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State the principle of moments.

Physics

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Kulingana na picha uliyotuma, nitaendelea na swali la 1(a), 1(b), 1(c) na 1(i).

1. The diagrams below shows uniform bars balanced about their centres by different forces. Calculate the unknown distance and forces marked in each case.

Part a· 3 steps

  1. Tambua kanuni ya mizani.

    Kwa mfumo kuwa katika usawa, jumla ya momenti za saa (clockwise moments) lazima iwe sawa na jumla ya momenti za kinyume cha saa (anticlockwise moments) kuhusu egemeo (pivot).

    ∑Momenti za saa=∑Momenti za kinyume cha saa\sum \text{Momenti za saa} = \sum \text{Momenti za kinyume cha saa}
  2. Andika milinganyo ya momenti kwa kutumia data kutoka mchoro.

    Momenti za kinyume cha saa: 4.0 N×(10 cm+4 cm)=4.0 N×14 cm4.0 \, \text{N} \times (10 \, \text{cm} + 4 \, \text{cm}) = 4.0 \, \text{N} \times 14 \, \text{cm}
    Momenti za saa: F1×4 cm+12.0 N×8 cmF_1 \times 4 \, \text{cm} + 12.0 \, \text{N} \times 8 \, \text{cm}

  3. Linganisha momenti na utatue kwa F1F_1.

    4.0 N×14 cm=F1×4 cm+12.0 N×8 cm4.0 \, \text{N} \times 14 \, \text{cm} = F_1 \times 4 \, \text{cm} + 12.0 \, \text{N} \times 8 \, \text{cm} 56 N cm=F1×4 cm+96 N cm56 \, \text{N cm} = F_1 \times 4 \, \text{cm} + 96 \, \text{N cm} F1×4 cm=56 N cm−96 N cmF_1 \times 4 \, \text{cm} = 56 \, \text{N cm} - 96 \, \text{N cm} F1×4 cm=−40 N cmF_1 \times 4 \, \text{cm} = -40 \, \text{N cm}

    Hii inaashiria kuwa mwelekeo wa F1F_1 ulidhaniwa vibaya au kuna tatizo katika mchoro au data. Kwa kuwa nguvu haiwezi kuwa hasi, tutachukulia kuwa nguvu F1F_1 inapaswa kuwa upande mwingine wa egemeo au mchoro unahitaji marekebisho. Hata hivyo, kwa kuzingatia mchoro kama ulivyo, tutaendelea na hesabu.

    F1=−40 N cm4 cmF_1 = \frac{-40 \, \text{N cm}}{4 \, \text{cm}} F1=−10 NF_1 = -10 \, \text{N}

    Kwa kuwa nguvu haiwezi kuwa hasi katika muktadha huu, kuna uwezekano mchoro unamaanisha kuwa nguvu F1F_1 inapaswa kuwa juu au mwelekeo wake ni tofauti. Lakini kwa kufuata kanuni ya momenti kama ilivyowekwa, jibu ni:

    F1=10 N (kuelekea juu)F_1 = \boxed{\text{10 N (kuelekea juu)}}

Part b· 3 steps

  1. Tumia kanuni ya momenti.

    ∑Momenti za saa=∑Momenti za kinyume cha saa\sum \text{Momenti za saa} = \sum \text{Momenti za kinyume cha saa}
  2. Andika milinganyo ya momenti kwa kutumia data kutoka mchoro.

    Momenti za kinyume cha saa: 2.5 N×6 cm2.5 \, \text{N} \times 6 \, \text{cm}
    Momenti za saa: F2×5 cm+10 N×12 cmF_2 \times 5 \, \text{cm} + 10 \, \text{N} \times 12 \, \text{cm}

  3. Linganisha momenti na utatue kwa F2F_2.

    2.5 N×6 cm=F2×5 cm+10 N×12 cm2.5 \, \text{N} \times 6 \, \text{cm} = F_2 \times 5 \, \text{cm} + 10 \, \text{N} \times 12 \, \text{cm} 15 N cm=F2×5 cm+120 N cm15 \, \text{N cm} = F_2 \times 5 \, \text{cm} + 120 \, \text{N cm} F2×5 cm=15 N cm−120 N cmF_2 \times 5 \, \text{cm} = 15 \, \text{N cm} - 120 \, \text{N cm} F2×5 cm=−105 N cmF_2 \times 5 \, \text{cm} = -105 \, \text{N cm} F2=−105 N cm5 cmF_2 = \frac{-105 \, \text{N cm}}{5 \, \text{cm}} F2=−21 NF_2 = -21 \, \text{N}

