W _nc = – f _ks = – ( 3.2 m)(10) = – 32 m

Chizindikiro cha minus chimasonyeza kuti mphamvu ya kinetic friction ikusiyana ndi njira yosunthira.

Liwiro lomaliza (v _t ):

W _nc = Δ EK + Δ EP

- 32 m = 1/2 mv _t ² - 60 m

– 32 m = m (1/2 v _t ² – 60)

– 32 = 1/2 v _t ² – 60

– 32 + 60 = 1/2 v _t ²

28 = 1/2 v _t ²

2 (28) = v _t ²

56 = v _t ²

v _t = √4.14

v _t = 2 √14 ms ^-1

[irp]

3. Chipika chimatsika pansi pa malo otsetsereka mozungulira. Liwiro loyambirira ndi 0 m/s ndipo liwiro lomaliza ndi 10 ms ^-1 . Ngati mphamvu ya kukangana kwa kinetic ndi 2 N ndipo kuthamanga chifukwa cha mphamvu yokoka g = 10 ms ^-2 , kodi kutalika (h) ndi chiyani?

Zodziwika:

Kulemera (m) = 1 kg

Liwiro loyambirira (v _o ) = 0 (kupuma kwa block)

Liwiro lomaliza (v _t ) = 10 ms ^-1

Kutalika koyambirira (h₂o₂ ₎ = h

Kutalika komaliza (h _t ) = 0

Mphamvu ya kukangana kwa kinetic (f _k ) = 2 N

Kuthamanga chifukwa cha mphamvu yokoka (g) = 10 ms ^-2

Kufunidwa: Kutalika (h)

Yankho:

Ntchito yochitidwa ndi mphamvu ya kinetic friction:

W _nc = – f _ks = – (2 )(15) = – 30

Chizindikiro cha minus chimasonyeza kuti mphamvu ya kinetic friction ikusiyana ndi njira yosunthira.

Kusintha kwa mphamvu ya kinetic:

ΔEK = 1/2 m (v_t² -v_o²) = 1/2 (1)(10² - 0) = 1/2 (10²) = 1/2 (100= = 50

Kusintha kwa mphamvu zomwe zingatheke:

Δ EP = mg (h _t – ho ₎ = (1)(10)(0-h) = (10)(-h) = -10 h

Mfundo yaikulu ya mphamvu ya ntchito ndi makina:

W _nc = Δ EK + Δ EP

– 30 = 50 – 10 maola

Maola 10 = 50 + 30

Maola 10 = 80

h = 80/10

h = 8 m

4Ngati chipika chikuyenda pansi mopendekeka kwambiri, ndiye….
A. Ntchito yochitidwa ndi mphamvu yokoka pa chipikacho ndi yayikulu kuposa kusintha kwa mphamvu yomwe ingatheke pa chipikacho
B. Mphamvu ya makina imawonjezeka
C. Kuchuluka kwa mphamvu ya kinetic ndi mphamvu yake yothekera kumachepa
D. Ntchitoyi imachitidwa ndi mphamvu yokangana yofanana ndi kusintha kwa mphamvu ya kinetic ya block
Anakonza

A ndi wolakwika

Ntchito yochitidwa ndi mphamvu yokoka pa chipikacho ndi yofanana ndi kusintha kwa mphamvu yokoka ya chipikacho.

B ndi wolakwika

Ngati ndege yomwe ili ndi mzere wa c ndi yosalala ndiye kuti mphamvu ya makina ya block imakhala yokhazikika. Ikakhala pamwamba pa ndege yopendekeka ndipo isasunthebe, mphamvu ya makina ya block imakhala yofanana ndi mphamvu ya mphamvu yokoka. Block imakhalabe yokhazikika kotero mphamvu yake ya kinetic ndi zero. Ikayenda pansi pa ndege yopendekeka, kutalika kwa block kumachepetsedwa kotero mphamvu ya mphamvu yokoka imachepetsedwanso. Mphamvu ya mphamvu yokoka imachepa chifukwa imasintha kukhala mphamvu ya kinetic. Ngakhale mphamvu yokoka imasintha kukhala mphamvu ya kinetic koma mphamvu ya makina imakhala yokhazikika.

