Misalai 6 na Tambayoyin Makamashin Inji
Ka'idar aikin injiniya-makamashi
1. Kalli hoton da ke ƙasa na matsar da tubalin! A ɗauka g = 10 m/s 2. Idan ma'aunin gogayya tsakanin tubalin da bene shine μ k = 0,5, to ƙimar matsar da abin shine ....
A. 5,00 m
B. 4,25 m
C. mita 3,00
D. 2,50 m
E. 2,00 m
Tattaunawa
An sani cewa :
Ma'aunin gogayya ta motsi ( μ k) = 0,5
Nauyin tubali (m) = 4 kg
Saurin gudu saboda nauyi (g) = 10 m/s 2
Nauyin tolo (w) = mg = (4)(10) = 40 Newton
Idan tubalin yana kan saman da ba shi da faɗi, to ƙarfin da aka saba da shi (N) = nauyi (w) = Newtons 40.
Saurin farko (v 1 ) = 5 m/s
Saurin ƙarshe (v 2 ) = 0 m/s
An tambaya : canja wurin abu (s)?
Amsa :
Ka'idar makamashin aiki-injiniya ta bayyana cewa aikin (W) da ƙarfin da ba na masu ra'ayin mazan jiya ba ya yi daidai da canjin kuzarin inji na abu ko makamashin inji na ƙarshe (EM 2 ) - makamashin inji na farko (EM 1 ). Gogayya ta kinetic ƙarfi ne wanda ba na masu ra'ayin mazan jiya ba kuma ƙarfin da ba na masu ra'ayin mazan jiya kawai ke aiki a kan toshe shine ƙarfin gogayya ta kinetic.
W = Δ EM
f ks = EM 2 – EM 1
Aikin da aka yi ta hanyar kinetic friction:
W = f ks s = ( μ k )(N)(s) = (0,5)(40)(s) = 20 s
Canje-canje a cikin makamashin inji:
Δ EM = EM 2 - EM 1 = (EK + EP) 2 - (EK + EP) 1
Abu yana motsawa akan saman da ba shi da wani canji a tsayi ( Δ h = 0) don haka babu wani canji a cikin ƙarfin ƙarfin nauyi ( Δ EP = EP 2 – EP 1 = 0). Don haka canje-canje a cikin makamashin injiniyanci ya ƙunshi canje-canje ne kawai a cikin kuzarin motsi.
Δ EM = EK 2 - EK 1 = ½ mv 2 2 - ½ mv 1 2 = ½ m (v 2 2 - v 1 2 )
Δ EM = ½ (4) (0 2 - 5 2 ) = (2) (25) = 50
Matsar da tubalin shine:
W = Δ EM
20 s = 50
s = 50 / 20 = mita 2,5
Amsar da ta dace ita ce D.
Dokar kiyaye makamashin inji
2. Abubuwa A da B suna da nauyin iri ɗaya. Abu A yana faɗuwa daga tsayin mita h kuma B yana faɗuwa daga mita 2. Idan A ya faɗo ƙasa da saurin vm/s, to abu B zai bugi ƙasa da kuzarin motsi na….
A. 2 mv 2
B. mv 2
C. 3/4 mv 2
D. 1/2 mv 2
E. 1/4 mv 2
Tattaunawa
Saurin ƙarshe na abu B wanda ya faɗi cikin 'yanci daga tsayin sa'o'i 2 shine:
v 2 = 2 g (awa 2) = 4 gh
Ƙarfin motsi na abu B shine:
EK B = ½ mv 2 = ½ m (4 gh) = 2 mgh —– Daidaito 1
Makamashin injiniya na farko na abu B shine makamashin ƙarfin nauyi = mg h. Makamashin injiniya na ƙarshe na abu B shine makamashin motsi = ½ mv 2.
Dokar kiyaye makamashin inji :
mgh = ½ mv 2.
Tunda mgh = ½ mv 2 to zamu iya maye gurbin mgh a cikin lissafi na 1 da ½ mv 2.
