1. Tasoshi biyu m 1 = 2 kg da m 2 = 5 kg suna kan layi mai karkata kuma an haɗa su tare da igiya kamar yadda aka nuna a cikin hoton. Matsakaicin gogayya tsakanin m 1 da karkata shine 0.2 kuma ƙimar gogayya tsakanin m 2 da karkata shine 0.1.
(a) Ƙayyade saurin su
(b) Ƙayyade ƙarfin tashin hankali
An sani:
Nauyi 1 (m 1 ) = 2 kg
Nauyi 2 (m2 ) = 4 kg
Ma'aunin gogayya tsakanin m 1 da jirgin sama mai karkata (μ k1 ) = 0.2
Ma'aunin gogayya tsakanin m2 da jirgin sama mai karkata (μ k2 ) = 0.1
Saurin gudu saboda nauyi (g) = 9.8 m/s 2
a) Girma da alkiblar saurin gudu
w 1 = nauyi 1 = m 1 g = (2 kg)(9.8 m/s 2 ) = 19.6 Newtons
w 1x = w 1 zunubi 30 o = (19.6 N)(0.5) = 9.8 Newtons
w 1y = w 1 cos 30 o = (19.6 N)(0.87) = Newtons 17
N 1 = Ƙarfin da aka saba da shi akan m 1 = w 1y = 17 Newtons
F k1 = Ƙarfin gogayya mai motsi akan m 1 = μ k1 N 1 = (0.2)(17 N) = 3.4 Newtons
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w 2 = nauyi 2 = m 2 g = (kilogiram 4)(9.8 m/s 2 ) = 39.2 Newtons
w 2x = w 2 zunubi 60 o = (39.2 N) (0.87) = 34.1 Newtons
w 2y = w 2 cos 60 o = (39.2 N)(0.5) = 19.6 Newtons
N 2 = Ƙarfin da aka saba da shi akan m 2 = w 2y = 19.6 Newtons
F k2 = Ƙarfin gogayya mai motsi akan m 2 = μ k2 N 2 = (0.1)(19.6 N) = 1.96 Newtons
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Girman hanzarin:
∑ F x = ma x
w 2x > w 1x don haka alkiblar hanzarin daidai take da alkiblar w 2x.
Ƙarfin da ke nuna guduwa yana da kyau, kuma ƙarfin da ke da akasin alkiblar guduwa yana da korau.
w2x - Fk2 - T2 + T1 - w1x - Fk1 = (m1 +m2) da kumax
w 2x – F k2 – w 1x – F k1 = (m 1 + m 2 ) a x
34.1 N - 1.96 N - 9.8 N - 3.4 N = (2 kg + 4 kg) a x
18.94 N = (6 kg) a x
a x = 18.94 N: 6 kg
a x = 3.16 m/s 2
Girman hanzarin = 3.16 m/s 2. Alkiblar hanzarin = alkiblar T 1 = alkiblar w 2x
b) Girman ƙarfin tashin hankali
Yi amfani da dokar Newton ta biyu akan abu na 2:
w 2x – F k2 – T 2 = m 2 a x
34.1 N - 1.96 N - T 2 = (4 kg) (3.16 m/s 2 )
32.14 N – T 2 = 12.64 N
T 2 = 32.14 N – 12.64 N = 19.5 Newtons
Ƙarfin tashin hankali = T = T 1 = T 2 = 19.5 Newtons
[irp]
2. m 1 = 4 kg, m 2 = 2 kg. Kayyade (a) girma da alkiblar hanzari (b) Girman ƙarfin tashin hankali wanda ya haɗa m 1 da m 2 (c) girman ƙarfin tashin hankali wanda ya haɗa pulley da rufin.
Magani
w 1 = m 1 g = (kilogiram 4)(9.8 m/s 2 ) = 39.2 Newtons
w 2 = m 2 g = (2 kg)(9.8 m/s 2 ) = 19.6 Newtons
a) Girma da alkiblar saurin gudu
∑ F y = may y
w 1 > w 2 don haka alkiblar abu iri ɗaya ce da alkiblar nauyin 1 ( w 1 ) . Ƙarfin da ke da alkibla iri ɗaya da hanzari suna da kyau kuma ƙarfin da ke da alkibla akasin gudu suna da korau.
w 1 – T 1 + T 2 – w 2 = (m 1 + m 2 ) a y
w 1 – w 2 = (m 1 + m 2 ) a y
39.2 N - 19.6 N = (4 kg + 2 kg) a y
19.6 N = (kilogiram 6) a y
a y = 19.6 N: 6 kg
a y = 3.26 m/s 2
Girman hanzari = 3.26 m/s 2. Alkiblar hanzari = alkiblar w 1.
b) Girman ƙarfin tashin hankali wanda ke haɗa m 1 da m 2
Yi amfani da dokar Newton ta biyu akan m 2 :
∑ F y = may y
w 1 – T 1 = m 1 a y
39.2 N - T 1 = (4 kg) (3.26 m/s 2 )
39.2 N – T 1 = 13.04 N
T 1 = 39.2 N – 13.04 N
T 1 = 26.16 Newton
Girman ƙarfin tashin hankali wanda ke haɗa abubuwa = T = T 1 = T 2 = 26.16 Newtons
c) Girman ƙarfin tashin hankali wanda ke haɗa pulley da rufin.
