Ƙoƙari da kuzari

Idan ka tura littafi a kan teburi har sai ya motsa, to kana yin aiki ne a kan littafin. Idan abu ya faɗi a saman duniya saboda ƙarfin nauyi yana jan sa, to ƙarfin nauyi yana aiki ne a kan abu. Akasin haka, idan ka tura abu da dukkan ƙarfinka har sai gumi ya jike ka amma abin bai motsa ba, to ba ka yi aiki a kan abu ba. A rayuwar yau da kullun, wasu mutane suna cewa ka yi aiki ko ka yi aiki tuƙuru don tura abu, amma a cewar kimiyyar lissafi , ba ka yi aiki a kan abu ba saboda abin ba ya fuskantar matsi.

Ana iya yin aiki akan abu ta hanyar amfani da ƙarfi mai ɗorewa (girman da alkiblar ƙarfin koyaushe suna kasancewa iri ɗaya) ko kuma wani ƙarfi mai canzawa (girman da alkiblar ƙarfin koyaushe suna canzawa). Misalin ƙarfin da yake da ɗorewa a girma da alkibla shine ƙarfin nauyi da ke aiki akan abu lokacin da abin yake kusa da saman Duniya. Lokacin da abu yake cikin faɗuwa kyauta kusa da saman Duniya, girma da alkiblar saurin faɗuwa kyauta na abu suna da ɗorewa saboda girma da alkiblar ƙarfin nauyi da ke hanzarta abu suna da ɗorewa. Misalin ƙarfin da ba shi da ɗorewa a girma (alkiblar ƙarfin yana da ɗorewa) shine ƙarfin bazara . Idan ka shimfiɗa bazara, girman ƙaruwar tsawon bazara, da wuya ka ja shi. Girman ƙarfin da aka yi a kan bazara ba shi da ɗorewa yayin da bazara ke miƙewa. Wani misali kuma shine lokacin da roka ke tafiya zuwa sararin samaniya ko kuma ya koma saman Duniya. Lokacin da roka ke cikin motsi, girman ƙarfin nauyi da ke aiki akan roka yana canzawa daidai gwargwado zuwa murabba'in nisan daga tsakiyar Duniya.

A fannin lissafi, aikin da wani ƙarfi mai ɗorewa ke yi a kan wani abu ana bayyana shi a matsayin samfurin motsi sau da ƙarfi ko kuma ɓangaren ƙarfin a alkiblar motsi na abin.

Ba za a iya ƙididdige aikin da ƙarfin da ba ya tsayawa kamar maɓuɓɓuga ba ta amfani da dabarar aiki ta hanyar ƙarfin da ba ya tsayawa. Idan maɓuɓɓuga ta miƙe, yayin da maɓuɓɓuga ta miƙe, ƙarfin da ake buƙata don shimfiɗa maɓuɓɓuga shi ma yana ƙaruwa. Haka nan, idan maɓuɓɓuga ta matse, lokacin da maɓuɓɓuga ta yi ƙarfi, ƙarfin da ake buƙata shi ma yana ƙaruwa. Muddin an matse ko an miƙe maɓuɓɓuga, ƙarfin maɓuɓɓuga yana canzawa daga 0 (x = 0) zuwa matsakaicin (F = kx) don haka ana ƙididdige ƙarfin maɓuɓɓuga ta amfani da matsakaicin.

Misalin matsalolin

1. Tambayoyin Jarrabawar Ƙasa ta 2018

Toshe mai nauyin m yana kan wani wuri mai santsi. Toshe yana hutawa a matsayi (1) kuma ana ja shi da ƙarfi F zuwa matsayi (2) a cikin tazara ta lokaci kamar yadda aka nuna a cikin hoton.