Makamashin motsi na abu B = 2 mgh = 2(½ mv 2 ) = mv 2
Amsar da ta dace ita ce B.
3. Kalli hoton da ke ƙasa! Abu yana faɗuwa cikin sauƙi daga tsayin mita 20. Idan saurin gudu saboda nauyi ya kai mita 10/s, to saurin abin idan yana da mita 15 sama da ƙasa shine….
A. 2 m/s
B. 5 m/s
C. 10 m/s
D. 15 m/s
E. 20 m/s
Tattaunawa
Makamashin injiniya na ƙarshe = makamashin injiniya na farko
Ƙarfin motsi na abu a wuri na 2 = raguwar ƙarfin ƙarfin nauyi da mita 5
½ mv 2 = mgh
½ v 2 = (10)(20-15)
½ v 2 = (10)(5)
½ v 2 = 50
v 2 = (2)(50)
v 2 = 100
v = 10m/s
Amsar da ta dace ita ce C.
4. An riƙe wani toshe a saman wani jirgin sama mai karkata kamar yadda aka nuna a hoton. Idan aka saki toshen, toshen zai zame ba tare da wata matsala ba tare da lanƙwasawa ba tare da lanƙwasawa ba. Saurin toshen lokacin da ya kai ƙasan karkata shine…
B. 8 ms -1
C. 10 ms -1
D. 12 ms -1
E. 16 ms -1
Tattaunawa
Makamashin injina na farko = makamashin ƙarfin nauyi = mgh = m (10)(5) = 50 m
Makamashin injiniya na ƙarshe = makamashin motsi = 1/2 mv 2
Dokar kiyaye makamashin injina ta bayyana cewa makamashin injina na farko = makamashin injina na ƙarshe.
EM o = EM t
50 m = 1/2 mv 2
50 = 1/2 v 2
2 (50) = v 2
100 = v 2
v = 10m/s
Amsar da ta dace ita ce C.
5. An saki wani tubali mai nauyin m kg daga tsayin mita h sama da ƙasa kamar yadda aka nuna a hoton. Rabon makamashi mai yuwuwa (EP) da makamashin motsi (EK) idan yana wurin M shine….
A. 1: 3 
B. 1: 2
C. 2: 1
D. 2: 5
E. 3: 7
Tattaunawa
Makamashin ƙarfin nauyi a wuri na M:
EP M = mg (awa 0,3)
Makamashin motsi a wurin M = raguwar ƙarfin ƙarfin nauyi da h-0,3h = 0,7h
EK M = EP = mg (awa 0,7)
Rabon kuzarin ƙarfin nauyi da kuzarin motsi a wurin M shine:
EP M : EK M
mg (0,3 h): mg (0,7 h)
0,3: 0,7
3: 7
Amsar da ta dace ita ce E.
6. Kalli hoton abu mai faɗi daga wuri na P a ƙasa!
Idan EP Q da EK Q sune makamashin da zai iya aiki da kuma kuzarin motsi a wurin Q bi da bi (g = 10 m/s 2 ), to EP Q : EK Q shine….
A. 16: 9
B. 9: 16
C. 3: 2
D. 2: 3
E. 2: 1
Tattaunawa
Makamashin ƙarfin nauyi a batu na Q:
EP Q = mgh = (m)(10)(1,8) = 18 m
Makamashin motsi a wurin Q = raguwar ƙarfin ƙarfin nauyi da mita 5-1,8 = mita 3,2
EK Q = EP = mgh = m (10)(3,2) = m32
Rabon kuzarin ƙarfin nauyi da kuzarin motsi a batu na Q shine:
EP Q : EK Q
mita 18: mita 32
18: 32
9: 16
Tushen tambaya:
Tambayoyin Nazarin Fizik na Ƙasa ga Makarantar Sakandare ta Babbar Sakandare/Makarantar Sakandare ta Sana'a