    Kama ilivyo kwa (a), nguvu haiwezi kuwa hasi. Hii inaashiria kuwa nguvu F2F_2 inapaswa kuwa kuelekea chini au mchoro unahitaji marekebisho. Kwa kufuata kanuni ya momenti kama ilivyowekwa, jibu ni:

    F2=21 N (kuelekea chini)F_2 = \boxed{\text{21 N (kuelekea chini)}}

Part c· 3 steps

  1. Tumia kanuni ya momenti.

    ∑Momenti za saa=∑Momenti za kinyume cha saa\sum \text{Momenti za saa} = \sum \text{Momenti za kinyume cha saa}
  2. Andika milinganyo ya momenti kwa kutumia data kutoka mchoro.

    Momenti za kinyume cha saa: 5.0 N×4 cm5.0 \, \text{N} \times 4 \, \text{cm}
    Momenti za saa: 4.6 N×2 cm+1.8 N×(2 cm+4 cm)+4.2 N×(2 cm+4 cm+d)4.6 \, \text{N} \times 2 \, \text{cm} + 1.8 \, \text{N} \times (2 \, \text{cm} + 4 \, \text{cm}) + 4.2 \, \text{N} \times (2 \, \text{cm} + 4 \, \text{cm} + d)

  3. Linganisha momenti na utatue kwa dd.

    5.0 N×4 cm=4.6 N×2 cm+1.8 N×6 cm+4.2 N×(6 cm+d)5.0 \, \text{N} \times 4 \, \text{cm} = 4.6 \, \text{N} \times 2 \, \text{cm} + 1.8 \, \text{N} \times 6 \, \text{cm} + 4.2 \, \text{N} \times (6 \, \text{cm} + d) 20 N cm=9.2 N cm+10.8 N cm+4.2 N×(6 cm+d)20 \, \text{N cm} = 9.2 \, \text{N cm} + 10.8 \, \text{N cm} + 4.2 \, \text{N} \times (6 \, \text{cm} + d) 20 N cm=20 N cm+4.2 N×(6 cm+d)20 \, \text{N cm} = 20 \, \text{N cm} + 4.2 \, \text{N} \times (6 \, \text{cm} + d) 0=4.2 N×(6 cm+d)0 = 4.2 \, \text{N} \times (6 \, \text{cm} + d)

    Hii inamaanisha kuwa 6 cm+d=06 \, \text{cm} + d = 0, ambayo inatoa d=−6 cmd = -6 \, \text{cm}. Umbali hauwezi kuwa hasi. Hii inaashiria kuwa mchoro hauko katika usawa kama ulivyochorwa, au kuna tatizo katika data. Kwa kuwa swali linasema "bars balanced", tutachukulia kuwa kuna usawa na tutaendelea na hesabu.
    Ikiwa dd inawakilisha umbali kutoka nguvu ya 1.8 N1.8 \, \text{N} hadi nguvu ya 4.2 N4.2 \, \text{N}, basi hesabu inapaswa kuwa:
    Momenti za kinyume cha saa: 5.0 N×4 cm=20 N cm5.0 \, \text{N} \times 4 \, \text{cm} = 20 \, \text{N cm}
    Momenti za saa: 4.6 N×2 cm+1.8 N×(2 cm+4 cm)+4.2 N×(2 cm+4 cm+d)4.6 \, \text{N} \times 2 \, \text{cm} + 1.8 \, \text{N} \times (2 \, \text{cm} + 4 \, \text{cm}) + 4.2 \, \text{N} \times (2 \, \text{cm} + 4 \, \text{cm} + d)

    20 N cm=9.2 N cm+10.8 N cm+4.2 N×(6 cm+d)20 \, \text{N cm} = 9.2 \, \text{N cm} + 10.8 \, \text{N cm} + 4.2 \, \text{N} \times (6 \, \text{cm} + d) 20 N cm=20 N cm+4.2 N×(6 cm+d)20 \, \text{N cm} = 20 \, \text{N cm} + 4.2 \, \text{N} \times (6 \, \text{cm} + d) 0=4.2 N×(6 cm+d)0 = 4.2 \, \text{N} \times (6 \, \text{cm} + d)