Ta hanyar canza nauyi da ƙarfi, ana samun bayanai masu zuwa:

Daga teburin da ke sama, aikin da abubuwa daga babba zuwa ƙarami ke yi shine…

Tattaunawa

An sani:

Saurin farko (v _o ) = 0

An tambaya:

Amsa:

Tsarin aiki:

W = Fs s ……. Tsarin 1

Tsarin GLBB:

s = v _o t + 1/2 a ²

s = 1/2 a ²

Sauya zuwa dabara ta 1

W = F ( 1/2 a ² ) ……. Tsarin 2

Tsarin ƙarfi:

F = ma

a = F / m

Sauya zuwa dabara ta 2

W = 0,5 F (F/m) t ²

W = 0,5 (F ² /m) t ² ……. Tsarin 3

Yi amfani da dabara ta 3 don ƙididdige ƙoƙarin.

1) W = 0,5 (F ² /m) t ² = 0,5 (3 ² /12)(4 ² ) = (0,5)(9/12)(16) = (9/12) 8 = 6

2) W = 0,5 (F ² /m) t ² = 0,5 (4 ² /16)(3 ² ) = (0,5)(16/16)(9) = (1) 4,5 = 4,5

3) W = 0,5 (F ² /m) t ² = 0,5 (5 ² /20)(2 ² ) = (0,5)(25/20)(4) = (1,25) 2 = 2,5

4) W = 0,5 (F ² /m) t ² = 0,5 (6 ² /24)(1 ² ) = (0,5)(36/24)(1) = (1,5) 0,5 = 0,75

Aikin da abubuwan suka yi daga babba zuwa ƙarami shine 1, 2, 3, 4.

2. Tambayoyin Jarrabawar Ƙasa ta SMA/MA ta 2017

Akwati mai nauyin kilogiram 6 yana zamewa a gudun mita 8/s ^-1 a kan wani jirgin sama mai karkata mai kusurwar karkata α zuwa jirgin sama na kwance. Idan ƙarfin gogayya da ke aiki akan akwatin shine 5 N kuma tan α = 3/4, to ƙarfin F da dole ne a yi amfani da shi don dakatar da akwatin a ƙasan jirgin sama mai karkata shine…

A. 15 N

B. 25 N

C. 45 N

D. 55 N

E. 69,4 N

Tattaunawa

An san cewa:

Nauyin akwati (m) = 6 kg

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

Saurin farko na akwatin (vo _o ) = 8 m/s

Saurin ƙarshe na akwatin (v _t ) = 0 m/s (akwatin dole ne ya tsaya kafin ya isa ƙasan jirgin da aka karkata)

Ƙarfin gogayya ( _gogayya F ) = 5 N

Tangent α = gefen gaba / gefen ƙasa = 3/4

Hauhawar jini = mita 5

An tambaya: F

Amsa:

Ka'idar aikin injiniya-makamashi:

Aikin da ba na masu ra'ayin mazan jiya ba ke yi = canjin makamashin inji

Aikin da wani ƙarfi mara ra'ayin mazan jiya ya yi = canjin kuzarin motsi da ƙarfin da ake da shi.

Akwai ƙarfi biyu marasa ra'ayin mazan jiya, wato kinetic friction da F force.

Aikin da ƙarfin gogayya na kinetic ke yi akan akwatin:

W = -(F _ges )(s) = -(5)(5) = -25

Komawa mara kyau saboda alkiblar ƙarfin gogayya ta saba wa alkiblar motsin akwatin.

Aikin da aka yi ta hanyar ƙarfi F:

W = (F)(s) = (F)(5) = -5F

Komawa mara kyau saboda alkiblar ƙarfin F ta saba wa alkiblar motsin akwatin.

Canji a cikin kuzarin motsi:

Δ EK = 1/2 m (v _t ² - v _o ² ) = 1/2 (6) (0 ² - 8 ² ) = (3) (0-64) = (3) (-64) = -192

Canji a cikin ƙarfin ƙarfin nauyi:

Δ EP = mgh = (6)(10)(-3) = -180

h yana da korau saboda matsayin ƙarshe yana ƙasa da matsayin farko

Ka'idar aikin injiniya-makamashi:

W _nc = Δ EM

W _ges + W _F = Δ EP + Δ EK

-25 – 5F = -180 -192

-25 – 5F = -372

-5F = -372 + 25

-5F = – 347

F = -347 / -5

F = 69,4 Newton

Amsar da ta dace ita ce E.