Pulley yana hutawa:
∑ F y = may y —— a y = 0
∑ F y = 0
Ƙarfin sama yana da kyau, ƙarfin ƙasa kuma yana da korau:
T 3 – T 1 – T 2 = 0
T3 = T1 + T2
T 1 da T 2 suna da girma iri ɗaya , T 1 = T 2 = T = 26.16 N:
T 3 = 2T = 2(26.16 N) = 52.32 Newtons
[irp]
3. Toshe na 1 (m 1 = 10 kg) da toshe na 2 (m 2 = 15 kg) an haɗa su da igiya akan pulley mara gogayya. Coefficient na gogayya mai tsayayye tsakanin toshe na 2 tare da karkacewa = 0.6. Coefficient na gogayya mai motsi tsakanin toshe na 2 tare da karkacewa = 0.42. Kayyade (a) Girman ƙaramin ƙarfin F da aka yi akan abubuwan don abubuwan su hanzarta sama (b) Kayyade girman ƙarfin tashin hankali.
Magani
w 1 = Nauyin tubalin 1 = m 1 g = (10 kg)(9.8 m/s 2 ) = Newtons 98
w 2 = Nauyin tubalin 2 = m 2 g = (15 kg)(9.8 m/s 2 ) = Newtons 147
w 2y = w 2 cos 30 o = (147 N)(0.87) = 127.89 Newtons
w 2x = w 2 zunubi 30 o = (147 N) (0.5) = 73.5 Newtons
N 2 = Ƙarfin da aka saba da shi akan toshe 2 = w 2y = 127.89 Newtons
F k2 = Ƙarfin gogayya mai motsi akan toshe 2 = μ k2 N 2 = (0.42)(127.89 N) = 53.7 Newtons
F s2 = Ƙarfin gogayya mai tsauri akan toshe 2 = μ s2 N 2 = (0.6)(127.89 N) = 76.7 Newtons
a) Girman ƙaramin ƙarfin F da aka yi wa abubuwan don haka abubuwan suka yi sauri sama
∑ F x = ma x —— a x = 0
∑ F x = 0
Sojojin sama da na dama suna da kyau, sojojin ƙasa kuma na hagu suna da kyau.
F – F k2 – w 2x – w 1 – T 2 + T 1 = 0
F - F k2 - w 2x - w 1 = 0
F = F k2 + w 2x + w 1
F = 53.7 N + 73.5 N + 98 N
F = 225.2 Newton
b) Girman ƙarfin tashin hankali
Yi amfani da dokar motsi ta Newton a kan toshe na 1:
∑ F y = may y —— a y = 0
∑ F y = 0
T 1 – w 1 = 0
T 1 = w 1 = 98 Newton
Yi amfani da dokar motsi ta Newton a kan toshe na 2:
F – F k2 – w 2x – T 2 = 0
T 2 = F – F k2 – w 2x
T 2 = 225.2 N – 53.7 N – 73.5 N
T 2 = 98 Newton
Girman ƙarfin tashin hankali = T 1 = T 2 = T = 98 Newtons
[irp]
4. Toshe na 1 (m 1 = 16 kg) yana kwance a saman kwance kuma toshe na 2 (m 2 = 12 kg) yana kwance a kan wani santsi mai karkata, wanda aka haɗa ta da igiya wacce ke ratsa ƙaramin injin da ba shi da gogayya. Toshe na 3 (m 3 = 5 kg) yana kwance akan toshe na 2. Haɗaɗɗen gogayya tsakanin toshe na 2 da saman kwance shine 0,4. Haɗaɗɗen gogayya tsakanin toshe na 2 da toshe na 3 shine 0,3.
(a) Idan aka saki tsarin daga hutu, toshe na 3 da toshe na 2 har yanzu suna zamewa tare?
(b) Idan akwai toshe na 3, menene hanzarin toshe na 1 da toshe na 2?
