Makamashin Inji - matsaloli da mafita

1. Ma'aunin gogayya tsakanin tubali da bene (μk ₎ shine 0.5. Menene matsar da abu(s)? Saurin gudu saboda nauyi shine 10 m/s ².

An sani: Makamashin injina - matsaloli da mafita 1

Ma'aunin gogayya mai motsi (μk ₎ = 0.5

Nauyin tubali (m) = 4 kg

Saurin gudu saboda nauyi (g) shine 10 m/s ²

Nauyin tolo (w) = mg = (4)(10) = 40 Newtons

Idan toshe a kan jirgin sama na kwance to ƙarfin da aka saba (N) = nauyi (w) = Newtons 40.

Saurin farko (v ₁ ) = 5 m/s

Saurin ƙarshe (v ₂ ) = 0 m/s

Ana so: canja wurin abu (d)?

Magani:

Ka'idar makamashin aiki-injini ta bayyana cewa aikin (W) da ƙarfin da ba na masu ra'ayin mazan jiya ba ke yi iri ɗaya ne da canjin makamashin inji na wani abu. Canjin makamashin inji = makamashin inji na ƙarshe - makamashin inji na farko.

Ƙarfin gogayya na motsi ɗaya ne daga cikin ƙarfin da ba na masu ra'ayin mazan jiya ba kuma ɗaya tilo da ba na masu ra'ayin mazan jiya ba ke aiki a kan toshe.

W = ΔME

f _k d = ME ₂ – ME ₁

Aikin da ƙarfin gogayya na kinetic ke yi:

W = f _k d = (μ _k )(N)(d) = (0.5)(40)(d) = 20 d

Canjin makamashin inji:

ΔME = ME ₂ - ME ₁ = (KE + PE) ₂ - (KE + PE) ₁

Abu yana motsawa tare da jirgin sama na kwance kuma babu canjin tsayi (Δh = 0) don haka babu canjin ƙarfin ƙarfin nauyi (ΔPE = PE ₂ – PE ₁ = 0). Don haka canjin makamashin injiniyanci kawai ya ƙunshi canjin kuzarin motsi.

ΔME = KE ₂ - KE ₁ = ½ mv ₂² - ½ mv ₁² = ½ m (v ₂² - v ₁² )

Δ M E = ½ (4) (0 ² - 5 ² ) = (2) (25) = 50

Canja wurin tubalan:

W = ΔME

20 s = 50

s = 50 / 20

s = mita 2.5

Ka'idar kiyaye makamashin inji

2. Abu A da abu B suna da nauyi iri ɗaya. Abu A free faɗuwa daga tsayin mita h kuma abu B free faɗuwa daga tsayin mita 2. Idan abu A ya bugi ƙasa a vm/s, to menene kuzarin motsi na abu B lokacin da ya bugi ƙasa.

Magani:

Saurin ƙarshe na abu B lokacin da ya faɗi daga tsayin sa'o'i 2:

v ² = 2 g (awa 2) = 4 gh

Makamashin motsi na abu B:

TO _B = ½ mv ² = ½ m (4 gh) = 2 mgh —– lissafi 1

Makamashin injina na farko na abu B = makamashin ƙarfin nauyi = mg h.

Makamashin injiniya na ƙarshe na abu B = makamashin motsi = ½ mv ².

Ka'idar kiyaye makamashin inji:

mgh = ½ mv ²

Domin mgh = ½ mv ² to za mu iya canza mgh a cikin lissafi na 1 tare da ½ mv ².

Ƙarfin motsi na abu B = 2 mgh = 2(½ mv ² ) = mv ²

3. Faɗuwar abu ba tare da wani abu ba daga tsayin mita 20. Saurin da aka samu sakamakon nauyi shine m 10/s. Menene saurin abu a mita 15 sama da ƙasa?

Magani: Makamashin injina - matsaloli da mafita 2

Makamashin injiniya na ƙarshe = makamashin injiniya na farko

Ƙarfin motsi a wuri na 2 = canjin ƙarfin ƙarfin nauyi har zuwa mita 5.

Makamashin injina - matsaloli da mafita 3

4. An saki wani toshe daga saman jirgin sama mai santsi. Menene saurin toshewar idan ta bugi ƙasa?

Magani:

Makamashin injina na farko = makamashin ƙarfin nauyi = mgh = m (10)(5) = mita 50 Makamashin injina - matsaloli da mafita 4

Makamashin injiniya na ƙarshe = makamashin motsi = 1/2 mv ²

Ka'idar kiyaye makamashin injiniya, ta bayyana cewa makamashin injiniya na farko = makamashin injiniya na ƙarshe.

NI _o = NI _t

50 m = 1/2 mv ²

50 = 1/2 v ²

2 (50) = v ²

100 = v ²

v = 10m/s

Toshe mai nauyin m-kg wanda aka saki daga tsayin mita h sama da ƙasa, kamar yadda aka nuna a cikin hoton da ke ƙasa. Kayyade rabon kuzarin da ake da shi ga kuzarin motsi (KE) a wurin M.