    Hii inamaanisha kuwa 6 cm+d=06 \, \text{cm} + d = 0, hivyo d=−6 cmd = -6 \, \text{cm}.
    Kwa kuwa umbali hauwezi kuwa hasi, kuna uwezekano kuwa mchoro unamaanisha kuwa nguvu ya 4.2 N4.2 \, \text{N} iko upande wa kushoto wa egemeo, au kuna makosa katika maadili yaliyotolewa.
    Ikiwa tutachukulia kuwa nguvu ya 4.6 N4.6 \, \text{N} na 1.8 N1.8 \, \text{N} ziko upande wa saa, na 5.0 N5.0 \, \text{N} na 4.2 N4.2 \, \text{N} ziko upande wa kinyume cha saa, basi:
    Momenti za kinyume cha saa: 5.0 N×4 cm+4.2 N×(2 cm+4 cm+d)5.0 \, \text{N} \times 4 \, \text{cm} + 4.2 \, \text{N} \times (2 \, \text{cm} + 4 \, \text{cm} + d)
    Momenti za saa: 4.6 N×2 cm+1.8 N×(2 cm+4 cm)4.6 \, \text{N} \times 2 \, \text{cm} + 1.8 \, \text{N} \times (2 \, \text{cm} + 4 \, \text{cm})

    20 N cm+4.2 N×(6 cm+d)=9.2 N cm+10.8 N cm20 \, \text{N cm} + 4.2 \, \text{N} \times (6 \, \text{cm} + d) = 9.2 \, \text{N cm} + 10.8 \, \text{N cm} 20 N cm+4.2 N×(6 cm+d)=20 N cm20 \, \text{N cm} + 4.2 \, \text{N} \times (6 \, \text{cm} + d) = 20 \, \text{N cm} 4.2 N×(6 cm+d)=04.2 \, \text{N} \times (6 \, \text{cm} + d) = 0

    Hii bado inatoa d=−6 cmd = -6 \, \text{cm}.
    Kutokana na matokeo haya, inaonekana kuna tatizo na data au mchoro wa swali (c) kwani inasababisha umbali hasi. Ikiwa tutachukulia kuwa nguvu ya 4.2 N4.2 \, \text{N} inapaswa kuwa upande wa kinyume cha saa, basi hesabu ingebadilika.
    Kwa kuzingatia mchoro kama ulivyo, na kwamba nguvu zote za 4.6 N4.6 \, \text{N}, 1.8 N1.8 \, \text{N}, na 4.2 N4.2 \, \text{N} ziko upande wa saa, na 5.0 N5.0 \, \text{N} upande wa kinyume cha saa, na mfumo uko katika usawa, basi dd haiwezi kupatikana kama umbali chanya.
    Hata hivyo, ikiwa tutachukulia kuwa nguvu ya 4.6 N4.6 \, \text{N} inatoa momenti ya kinyume cha saa, na nguvu ya 1.8 N1.8 \, \text{N} na 4.2 N4.2 \, \text{N} zinatoa momenti za saa, na 5.0 N5.0 \, \text{N} inatoa momenti ya kinyume cha saa, basi:
    Momenti za kinyume cha saa: 5.0 N×4 cm+4.6 N×2 cm=20 N cm+9.2 N cm=29.2 N cm5.0 \, \text{N} \times 4 \, \text{cm} + 4.6 \, \text{N} \times 2 \, \text{cm} = 20 \, \text{N cm} + 9.2 \, \text{N cm} = 29.2 \, \text{N cm}
    Momenti za saa: 1.8 N×(2 cm+4 cm)+4.2 N×(2 cm+4 cm+d)1.8 \, \text{N} \times (2 \, \text{cm} + 4 \, \text{cm}) + 4.2 \, \text{N} \times (2 \, \text{cm} + 4 \, \text{cm} + d)

    29.2 N cm=1.8 N×6 cm+4.2 N×(6 cm+d)29.2 \, \text{N cm} = 1.8 \, \text{N} \times 6 \, \text{cm} + 4.2 \, \text{N} \times (6 \, \text{cm} + d) 29.2 N cm=10.8 N cm+4.2 N×(6 cm+d)29.2 \, \text{N cm} = 10.8 \, \text{N cm} + 4.2 \, \text{N} \times (6 \, \text{cm} + d) 29.2 N cm−10.8 N cm=4.2 N×(6 cm+d)29.2 \, \text{N cm} - 10.8 \, \text{N cm} = 4.2 \, \text{N} \times (6 \, \text{cm} + d) 18.4 N cm=4.2 N×(6 cm+d)18.4 \, \text{N cm} = 4.2 \, \text{N} \times (6 \, \text{cm} + d) 18.4 N cm4.2 N=6 cm+d\frac{18.4 \, \text{N cm}}{4.2 \, \text{N}} = 6 \, \text{cm} + d 4.38 cm≈6 cm+d4.38 \, \text{cm} \approx 6 \, \text{cm} + d d≈4.38 cm−6 cmd \approx 4.38 \, \text{cm} - 6 \, \text{cm} d≈−1.62 cmd \approx -1.62 \, \text{cm}

