Misalai 9 na Tambayoyin Kasuwanci
1. Ana amfani da ƙarfin Newton guda 20 a kan toshe har sai toshen ya yi tafiyar mita 2. Aikin da ƙarfin F ke yi a kan toshen shine…
Tattaunawa
An sani :
Ƙarfi (F) = 20 N
Matsugunin (s) = mita 2
Kusurwa = 0 (alkiblar ƙarfin iri ɗaya ce da alkiblar motsi ko kuma alkiblar ƙarfin ta yi daidai da alkiblar motsi ta yadda kusurwar da ƙarfin da motsi suka samar ta zama sifili)
An tambaya : Ƙoƙari (W)
Jawab :
Catatan :
Idan alkiblar ƙarfin iri ɗaya ce da alkiblar matsar da aka yi, ƙididdige aikin ta amfani da dabarar W = Fs, ba tare da buƙatar ƙara cos ba inna.
2. Abu yana tsaye a kan saman bene mai santsi. Ana amfani da ƙarfi F = 10 N a kan abin, yana samar da kusurwar 30o a saman bene. Idan abin ya motsa mita 1, nawa ne aikin da ƙarfin F ke yi akan abin?
Tattaunawa
An sani :
Ƙarfi (F) = Newtons 10
Ƙarfin da ke fuskantar ƙaura (F)x) = F cos 30o = (10)(0,5√3) = 5√3 Newtons
Matsugunin (s) = mita 1
An tambaya : ƙoƙari (W) ?
Jawab :
W = Fx s = (5√3)(1) = 5√3 Joule
3. Abu mai nauyin kilogiram 1 yana faɗuwa cikin sauƙi daga tsayin mita 2. Idan saurin gudu saboda nauyi shine mita 10/s2, ƙayyade aikin da ƙarfin nauyi ya yi akan abu!
Tattaunawa
An sani :
Nauyin abu (m) = 1 kg
Tsawo (h) = mita 2
Saurin gudu saboda nauyi (g) = 10 m/s2
An tambaya : Aikin da ƙarfin nauyi ke yi akan wani abu (W)
Jawab :
Alkiblar ƙarfin nauyi ko nauyi (w) tana tsaye ne zuwa ƙasa, alkiblar matsar da abu (s) kuma tana tsaye ne zuwa ƙasa don ƙarfin nauyi ya kasance daidai da alkiblar matsar da abu.
W = Fs = wh = mgh
W = (1)(10)(2) = Joule 20
4. Ana rataye maɓuɓɓugar ruwa da nauyin kilogiram 1 don haka maɓuɓɓugar ruwa ta sami ƙaruwa a tsawon santimita 2. Idan saurin gudu saboda nauyi ya kai mita 10/s2, ƙayyade (a) ma'aunin bazara (b) aikin da maɓuɓɓugar ruwa ta yi akan kaya
Tattaunawa
An sani :
Mass (m) = 1 kg
Saurin gudu saboda nauyi (g) = 10 m/s2
Ƙara tsawon bazara (x) = 2 cm = mita 0,02
An tambaya : madaidaitan bazara da aikin da ƙarfin bazara ke yi
Jawab :
(a) Madaidaitan bazara
Tsarin dokar Hooke :
F = k x.
Juya wannan dabarar don ƙididdige ma'aunin bazara:
k = F / x = w / x = mg / x
k = (1)(10) / 0,02 = 10 / 0,02
k = 500 Newton/mita
(b) Aikin da rundunar ma'aikatan bazara ta yi
W = – ½ kx2
W = – ½ (500)(0,02)2
W = – (250)(0,0004)
W = -0,1 Joule
Aikin da ƙarfin bazara ke yi akan nauyin ba shi da kyau saboda alkiblar ƙarfin bazara ta saba wa alkiblar canja wurin nauyin.
5. Akwatin da har yanzu yake a saman bene yana hanzarta da ƙarfin N 10 don haka akwatin ya motsa nisan mita 2. Idan ƙarfin turawa yana daidai da alkiblar da akwatin ya motsa kuma akwatin ya yi aiki da ƙarfin gogayya na Newtons 2, to jimlar aikin da aka yi akan akwatin shine...
Tattaunawa
An sani :
Ƙarfi (F) = Newtons 10
Ƙarfin gogayya na motsi (F)k) = 2 Newton
Matsugunin (s) = mita 2
An tambaya : Jimlar ƙoƙari (WTotal)
Jawab :
Aikin da aka yi da ƙarfi (F):
W1 = Fs cos 0 = (10)(2)(1) = Joules 20
Aikin da ƙarfin gogayya na motsi (F) ke yik):
W2 = Fk s = (2)(2)(cos 180) = (2)(2)(-1) = -4 Joules
Jimlar ƙoƙari shine:
WTotal = W1 - W2
WTotal = 20-4
WTotal = Joule 16
6. Abu mai nauyin kilogiram 5 yana da nisan mita 10 sama da saman Duniya. Saurin gudu saboda nauyi shine 10 m/s -2 . Adadin aikin da ake buƙata don motsa abu zuwa tsayin mita 15 sama da saman Duniya shine...
