Misali na makamashin roba mai yuwuwa na marmaro

Misalan tambayoyi 5 game da makamashin roba na maɓuɓɓugan ruwa

1. Ana ba wa maɓuɓɓuga nauyi na kilogiram 2 sannan a rataye shi a tsaye a kan maɓuɓɓuga. Idan maɓuɓɓugar ta yi tsayi da santimita 4, to canjin ya faru. makamashi mai yuwuwa Ƙarfin roba na maɓuɓɓugar ruwa shine… g = 10 m/s²
Tattaunawa
An sani :
Nauyin kaya (m) = 2 kg
Saurin gudu saboda nauyi (g) = 10 m/s²
Nauyin kaya (w) = mg = (2)(10) = 20 Newton
Ƙara tsawon bazara (x) = 4 cm = mita 0,04
An tambaya : Ƙarfin ƙarfin sakewa na bazara
Jawab :
Tsarin dabara Dokar Hooke shine F = kx, inda F = ƙarfi, k = ma'aunin bazara da x = ƙaruwa a tsawon bazara. Idan aka daidaita da wannan matsalar to za a canza dabarar dokar Hooke zuwa w = kx, inda w = nauyiDon ƙididdige ma'aunin bazara, canza dabarar dokar Hooke zuwa k = w / x. Don haka ma'aunin bazara shine k = w / x = 20 / 0,04 = 500 Newton/mita.
Canjin da ke cikin ƙarfin elasticity na bazara shine:
EP = ½ kx² = ½ (500)(0,04)² = (250)(0,0016) = Joules 0,4

Ana iya ƙididdige canjin kuzarin roba na maɓuɓɓuga ta amfani da dabara guda ɗaya:
EP = ½ kx² = ½ (w / x) x² = ½ wx = ½ mgx
Bayani: w = ƙarfin nauyin kayan, m = nauyin kayan, x = canjin tsawon bazara.
EP = ½ (2)(10)(0,04) = (10)(0,04) = 0,4 Joules.

2. Don shimfiɗa maɓuɓɓugar ruwa mai tsawon santimita 10, ana buƙatar ƙarfin N 50. Ƙarfin da ake buƙata don shimfiɗa maɓuɓɓugar ruwa mai tsawon santimita 12 shine…
Tattaunawa
An sani :
Ƙara tsawon bazara (x) = 10 cm = mita 0,1
Ƙarfi (F) = Newtons 50
An tambaya : ƙarfin roba na maɓuɓɓugar ruwa don shimfiɗa maɓuɓɓugar ruwa har zuwa 12 cm ko mita 0,12.
Jawab :
Ma'aunin bazara shine:
k = F / x = 50 / 0,1 = 500 Newtons/mita
Maɓuɓɓugar da aka yi amfani da ita iri ɗaya ce, don haka ana amfani da ma'aunin maɓuɓɓugar da aka samu a lissafin da ya gabata don ƙididdige ƙarfin ƙarfin maɓuɓɓugar don shimfiɗa maɓuɓɓugar da mita 0,12.
EP = ½ kx² = ½ (500)(0,12)² = (250)(0,0144) = Joules 3,6.

3. Jadawalin da ke ƙasa yana nuna alaƙar da ke tsakanin ƙarfi (F) da ƙaruwar tsawon bazara (x). Idan bazara ta karkace da 10 cm, to kuzarin da ke tattare da bazarar zai kasance…

Tattaunawa
An sani :
Ƙarfi (F) = Newtons 5
Ƙara tsawon bazara (x) = 2 cm = mita 0,02
An tambaya : ƙarfin kuzarin bazara idan bazara ta karkace da santimita 10 ko mita 0,1.
Jawab :
Madawwamin bazara:
k = F / x = 5 / 0,02 = 250 Newtons/mita
Ƙarfin da za a iya samu daga bazara idan bazara ta karkace da mita 0,1:
EP = ½ kx² = ½ (250)(0,1)² = (125)(0,01) = Joules 1,25.

Makamashin Ƙarfin Nauyi Mai Ragewa
4. Ana ba wa maɓuɓɓuga nauyi na kilogiram 2 kamar yadda aka nuna a cikin hoton da ke ƙasa. Idan maɓuɓɓugar ta sami ƙaruwa a tsawonta na santimita 5 kuma hanzartawa saboda nauyi duniya 10 ms^-2, to, ƙarfin roba na bazara shine...
A. 4,0 J
B. 3,0 J
C. 2,5 J
D. 1,0 J
E. 0,5 J
Tattaunawa
An sani :
Ƙara tsayi (Δx) = 5 cm = mita 0,05
Saurin gudu saboda nauyi (g) = 10 m/s²
Nauyin kaya (m) = 2 kg
Nauyin kaya (w) = mg = (2)(10) = 20 Newton
An tambaya : Ƙarfin roba mai yuwuwa?
Jawab :
Da farko, ƙididdige ma'aunin ma'aunin roba na bazara ta amfani da dabarar dokar Hooke:
k = w / Δx = 20 / 0,05 = 400 N/m
Ƙarfin ƙarfin roba na bazara shine:
EP = ½ k Δx² = ½ (400)(0,05)² = (200)(0,0025)
EP = Joule 0,5
Amsar da ta dace ita ce E.

5. Don miƙewa da maɓuɓɓugar ruwa mai tsawon santimita 5, ana buƙatar ƙarfin N20. Ƙarfin da maɓuɓɓugar ruwa ke da shi lokacin da ya miƙe santimita 10…
A. Joule 2
B. 4 Joule
C. 20 Joule
D. 50 Joule
E. 100 Joule
Tattaunawa
An sani :
Ƙara tsayi (Δx) = 5 cm = mita 0,05
Ƙarfi (F) = Newtons 20
An tambaya : EP na bazara lokacin da bazara ta miƙe 10 cm?
Jawab :
Madawwamin bazara:
k = F / Δx = 20 / 0,05 = 400 N/m
Ƙarfin da za a iya samu daga bazara idan Δx = 10 cm = mita 0,1:
EP = ½ k Δx² = ½ (400)(0,1)² = (200)(0,01)
EP = Joule 2
Amsar da ta dace ita ce A.