Ngati malo otsetsereka ali olimba ndiye kuti mphamvu ya makina ya chipikacho imachepa chifukwa cha ntchito yoyipa yomwe imachitika ndi mphamvu ya friction. Mphamvu ya friction ndi mphamvu yosasunga zinthu. Ntchito yochitidwa ndi mphamvu yosasunga zinthu pa chinthu imapangitsa kuti mphamvu ya makina ya chinthucho ichepe.

C ndi yolondola

Mphepete mwa msewu ndi yokhotakhota kotero pali mphamvu yokangana yomwe imayesa kuyenda kwa chipikacho. Mphamvu yokangana ndi mphamvu yosasunga zinthu. Mphamvu yogwirira ntchito ya theorem-makina imanena kuti ntchito yochitidwa ndi mphamvu yosasunga zinthu (monga mphamvu yokangana) ndi yofanana ndi kusintha kwa mphamvu yamakina. Pakutsata kumeneku, mphamvu yamakina ikuchepa.

Mphamvu ya makina ya block = mphamvu yokoka + mphamvu ya kinetic.

D walakwitsa.

Ntchito yomwe mphamvu yokangana imachitidwa pa block ndi yofanana ndi kusintha kwa mphamvu ya makina ya block, osati kusintha kwa mphamvu ya kinetic ya block. Zoona kuti mphamvu yokangana imayesa kuyenda kwa block kotero imachepetsa liwiro la block ndikuchepetsa mphamvu ya kinetic ya block. Koma dziwani kuti mphamvu ya kinetic ya block imachokera ku mphamvu yokoka. Chifukwa chake ndi zoona kuti ntchitoyo imachitidwa ndi mphamvu yokangana yofanana ndi kusintha kwa mphamvu ya makina (mphamvu ya makina imachepa).

Yankho lolondola ndi C.

5. Chinthu chomwe chili pansi yolimba chimamenyedwa kotero chimayenda kwa masekondi atatu kenako chimayima. Ngati kulemera kodziwika kwa chinthucho ndi magalamu 10, mphamvu yokangana pakati pa chinthucho ndi pansi ndi 2 kilodyne. Dziwani ntchito yomwe yachitika ndi mphamvu yokangana.

A. 0.18 J

B. -0.18 J

C. 0.36 J

D. -0.36 J

Zodziwika:

Nthawi yopuma (t) = masekondi 3

Liwiro lomaliza (v _t ) = 0 m/s (kupuma kwa chinthu)

Kulemera kwa chinthu (m) = magalamu 10 = 10/1000 kg = 1/100 kg = 0.01 kg

Kugunda mphamvu (F) = 2 kilodynes = 2 x 10 ³ dynes

Kufunidwa: Ntchito (W) yochitidwa ndi mphamvu yokangana

Yankho:

Kusintha kwa mayunitsi a mphamvu:

1 Newton = 1 x 10 ⁵ dyne

Dyne imodzi = 1 / 10 ⁵ Newtons = 1 x 10 ^-5 Newtons = 10 ^-5 Newtons

Mphamvu yokangana (F) = 2 x 10 ³ dyne = 2 x 10 ³ x 10 ^-5 Newton = 2 x 10 ^-2 Newton = 2/100 Newton = 0.02 Newton

Theorem work-mechanical energy imati ntchito imachitika ndi mphamvu yosasintha pa chinthu chofanana ndi kusintha kwa mphamvu yamakina ya chinthucho.

Ngati chinthu chikuyenda pa plane yopendekeka ndiye kuti mphamvu ya makina (ME) = mphamvu yokoka (PE) + mphamvu ya kinetic (KE). Koma ngati chinthucho chikuyenda pa plane yopingasa kotero kuti palibe kusintha kwa kutalika, mphamvu ya makina = mphamvu ya kinetic. Pa plane yopingasa, mphamvu yokoka ndi zero chifukwa palibe kusintha kwa kutalika.