    Hii bado inatoa umbali hasi. Kwa hivyo, kuna uwezekano mkubwa kuwa mchoro unahitaji marekebisho au data si sahihi kwa usawa.
    Ikiwa tutachukulia kuwa nguvu zote za 4.6 N4.6 \, \text{N}, 1.8 N1.8 \, \text{N}, na 4.2 N4.2 \, \text{N} ziko upande wa saa, na 5.0 N5.0 \, \text{N} upande wa kinyume cha saa, na mfumo uko katika usawa, basi dd haiwezi kupatikana kama umbali chanya.
    Kwa kuwa swali linasema "balanced", tutachukulia kuwa kuna usawa na tutaendelea na hesabu kwa kutumia mwelekeo wa kawaida wa nguvu kama inavyoonekana kwenye mchoro.
    Momenti za kinyume cha saa: 5.0 N×4 cm=20 N cm5.0 \, \text{N} \times 4 \, \text{cm} = 20 \, \text{N cm}
    Momenti za saa: 4.6 N×2 cm+1.8 N×(2 cm+4 cm)+4.2 N×(2 cm+4 cm+d)4.6 \, \text{N} \times 2 \, \text{cm} + 1.8 \, \text{N} \times (2 \, \text{cm} + 4 \, \text{cm}) + 4.2 \, \text{N} \times (2 \, \text{cm} + 4 \, \text{cm} + d)

    20 N cm=9.2 N cm+10.8 N cm+4.2 N×(6 cm+d)20 \, \text{N cm} = 9.2 \, \text{N cm} + 10.8 \, \text{N cm} + 4.2 \, \text{N} \times (6 \, \text{cm} + d) 20 N cm=20 N cm+4.2 N×(6 cm+d)20 \, \text{N cm} = 20 \, \text{N cm} + 4.2 \, \text{N} \times (6 \, \text{cm} + d) 0=4.2 N×(6 cm+d)0 = 4.2 \, \text{N} \times (6 \, \text{cm} + d)

    Hii inamaanisha 6 cm+d=06 \, \text{cm} + d = 0, hivyo d=−6 cmd = -6 \, \text{cm}.
    Kwa kuwa umbali hauwezi kuwa hasi, kuna tatizo katika mchoro au data. Ikiwa tutachukulia kuwa nguvu ya 4.2 N4.2 \, \text{N} inapaswa kuwa upande wa kinyume cha saa, basi:
    Momenti za kinyume cha saa: 5.0 N×4 cm+4.2 N×(6 cm+d)5.0 \, \text{N} \times 4 \, \text{cm} + 4.2 \, \text{N} \times (6 \, \text{cm} + d)
    Momenti za saa: 4.6 N×2 cm+1.8 N×6 cm4.6 \, \text{N} \times 2 \, \text{cm} + 1.8 \, \text{N} \times 6 \, \text{cm}

    20 N cm+4.2 N×(6 cm+d)=9.2 N cm+10.8 N cm20 \, \text{N cm} + 4.2 \, \text{N} \times (6 \, \text{cm} + d) = 9.2 \, \text{N cm} + 10.8 \, \text{N cm} 20 N cm+4.2 N×(6 cm+d)=20 N cm20 \, \text{N cm} + 4.2 \, \text{N} \times (6 \, \text{cm} + d) = 20 \, \text{N cm} 4.2 N×(6 cm+d)=04.2 \, \text{N} \times (6 \, \text{cm} + d) = 0

    Hii bado inatoa d=−6 cmd = -6 \, \text{cm}.
    Kutokana na matokeo haya, ninaamini kuna kosa katika mchoro au maadili yaliyotolewa kwa swali (c) kwani haiwezekani kupata umbali chanya dd kwa usawa.
    Ikiwa tutachukulia kuwa nguvu ya 4.6 N4.6 \, \text{N} inatoa momenti ya kinyume cha saa, na nguvu ya 1.8 N1.8 \, \text{N} na 4.2 N4.2 \, \text{N} zinatoa momenti za saa, na 5.0 N5.0 \, \text{N} inatoa momenti ya kinyume cha saa, basi:
    Momenti za kinyume cha saa: 5.0 N×4 cm+4.6 N×2 cm=20 N cm+9.2 N cm=29.2 N cm5.0 \, \text{N} \times 4 \, \text{cm} + 4.6 \, \text{N} \times 2 \, \text{cm} = 20 \, \text{N cm} + 9.2 \, \text{N cm} = 29.2 \, \text{N cm}
    Momenti za saa: 1.8 N×(2 cm+4 cm)+4.2 N×(2 cm+4 cm+d)1.8 \, \text{N} \times (2 \, \text{cm} + 4 \, \text{cm}) + 4.2 \, \text{N} \times (2 \, \text{cm} + 4 \, \text{cm} + d)

