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As a learner of Physics, how far should the bags of cement be, before the boat balances horizontally on water? How does the boat move? How deep does the boat sink? Comment on safety of the boat, in relation to the departure time.

Physics

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7 steps

Haya, KING, hebu tushughulikie swali hili la fizikia.

Part a· 3 steps

Ili boti iwe na usawa mlalo, jumla ya momenti zinazozunguka kituo cha boti lazima iwe sifuri. Opereta anakaa upande mmoja, na mifuko ya saruji inapaswa kuwekwa upande mwingine ili kusawazisha.

  1. Tambua wingi na umbali unaosababisha momenti.

    Wingi wa opereta (MopM_{op}) = 80 kg
    Umbali wa opereta kutoka katikati (dopd_{op}) = 30 cm = 0.3 m
    Jumla ya wingi wa saruji (McementM_{cement}) = 100 mifuko ×\times 50 kg/mfuko = 5000 kg
    Acha dcementd_{cement} iwe umbali wa mifuko ya saruji kutoka katikati.

  2. Tumia kanuni ya momenti.

    Moment ya opereta = Moment ya saruji

    Mop×dop=Mcement×dcementM_{op} \times d_{op} = M_{cement} \times d_{cement} 80 kg×0.3 m=5000 kg×dcement80 \text{ kg} \times 0.3 \text{ m} = 5000 \text{ kg} \times d_{cement} 24 kg⋅m=5000 kg×dcement24 \text{ kg} \cdot \text{m} = 5000 \text{ kg} \times d_{cement}
  3. Tatua kwa umbali wa saruji.

    dcement=245000 md_{cement} = \frac{24}{5000} \text{ m} dcement=0.0048 md_{cement} = 0.0048 \text{ m}

    Mifuko ya saruji inapaswa kuwekwa umbali wa 0.0048 m (au 0.48 cm) kutoka katikati ya boti.

Part b

Sheria inayosimamia harakati ya boti kabla ya kuzama ni *Kanuni ya Archimedes

Kanuni ya Archimedes inasema kwamba:
Nguvu ya kuelea inayofanya kazi kwenye kitu kilichozamishwa kabisa au kwa sehemu kwenye kiowevu ni sawa na uzito wa kiowevu kilichohamishwa na kitu hicho. Kwa kitu kinachoelea, nguvu ya kuelea ni sawa na uzito wa jumla wa kitu hicho.

Part c· 4 steps

Ili kujua boti inazama kwa kina gani, tunahitaji kuhesabu wingi wake wote na kutumia Kanuni ya Archimedes.

  1. Kokotoa jumla ya wingi wa boti na mizigo yake.

    Wingi wa boti ni mdogo sana (negligible).
    Jumla ya wingi (MtotalM_{total}) = Wingi wa opereta + Wingi wa saruji

    Mtotal=80 kg+5000 kg=5080 kgM_{total} = 80 \text{ kg} + 5000 \text{ kg} = 5080 \text{ kg}
  2. Kokotoa uzito wa jumla.

    Tumia g=10 m/s2g = 10 \text{ m/s}^2.
    Uzito wa jumla (WtotalW_{total}) = Mtotal×gM_{total} \times g

    Wtotal=5080 kg×10 m/s2=50800 NW_{total} = 5080 \text{ kg} \times 10 \text{ m/s}^2 = 50800 \text{ N}
  3. Tumia Kanuni ya Archimedes kupata ujazo wa maji yaliyohamishwa.

    Nguvu ya kuelea (FBF_B) = Uzito wa jumla (WtotalW_{total})
    Pia, FB=ρwater×Vdisplaced×gF_B = \rho_{water} \times V_{displaced} \times g
    Ambapo ρwater=1000 kg/m3\rho_{water} = 1000 \text{ kg/m}^3 (msongamano wa maji) na VdisplacedV_{displaced} ni ujazo wa maji yaliyohamishwa.

    50800 N=1000 kg/m3×Vdisplaced×10 m/s250800 \text{ N} = 1000 \text{ kg/m}^3 \times V_{displaced} \times 10 \text{ m/s}^2 50800=10000×Vdisplaced50800 = 10000 \times V_{displaced} Vdisplaced=5080010000 m3=5.08 m3V_{displaced} = \frac{50800}{10000} \text{ m}^3 = 5.08 \text{ m}^3
  4. Tumia eneo la sehemu-mtambuka kupata kina cha kuzama.

    Ujazo wa maji yaliyohamishwa (VdisplacedV_{displaced}) = Eneo la sehemu-mtambuka (AA) ×\times kina (hh)
    Eneo la sehemu-mtambuka (AA) = 200 m2200 \text{ m}^2.

    5.08 m3=200 m2×h5.08 \text{ m}^3 = 200 \text{ m}^2 \times h h=5.08200 mh = \frac{5.08}{200} \text{ m} h=0.0254 mh = 0.0254 \text{ m}

    Boti inazama kwa kina cha 0.0254 m (au 2.54 cm).

Part d

Maoni juu ya usalama wa boti, kuhusiana na muda wa kuondoka

Muda wa kuondoka ni saa sita mchana, wakati jua linapokanzwa sana.

  • Jua kali saa sita mchana huongeza joto la maji ya uso.
  • Maji yenye joto huwa na msongamano mdogo kuliko maji baridi.
  • Kulingana na Kanuni ya Archimedes, ili boti iweze kuelea na kubeba uzito uleule, ikiwa msongamano wa maji ni mdogo, boti inapaswa kuhamisha ujazo mkubwa zaidi wa maji.
  • Hii inamaanisha boti itazama zaidi ndani ya maji.
  • Kuzama zaidi kunapunguza urefu wa boti ulio juu ya maji (freeboard), na kuifanya iwe hatarini zaidi kuingiliwa na mawimbi au maji kuingia ndani ya boti, hasa katika maji yenye mawimbi au ikiwa boti imebeba mizigo mingi. Hali hii inahatarisha usalama wa boti na abiria wake.
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