Magani:
a) Idan aka saki tsarin daga hutu, toshe na 3 da toshe na 2 har yanzu suna zamewa tare?
w 1 = Nauyin tubalin 1 = m 1 g = (kilogiram 16)(9.8 m/s 2 ) = Newtons 156.8
w 1x = w 1 zunubi 60 o = (156.8 N)(0.87) = 136.4 Newtons
w 1y = w 1 cos 60 o = (156.8 N)(0.5) = 78.4 Newtons
N 1 = Ƙarfin da aka saba amfani da shi a kan toshe 1 ta hanyar jirgin sama mai karkata = w 1y = 78.4 Newtons
w 3 = Nauyin tubalin 3 = m 3 g = (kilogiram 5)(9.8 m/s 2 ) = Newtons 49
N 23 = Ƙarfin da aka saba amfani da shi a kan toshe 3 ta hanyar toshe 2 = w 3 = 49 Newtons
N 32 = Ƙarfin da aka saba amfani da shi a kan toshe na 2 ta hanyar toshe na 3 = N 23 = w 3 = 49 Newtons
(N23 da N32 nau'i biyu ne na martanin aiki da martani )
F s23 = Ƙarfin gogayya mai tsauri da aka yi a kan toshe 3 ta hanyar toshe 2 = μ s N 23 = (0.3)(49 N) = 14.7 Newtons
F s32 = Ƙarfin gogayya mai tsauri da aka yi a kan toshe na 2 ta toshe na 3 = F s 23 = 14.7 Newtons
(F s23 da F s32 sune haɗin kai-da martani )
w 2 = Nauyin tubalin 2 = m 2 g = (12 kg)(9.8 m/s 2 ) = 117.6 Newtons
N 2 = Ƙarfin da aka saba amfani da shi akan abu 2 ta saman kwance = w 2 + N 32 = 117.6 Newtons + 49
Newton = 166.6 Newton
F k2 = Ƙarfin gogayya mai motsi akan toshe 2 = μ k N 2 = (0.4)(166.6 N) = 66.64 Newtons
Yi amfani da dokar motsi ta Newton a kan toshe na 3:
∑ F x = ma x
F s23 = m 3 a x
—–> Fs23 = μs N23 = μs w3 = μs m3 g
μ s m 3 g = m 3 a x
μ s g = x
a x = (0.3)(9.8 m/s 2 ) = 2.94 m/s 2
Matsakaicin hanzarin toshe na 3 don toshe na 3 da toshe na 2 su ci gaba da zamewa tare shine 2.94 m/s 2.
Yanzu mun ƙididdige girman saurin tsarin bayan an sake shi daga hutu.
Alkiblar matsar da tubalan = alkiblar hanzarta tubalan = alkiblar T 2 = alkiblar w 1x.
∑ F x = ma x
w1x - T1 + T2 - Fk2 - Fs32 +Fs23 = (m1 +m2 +m3) da kumax
w 1x – F k2 = (m 1 + m 2 + m 3 ) a x
136.4 N - 66.64 N = (16 kg + 12 kg + 5 kg) a x
69.76 N = (33 kg) a x
a x = 2.11 m/s 2
x yana da kyau, ma'ana alkiblar matsar da tubalan ko alkiblar hanzarin iri ɗaya ne da alkiblar T 2 ko alkiblar w 1x.
Girman saurin gudu shine 2.11 m/s 2 , ƙasa da 2.94 m/s 2 don haka za mu iya kammala cewa toshe na 3 da toshe na 2 har yanzu suna zamewa tare bayan an sake su daga hutu.
b) Girman hanzarin toshe 1 da toshe 2
∑ F x = ma x
w 1x – F k2 = (m 1 + m 2 ) a x
—–> Fk2 = μk N2 = μk w2 = μk m2 g = (0.4)(kilogiram 12)(mita 9.8/s2) = 47.04 Newton
136.4 N - 47.04 N = (16 kg + 12 kg) a x
89.36 N = (28 kg) a x
a x = 89.36 N: 28 kg = 3.19 m/s 2
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- Nauyi da nauyi
- ƙarfin al'ada
- Dokar motsi ta biyu ta Newton
- Ƙarfin gogayya
- Motsi a saman kwance ba tare da ƙarfin gogayya ba
- Motsin gawawwaki biyu tare da hanzari iri ɗaya a kan saman kwance mai tsauri tare da ƙarfin gogayya
- Motsi a kan jirgin sama mai karkata ba tare da ƙarfin gogayya ba
- Motsi a kan jirgin sama mai karkata da ƙarfin gogayya
- Motsi a cikin lif
- Motsin jikin mutum yana da alaƙa da igiyoyi da kuma ƙwallo
- Jikuna biyu masu girman gudu iri ɗaya
- Zagaye lanƙwasa mai faɗi - yanayin motsi na zagaye
- Zagaye lanƙwasa mai banked - yanayin motsi na zagaye
- Motsi iri ɗaya a cikin da'irar kwance
- Ƙarfin tsakiya a cikin motsi na zagaye iri ɗaya
