Misalai 4 na tambayoyi kan aiwatar da dokokin Newton game da motsi kai tsaye na lif ko lif
1. Mutumin da nauyinsa ya kai kilogiram 50 yana cikin lif. Saurin gudu saboda nauyi = 10 m/s2A tantance girman ƙarfin da benen lif ke yi wa mutumin idan:
(a) lif mai shiru
(b) lif ɗin yana motsawa ƙasa da gudu akai-akai
(c) lif ɗin yana motsawa sama da sauri na 5 m/s2
(d) lif ɗin yana motsawa ƙasa da hanzarin 5 m/s2
(e) lif ɗin faɗuwa kyauta
Tattaunawa
An sani :
Nauyin mutum (m) = 50 kg
Saurin gudu saboda nauyi (g) = 10 m/s2
Nauyin mutum (w) = mg = (50)(10) = 500 Newtons
Jawab :
(a) lif mai shiru
Lif ɗin yana hutawa, babu hanzari (a = 0)
Ƙarfin da aka tura sama yana da kyau, ƙarfin da aka tura ƙasa yana da kyau.
(b) lif ɗin yana motsawa ƙasa da gudu akai-akai
Lifta tana motsawa a daidai gudun, babu hanzari (a = 0)
Ƙarfin da aka tura sama yana da kyau, ƙarfin da aka tura ƙasa yana da kyau.
(c) lif ɗin yana motsawa sama da sauri na 5 m/s2
Lif ɗin yana tafiya sama da sauri (a) na 5 m/s2
Ƙarfin da ke daidai da motsin ɗagawa yana da kyau, ƙarfin da ke akasin motsin ɗagawa yana da kyau.
N – w = ma
N = w + ma
N = 500 + (50)(5)
N = 500 + 250
N = 750 Newton
Girman ƙarfin da aka saba da shi (N) daidai yake da nauyin (w), don haka lokacin da lif ɗin ya motsa sama, jikin mutum yana jin nauyi. A wata ma'anar, lokacin da lif ɗin ya motsa sama, nauyin da ke bayyane ga mutum zai ƙaru. Idan mutumin yana tsaye a kan sikeli, lokacin da lif ɗin ya motsa sama, sikelin zai nuna girman mutumin ya fi girma.
(d) lif ɗin yana motsawa ƙasa da hanzarin 5 m/s2
Lif ɗin yana motsawa ƙasa da hanzarin (a) na 5 m/s2
Ƙarfin da ke daidai da motsin ɗagawa yana da kyau, ƙarfin da ke akasin motsin ɗagawa yana da kyau.
w – N = ma
N = w – ma
N = 500 – (50)(5)
N = 500 – 250
N = 250 Newton
Yayin da lif ɗin ke motsawa ƙasa, jikin mutumin yana jin sauƙi. A wata ma'anar, yayin da lif ɗin ke motsawa ƙasa, nauyin mutumin da ke bayyane yana ƙaruwa. Idan mutumin yana tsaye a kan sikeli, yayin da lif ɗin ke motsawa ƙasa, sikelin zai nuna ƙaramin nauyi.
(e) lif ɗin faɗuwa kyauta
Lif ɗin faɗuwa kyauta yana nufin lif ɗin yana motsawa ƙasa, inda hanzarin lif ɗin (a) = hanzarin nauyi (g). Misali, g = 10 m/s2 sannan a = 10 m/s2
Ƙarfin da ke daidai da motsin ɗagawa yana da kyau, ƙarfin da ke akasin motsin ɗagawa yana da kyau.
w – N = ma
N = w – ma
N = 500 – (50)(10)
N = 500 – 500
N = 0
Idan lif ɗin yana cikin faɗuwa daga sama, nauyin mutumin da ke bayyane shine sifili. A wata ma'anar, mutumin zai ɗauki kansa a matsayin wanda ba shi da nauyi. Idan mutumin yana tsaye a kan sikeli, yayin da lif ɗin ke motsawa ƙasa, sikelin zai nuna cewa nauyinsa sifili ne. Wannan yanayin yana kama da kasancewa a cikin sarari ba tare da nauyi ba.
2. Kayyade girman ƙarfin matsin lamba akan kebul na tallafi na ɗagawa tare da nauyin kilogiram 2000, idan:
(a) lif mai shiru
(b) lif ɗin yana motsawa ƙasa da hanzarin 5 m/s2
(c) lif ɗin yana motsawa sama da sauri na 5 m/s2
(d) lif ɗin faɗuwa kyauta
A ɗauka cewa saurin gudu saboda nauyi (g) = 10 m/s2
Tattaunawa
An sani :
Nauyin ɗagawa (m) = 2000 kg
Saurin gudu saboda nauyi (g) = 10 m/s2
Nauyin ɗagawa (w) = mg = (2000)(10) = 20.000 Newtons
Jawab :
(a) lif mai shiru
Lif ɗin yana hutawa, babu hanzari (a = 0)
Ƙarfin da aka tura sama yana da kyau, ƙarfin da aka tura ƙasa yana da kyau.