Magani:

Ƙarfin ƙarfin nauyi a wurin M: Makamashin injina - matsaloli da mafita 5

PE _M = mg (awa 0.3)

Ƙarfin motsi a wurin m = canjin ƙarfin ƙarfin nauyi har zuwa h-0.3h = 0.7h

KE _M = PE = mg (awa 0.7)

Rabon kuzarin ƙarfin nauyi zuwa makamashin motsi a wurin M:

PE _M : KE _M

mg (0.3 h): mg (0.7 h)

0.3: 0.7

3: 7

6. Idan PE _Q da KE _Q suna da ƙarfin kuzari da kuzarin motsi a wurin Q (g = 10 m/s ² ), to PE _Q : KE _Q =…

Magani:

Ƙarfin ƙarfin nauyi a batu na Q: Makamashin injina - matsaloli da mafita 6

PE _Q = mgh = (m)(10)(1.8) = mita 18

Ƙarfin motsi a wurin Q = canjin ƙarfin ƙarfin nauyi har zuwa mita 5-1.8 = mita 3.2

TO _Q = PE = mgh = m (10)(3.2) = 32 m

Rabon kuzarin ƙarfin nauyi zuwa makamashin motsi a batu na Q:

_Q PE : KE _Q

mita 18: mita 32

18: 32

9: 16

Menene makamashin inji? Amsa: Makamashin injiniya shine jimlar kuzarin da ake da shi da kuma kuzarin motsi a cikin tsarin. Yana wakiltar jimlar adadin kuzarin da ke da alaƙa da motsi da matsayin abu.
Ta yaya makamashin motsi ya bambanta da makamashin da ake iya samu? Amsa: Makamashin motsa jiki shine makamashin motsi, yayin da makamashin yuwuwa shine makamashin da aka adana saboda matsayin abu ko tsarinsa. Misali, mota mai motsi tana da kuzarin motsi, yayin da maɓuɓɓugar ruwa ko abu mai tsayi a filin nauyi ke da kuzarin yuwuwa.
Shin makamashin injina koyaushe ana kiyaye shi? Amsa: A cikin tsari mai kyau, wanda ba shi da ƙarfin waje, ana adana makamashin injiniya. Duk da haka, a cikin yanayi na zahiri, wasu nau'ikan makamashi kamar makamashin zafi ko sauti na iya shiga cikin aiki saboda gogayya ko wasu ƙarfin da ba na masu ra'ayin mazan jiya ba, wanda ke haifar da raguwar cikakken kuzarin injiniya.
Ta yaya kiyaye makamashin injiniya ke taimakawa wajen magance matsaloli? Amsa: Idan aka adana makamashin injiniya a cikin tsarin (babu ƙarfin da ba na masu ra'ayin mazan jiya ba kamar gogayya), jimlar kuzarin da ke farawa daidai yake da jimlar kuzarin da ke ƙarshe. Wannan ƙa'ida tana ba mu damar danganta ƙarfin kuzarin da kuzarin motsi a wurare daban-daban a lokaci, yana sauƙaƙa tsarin magance matsaloli.
Me zai faru da kuzarin injina na ƙwallon idan aka jefa ta sama ta tsaya na ɗan lokaci kafin ta faɗi? Amsa: Yayin da ƙwallon ke tashi, ƙarfin motsinsa yana raguwa yayin da ƙarfin ƙarfinsa ke ƙaruwa. A lokacin kololuwar, duk ƙarfin injina nasa makamashi ne mai yuwuwa. Yayin da yake sauka, wannan tsari yana juyawa. A cikin yanayi mai kyau ba tare da juriyar iska ba, cikakken ƙarfin injina na ƙwallon yana nan a duk tsawon tafiyarsa.
Shin abu zai iya samun makamashin motsi da kuma makamashi mai yuwuwa a lokaci guda? Amsa: Eh, abu zai iya mallakar nau'ikan makamashi guda biyu a lokaci guda. Misali, pendulum a tsakiyar juyawarsa yana da kuzarin motsi saboda motsinsa da kuma kuzarin da zai iya samu saboda tsayinsa sama da mafi ƙasƙancin wurinsa.
Ta yaya na'urar jujjuyawa ke nuna kiyaye makamashin injiniya? Amsa: Jirgin ruwa mai juyawa yana farawa da ƙarfin da zai iya samu a mafi girman matsayi. Yayin da yake sauka, wannan ƙarfin da zai iya samu yana canzawa zuwa kuzarin motsi, yana sa jirgin ruwa ya yi sauri. Yayin da yake hawa sama, ƙarfin motsi yana raguwa yayin da ƙarfin da zai iya samu ke ƙaruwa. Yin watsi da gogayya da juriyar iska, jimlar ƙarfin injiniya yana nan kusan babu makawa.
Wadanne abubuwa ne zasu iya haifar da asarar makamashin inji a tsarin zahiri? Amsa: Karyewar yanayi, juriyar iska, da kuma samar da sauti wasu abubuwa ne da ka iya haifar da asarar makamashi a tsarin duniya ta zahiri. Ba a lalata makamashin (saboda dokar kiyaye makamashi) amma ana canza shi zuwa wasu siffofi kamar zafi ko sauti.
Menene alaƙar da ke tsakanin aiki da makamashin inji? Amsa: Aikin da ƙarfin waje ke yi a kan wani tsari na iya haifar da canji a cikin kuzarin injina na tsarin. A fannin lissafi, aiki daidai yake da canjin makamashin injina.
Idan ƙarfin ƙarfin nauyi yana da alaƙa da wurin tunani, ta yaya za mu iya auna canje-canje a cikinsa akai-akai? Amsa : Duk da cewa cikakken ƙimar ƙarfin ƙarfin nauyi ya dogara ne akan zaɓin wurin tunani, canje-canje a cikin kuzarin da ake iya samu (kamar lokacin da aka ɗaga ko aka rage abu) suna da daidaito ba tare da la'akari da ma'anar ba. Don haka, sau da yawa muna mai da hankali kan canje-canje a cikin kuzarin da ake iya samu ba tare da cikakkiyar ƙima ba.