3. Tambayoyin Jarrabawar Ƙasa ta SMA/MA ta 2017

Toshe mai nauyin kilogiram 10 yana zamewa ƙasa daga wurin A zuwa B kuma yana tsayawa a wurin C kamar yadda aka nuna a cikin hoton. Matsakaicin gogayya tsakanin toshe da saman da ba shi da kyau shine 0,2, don haka tsawon hanyar ABC shine…

A. 250 cm

B. 200 cm

C. 150 cm

D. 100 cm

E. 80 cm

Tattaunawa

An san cewa:

Nauyin tubali (m) = 10 kg

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

Nauyin tubalin (w) = mg = (10 kg)(10 m/s ² ) = Newtons 100

Tsawon jirgin sama mai karkata (h) = 30 cm = mita 0,3

Tsawon saman da aka karkata = 50 cm = mita 0,5

Ma'aunin gogayya ta motsi ( μ _k ) = 0,2

Ƙarfin gogayya na motsi (f _k ) = μ _k N = μ _k w = (0,2)(100 N) = 20 N

Tambaya: Tsawon hanyar ABC

Amsa:

Yi la'akari da motsin abin daga wurin AB.

Makamashin injiniya na farko a wurin A = makamashin ƙarfin nauyi = mgh = (10)(10)(0,3) = (10)(3) = Joules 30

Makamashin injiniya na ƙarshe a wurin B = makamashin motsi

Dokar kiyaye makamashin inji:

Makamashin injina na farko = makamashin injina na ƙarshe

Joules 30 = Makamashin motsa jiki

Don haka kuzarin motsi a wurin B = Joules 30.

Ka yi la'akari da motsin abin daga wurin BC.

Ka'idar makamashin aiki-injiniya ta bayyana cewa aikin da ƙarfin da ba na masu ra'ayin mazan jiya ba ya yi daidai da canjin makamashin inji na abu. Canji a cikin makamashin inji = makamashin inji na ƙarshe - makamashin inji na farko. A lissafi:

W _NC = Δ EM

W _NC = EM ₂ – EM ₁

An sanya abin a kan wani wuri mai faɗi don ƙarfin ƙarfin nauyi ya zama sifili. Makamashin injiniya (EM) = makamashin motsi (EK).

Makamashin motsi na farko (EK ₁ ) = kuzarin motsi a wurin B = Joules 30

Makamashin motsi na ƙarshe (EK ₂ ) = kuzarin motsi a wurin C = 0 (tashoshin toshewa).

Aikin da rundunar da ba ta da ra'ayin mazan jiya ta BC ke yi shi ne aikin da ƙarfin gogayya na motsi ke yi.

W _NC = – f _ks s = – 20 s

Jadi

W _NC = EK ₂ – EK ₁

– 20 s = 0 – 30

– 20 s = – 30

20 s = 30

s = 30/20 = 3/2 = mita 1,5 = 1,5 x 100 cm = 150 cm.

Tsawon layin ABC = 50 cm + 150 cm = 200 cm.

Amsar da ta dace ita ce B.

4. 2014/2015 SMA/MA Physics Tambaya Mai Lamba 8

Kalli hoton da ke ƙasa! Toshe yana zamewa a kan wani jirgin sama mai karkata mai ma'aunin gogayya na 0,4. Idan g = 10 ms ^-2 , to saurin toshewar lokacin da ya kai ƙasan jirgin sama mai karkata shine...