Idan ɗagawa ta tsaya cak, ƙarfin tashin hankali akan igiya (T) = nauyin ɗagawa (w) = Newtons 20.000
(b) lif ɗin yana motsawa ƙasa da hanzarin 5 m/s2
Lif ɗin yana motsawa ƙasa da hanzarin (a) na 5 m/s2
Ƙarfin da ke daidai da motsin ɗagawa yana da kyau, ƙarfin da ke akasin motsin ɗagawa yana da kyau.
w – T = ma
T = w – ma
T = 20.000 – (2000)(5)
T = 20.000 – 10.000
T = 10.000 Newtons
Lokacin da lif ɗin ya motsa ƙasa, ƙarfin matsin lamba akan igiyar (T) ya zama ƙarami fiye da lokacin da lif ɗin yake tsaye.
(c) lif ɗin yana motsawa sama da sauri na 5 m/s2
Lif ɗin yana tafiya sama da sauri (a) na 5 m/s2
Ƙarfin da ke daidai da motsin ɗagawa yana da kyau, ƙarfin da ke akasin motsin ɗagawa yana da kyau.
T – w = ma
T = w + ma
T = 20.000 + (2000)(5)
T = 20.000 + 10.000
T = 30.000 Newtons
Idan lif ɗin ya motsa sama, ƙarfin matsin lamba akan igiyar (T) ya fi girma fiye da lokacin da lif ɗin yake tsaye.
(d) lif ɗin faɗuwa kyauta
Lif ɗin faɗuwa kyauta yana nufin lif ɗin yana motsawa ƙasa, inda hanzarin lif ɗin (a) = hanzarin nauyi (g). Misali, g = 10 m/s2 sannan a = 10 m/s2
Ƙarfin da ke daidai da motsin ɗagawa yana da kyau, ƙarfin da ke akasin motsin ɗagawa yana da kyau.
w – T = ma
T = w – ma
T = 20.000 – (2000)(10)
T = 20.000 – 20.000
T = 0
Idan lif yana cikin faɗuwa kyauta, tashin hankalin da ke cikin igiyar (T) zai zama sifili. Saboda tashin hankalin da ke cikin igiyar yana daidai da nauyin lif, idan tashin hankalin da ke cikin igiyar sifili ne, nauyin lif ɗin shi ma ya zama sifili. Wannan yanayin yana kama da lokacin da abu yake cikin injin nauyi ko sarari inda babu ƙarfin nauyi.
[Turanci: Aiwatar da dokar motsi ta Newton a cikin lif]
3. Mutumin da nauyinsa ya kai kilogiram 60 yana cikin wani lif wanda ke tafiya ƙasa da sauri na mita 3/s.-2Idan saurin nauyi a Duniya ya kai mita 10/s-2, to girman ƙarfin da benen lif ke yi wa mutum shine….
A. 180 N
B. 200 N
C. 340 N
D. 420 N
E. 600 N
Tattaunawa
An san cewa:
Mass (m) = 60 kg
Hawan mutum da lif (a) = 3 m/s2
Saurin gudu saboda nauyi (g) = 10 m/s2
Nauyi (w) = mg = (60)(10) = 600 Newtons
An tambaya: ƙarfin yau da kullun (N)
Amsa:
Akwai ƙarfi biyu da ke aiki a kan mutum a cikin lif, wato nauyi (w) da ƙarfin da ake amfani da shi a ƙasan lif (N). Akwai adadi uku na vector, wato nauyi, ƙarfin yau da kullun, da kuma hanzarin lif, inda ake karkatar da nauyi zuwa ƙasa, ƙarfin yau da kullun ana karkatar da shi zuwa sama, kuma hanzarin lif ana karkatar da shi zuwa ƙasa. Ana zaɓar adadin vector da aka karkatar da shi zuwa ƙasa don samun alama mai kyau kuma ana zaɓar adadin vector da aka jagoranta zuwa sama don samun alama mara kyau.
∑F = ma
w – N = (60)(3)
600 – N = 180
N = 600 – 180
N = 420 Newton
Amsar da ta dace ita ce D.
4. Reza, mai nauyin kilogiram 40, yana cikin lif wanda ke tafiya sama. Idan ƙarfin benen lif ɗin da ke kan ƙafafun Reza shine 520 N kuma saurin gudu saboda nauyi shine 10 m/s-2, to hanzarta lif ɗin shine….
A. 1,0 ms-2
B. 1,5 ms-2
C. 2,0 ms-2
D. 2,5 ms-2
E. 3,0 ms-2
Tattaunawa
An san cewa:
Mass (m) = 40 kg
Ƙarfin da aka saba (N) = 520 N
Saurin gudu saboda nauyi (g) = 10 m/s2
Ƙarfin nauyi (w) = mg = (40)(10) = 400 N
An tambaya: Haɓaka lif
Amsa:
∑F = ma
400 – 520 = (40)(a)
-120 = (40)(a)
a = -120/40
a = -3 m/s2
Saurin lif ɗin shine 3 m/s2Alamar mara kyau tana nufin lif ɗin yana hawa sama.
Amsar da ta dace ita ce E.
Tushen tambaya:
Tambayoyin Nazarin Fizik na Ƙasa ga Makarantar Sakandare ta Babbar Sakandare/Makarantar Sakandare ta Sana'a