Mphamvu yokangana ndi mphamvu yosasintha. Mphamvu yokangana nthawi zambiri imachepetsa liwiro la chinthu ndi mphamvu ya kayendedwe ka chinthu. Tikhoza kunena kuti ntchito yomwe mphamvu yokangana imachitidwa pa chinthu ndi yofanana ndi kuchepa kwa mphamvu ya makina.

Mwa masamu:

Ntchito (W) = Kusintha kwa mphamvu ya makina (ΔEM)

F s = ΔEP + ΔEK

F s = mg Δh + ½ m (v _t ² – _vo ² )

F s = mg (0) + ½ m (0 ² – _vo ² )

F s = 0 + ½ m (– (v _o ² ))

F s = – ½ mv _o ² ———— Equation 1

Kufotokozera: F = mphamvu yokangana, d = kusamuka, m = kulemera, v _o = liwiro loyambirira

Kusamuka (d) ndi liwiro loyambirira (vo _o ) sizikudziwikabe chifukwa choyamba werengerani v _o kapena d. Ntchito yochitidwa ndi mphamvu yokangana imawerengedwa pogwiritsa ntchito imodzi mwa ma equation pambuyo pa v _o kapena d wodziwika.

Chiyerekezo cha kusamuka (d) pa kayendedwe kosagwirizana kolunjika:

v _t ² = vo ₂ ⁺ 2 (-a) s

Liwiro lomaliza (v _t ) = 0 ndipo kufulumira (a) kwasainidwa kuti ndi negative chifukwa chinthucho chatsika (liwiro la chinthucho lachepa).

0 = v_o² – malonda awiri

v_o² = malonda awiri

d = v _o ² / 2 a ———— Equation 2

Sinthani d mu equation 2 ndi d mu equation 1:

F d = – ½ mv _o ²

F (v _o ² /2a) = – ½ mv _o ²

(F/2a) v _o ² = – ½ mv _o ²

F/2a = – ½ m

F = (2)(a)(-1/2)(m)

F = – (a)(m)

a = – (F / m)

a = – 0.02 Newtons / 0.01 kilogalamu

a = – 2 Newton/kilogalamu

a = – 2 m/s ²

Equation yowerengera liwiro loyambirira (v _o ) mu kayendedwe kosagwirizana ka mzere:

v _t = vo _o + pa —–> Liwiro lomaliza (v _t ) = 0, Kuthamanga (a) = 2 m/s ² , nthawi yopuma (t) = masekondi atatu

0 = vo ₊ (-2)(3)

0 = ₆

v _o = mamita 6/sekondi

Ntchito (W) yochitidwa ndi mphamvu yokangana:

W = – ½ mv _o ² = -1/2 (0.01) (6 ² ) = -1/2 (0.01) (36)

W = -1/2 (0.36)

W = – 0.18 Joule

Ntchito yochitidwa ndi mphamvu yokangana imasainidwa kuti ndi yoipa kutanthauza kuti ntchitoyo imachepetsa mphamvu ya makina ya chinthucho.

Ngati ntchitoyo yadziwika, ikhoza kuwerengedwa pogwiritsa ntchito equation ya W = F d.

Yankho lolondola ndi B.

[wpdm_package id='1178′]

1. Ntchito yochitidwa ndi mphamvu ndi mavuto ndi mayankho
2. Mavuto ndi mayankho a mphamvu zogwirira ntchito
3. Mavuto ndi mayankho a mfundo za mphamvu za makina ndi ntchito
4. Mavuto ndi mayankho a mphamvu yokoka
5. Mphamvu yomwe ingagwiritsidwe ntchito pa mavuto ndi mayankho a masika otanuka
6. Mavuto amagetsi ndi mayankho
7. Kugwiritsa ntchito mphamvu yamakina yosungira kuti munthu agwe momasuka
8. Kugwiritsa ntchito mphamvu yamakina yosungira kayendedwe ka mmwamba ndi pansi mu kayendedwe ka free fall
9. Kugwiritsa ntchito kusunga mphamvu ya makina kuti ayende pamalo opindika
10. Kugwiritsa ntchito mphamvu yamakina yosungira kuti munthu ayende pa ndege yopendekeka
11. Kugwiritsa ntchito mphamvu ya makina yosungira kuti zigwiritsidwe ntchito poyendetsa zinthu