A. 2√5 ms^-1

B. 2 √7 ms ^-1

C. 2 √14 ms ^-1

D. 2 √19 ms ^-1

E. 2 √23 ms ^-1

Tattaunawa

Yayin da nake kallon hoton da ke ƙasa

An san cewa:

Tsawon farko (h _o ) = 6 m

Tsawon ƙarshe (h _t ) = 0 m

Saurin farko (v _o ) = 0 (da farko toshe yana nan har yanzu)

Ma'aunin gogayya na kinetic ( μ _k ) = 0,4 ( toshe yana zamewa don haka ma'aunin gogayya na kinetic, ba ma'aunin gogayya na tsaye ba )

Saurin gudu saboda nauyi (g) = 10 ms ^-2

cos θ = kasa / oblique = 8/10

Sashen nauyi a tsaye = _wy = w cos θ = mg cos θ = m (10) (8/10) = m (10)(4/5) = m (40/5) = 8 m

Ƙarfin da aka saba = N = w _y = 8 m

Ƙarfin gogayya na motsi = f _k = μ _k N = μ _k w _y = (0,4)(8 m) = 3,2 m

Tambaya: Saurin ƙarshe (v _t )

Amsa:

Ka'idar aiki-makamashi ta bayyana cewa aikin da ƙarfin da ba na masu ra'ayin mazan jiya ba ke yi a kan wani abu daidai yake da canjin kuzarin injina na abu. Misalin ƙarfin da ba na masu ra'ayin mazan jiya ba shine gogayya ta motsi.

W_nc = ΔEM

W _nc = Δ EK + Δ EP

Bayani:

W _nc = Aikin da ƙarfin da ba na masu ra'ayin mazan jiya ba ke yi, Δ EM = Canjin makamashin injiniya, Δ EK = Canjin makamashin motsi, Δ EP = Canjin makamashin da ake iya samu.

Canji a cikin kuzarin motsi:

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

Canji a cikin makamashi mai yuwuwa:

Δ EP = mg (h _t – h _o ) = m (10)(0-6) = m (10)(-6) = – m60

Aikin da aka yi ta hanyar kinetic friction:

Wnc = – f _ks s = – ( 3,2 m)(10) = – 32 m

Yana da mummunan aiki saboda ƙarfin gogayya na motsi yana yin aiki mara kyau, inda alkiblar ƙarfin gogayya na motsi (sama) take akasin alkiblar matsar da abu (zuwa ƙasa).

Lissafa saurin ƙarshe (v _t ):

Wnc = 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

Amsar da ta dace ita ce C.

5. 2014/2015 Jarrabawar Ƙasa ta SMA/MA Physics Tambaya Mai Lamba 8

Kalli hoton da ke gefe!

Toshe yana zamewa ƙasa da wani jirgin sama mai karkata, yana isa ga ƙafar jirgin sama mai karkata a gudun 10 ms ^-1 . Idan ƙarfin gogayya shine 2 N da g = 10 ms ^-2 , to ƙimar h shine ....

A. 10 m

B. 8 m

C. mita 6

D. 4 m

E. 2 m

Tattaunawa

An san cewa:

Nauyin tubali (m) = 1 kg

Saurin farko (v _o ) = 0 (da farko toshe yana nan har yanzu)

Saurin ƙarshe (v _t ) = 10 ms ^-1

Tsawon farko (h _o ) = h

Tsawon ƙarshe (h _t ) = 0

Ƙarfin gogayya na motsi (f _k ) = 2 N

Saurin gudu saboda nauyi (g) = 10 ms ^-2

An tambaya: Tsawo (h)

Amsa:

Aikin da aka yi ta hanyar kinetic friction:

Wnc = – f _k s = – (2 )(15) = – 30

Yana da mummunan aiki saboda ƙarfin gogayya na motsi yana yin aiki mara kyau, inda alkiblar ƙarfin gogayya na motsi (sama) take akasin alkiblar matsar da abu (zuwa ƙasa).

Canji a cikin kuzarin motsi:

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

Canji a cikin makamashi mai yuwuwa:

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

Tsarin ka'idar aikin-makamashi ta injiniya:

Wnc = Δ EK + Δ EP

– 30 = 50 – 10 hours

Awa 10 = 50 + 30

Awa 10 = 80

h = 80/10

h = mita 8

Amsar da ta dace ita ce B.