A. . 75 Joule
B.. 250 Joule
C.. Joule 500
D.. 750 Joule
E. 1.250 Joule
Tattaunawa
An san cewa:
Nauyin abu (m) = 5 kg
Tsawo (h) = mita 10
Saurin gudu saboda nauyi (g) = 10 m/s 2
Tambaya: Ƙoƙarin motsa abu zuwa tsayin mita 15
Amsa:
Kokarin motsa abu aƙalla daidai yake da ƙarfin nauyi da ke aiki akan abu.
Tsarin aikin da ƙarfin nauyi ke yi:
W = w = mgh
Bayani: W = ƙoƙari, w = nauyi, h = tsayi, m = nauyi, g = hanzarin nauyi
Tsarin aikin da aka yi shine:
W = wh = mgh = (5 kg)(10 m/s 2 )(10 m) = 500 kg m 2 / s 2 = 500 Joules
Amsar da ta dace ita ce C.
7. Wani abu mai nauyin kilogiram 2 yana motsawa akan wani wuri mai santsi a gudun mita 2/s –1 . Bayan 'yan mintuna kaɗan, abin yana motsawa a gudun mita 5/s –1 . Aikin da aka yi akan abin a wannan lokacin shine…
A. Joule 4
B. 9 Joule
C. 15 Joule
D. 21 Joule
E. 25 Joule
Tattaunawa
An san cewa:
Nauyin abu (m) = 2 kg
Saurin farko (v o ) = 2 ms –1
Saurin ƙarshe (v t ) = 5 ms –1
Tambaya: Aikin da aka yi a kan abu a lokacin tazara tsakanin lokaci
Amsa:
Ka'idar makamashin aiki-kinetic ta bayyana cewa jimlar aikin da aka yi akan wani abu daidai yake da canjin kuzarin motsi na abu. A lissafi:
W = ΔEK = EK 2 - EK 1 = 1/2 mv t 2 - 1/2 mv o 2 = 1/2 m (v t 2 - v o 2 ) = 1/2 (2) (5 2 -2 2 ) = (1) (25-4) = 21 Joules
8. Teburin da nauyinsa ya kai kilogiram 10 da farko yana kan bene mai santsi, ana tura shi na tsawon daƙiƙa 3 sannan ya yi tafiya a layi madaidaiciya tare da saurin gudu na 2 ms −2 . Adadin aikin da aka yi shine…
A. Joule 20
B. 30 Joule
C. 60 Joule
D. 180 Joule
E. 360 Joule
Tattaunawa
An sani cewa :
Mass (m) = 10 kg
Saurin farko (v o ) = 0 (da farko teburin yana tsaye)
Tazarar lokaci (t) = daƙiƙa 3
Hanzari (a) = 2 m/s 2
An tambaya : ƙoƙari (W)?
Amsa :
Da farko, ƙididdige nisan da aka yi amfani da dabarar GLBB:
s = v o t + ½ a 2 = (0)(3) + ½ (2)(3) 2
s = 0 + (1)(9) = 9
Aikin da aka yi a kan tebur:
W = Fs = (ma)(s) = (10)(2)(9) = Joules 180
Amsar da ta dace ita ce D.
9. An tura tubalan da nauyinsu ya kai kilogiram 1,5 sama ta hanyar ƙarfin da ba ya canzawa F = 15 N a kan jirgin da aka karkata kamar yadda aka nuna a cikin hoton. A ɗauka cewa saurin da aka samu sakamakon nauyi (g) shine 10 ms -2 kuma gogayya tsakanin tubalan da jirgin da aka karkata sifili ne. Jimillar aikin da aka yi a kan tubalan shine…
A. 15 J
B. 30 J
C. 35 J
D. 45 J
E. 50 J
Tattaunawa
An sani cewa :
Nauyin tubali (m) = 1,5 kg
Saurin gudu saboda nauyi (g) = 10 m/s 2
Nauyin tolo (w) = mg = (1,5)(10) = 15 Newton
Ƙarfin turawa (F) = 15 Newton
Tambaya : jimlar aikin da aka yi a kan tubalin (W)?
Amsa :
Akwai ƙarfi biyu da ke aiki a kan tubalin; ƙarfin da ke daidai da matsar da tubalin, wato ƙarfin turawa (F) da nauyin tubalin da ke daidai da saman jirgin sama mai karkata (w x ).
Aikin da ƙarfin turawa ke yi shine:
W 1 = F s = (15 N)(2 m) = 30 N m = Joules 30
Aikin da gravity wx ke yi:
W 2 = w x s = (w sin 30 o )(2 m) = (15 N)(1/2)(2 m) = 15 N m = 15 Joules
Jimlar aikin da aka yi a kan tubalin:
Jimlar W = W 1 – W 2 = 30 J – 15 J = Joules 15
Amsar da ta dace ita ce A.