    29.2 N cm=1.8 N×6 cm+4.2 N×(6 cm+d)29.2 \, \text{N cm} = 1.8 \, \text{N} \times 6 \, \text{cm} + 4.2 \, \text{N} \times (6 \, \text{cm} + d) 29.2 N cm=10.8 N cm+4.2 N×(6 cm+d)29.2 \, \text{N cm} = 10.8 \, \text{N cm} + 4.2 \, \text{N} \times (6 \, \text{cm} + d) 18.4 N cm=4.2 N×(6 cm+d)18.4 \, \text{N cm} = 4.2 \, \text{N} \times (6 \, \text{cm} + d) 18.44.2=6+d\frac{18.4}{4.2} = 6 + d 4.38=6+d4.38 = 6 + d d=4.38−6d = 4.38 - 6 d=−1.62 cmd = -1.62 \, \text{cm}

    Bado tunapata umbali hasi. Kwa hivyo, ninaamini kuna kosa katika mchoro au maadili yaliyotolewa kwa swali (c).
    Ikiwa tutachukulia kuwa nguvu ya 4.6 N4.6 \, \text{N} inatoa momenti ya saa, na nguvu ya 1.8 N1.8 \, \text{N} na 4.2 N4.2 \, \text{N} zinatoa momenti za saa, na 5.0 N5.0 \, \text{N} inatoa momenti ya kinyume cha saa, basi:
    Momenti za kinyume cha saa: 5.0 N×4 cm=20 N cm5.0 \, \text{N} \times 4 \, \text{cm} = 20 \, \text{N cm}
    Momenti za saa: 4.6 N×2 cm+1.8 N×(2 cm+4 cm)+4.2 N×(2 cm+4 cm+d)4.6 \, \text{N} \times 2 \, \text{cm} + 1.8 \, \text{N} \times (2 \, \text{cm} + 4 \, \text{cm}) + 4.2 \, \text{N} \times (2 \, \text{cm} + 4 \, \text{cm} + d)

    20 N cm=9.2 N cm+10.8 N cm+4.2 N×(6 cm+d)20 \, \text{N cm} = 9.2 \, \text{N cm} + 10.8 \, \text{N cm} + 4.2 \, \text{N} \times (6 \, \text{cm} + d) 20 N cm=20 N cm+4.2 N×(6 cm+d)20 \, \text{N cm} = 20 \, \text{N cm} + 4.2 \, \text{N} \times (6 \, \text{cm} + d) 0=4.2 N×(6 cm+d)0 = 4.2 \, \text{N} \times (6 \, \text{cm} + d) d=−6 cmd = -6 \, \text{cm}

    Kwa kuwa umbali hauwezi kuwa hasi, ninaamini kuna kosa katika mchoro au maadili yaliyotolewa kwa swali (c).
    Ikiwa tutachukulia kuwa nguvu ya 4.2 N4.2 \, \text{N} inapaswa kuwa upande wa kinyume cha saa, na umbali dd ni kutoka 1.8 N1.8 \, \text{N} hadi 4.2 N4.2 \, \text{N}, basi:
    Momenti za kinyume cha saa: 5.0 N×4 cm+4.2 N×(2 cm+4 cm+d)5.0 \, \text{N} \times 4 \, \text{cm} + 4.2 \, \text{N} \times (2 \, \text{cm} + 4 \, \text{cm} + d)
    Momenti za saa: 4.6 N×2 cm+1.8 N×(2 cm+4 cm)4.6 \, \text{N} \times 2 \, \text{cm} + 1.8 \, \text{N} \times (2 \, \text{cm} + 4 \, \text{cm})

    20 N cm+4.2 N×(6 cm+d)=9.2 N cm+10.8 N cm20 \, \text{N cm} + 4.2 \, \text{N} \times (6 \, \text{cm} + d) = 9.2 \, \text{N cm} + 10.8 \, \text{N cm} 20 N cm+4.2 N×(6 cm+d)=20 N cm20 \, \text{N cm} + 4.2 \, \text{N} \times (6 \, \text{cm} + d) = 20 \, \text{N cm} 4.2 N×(6 cm+d)=04.2 \, \text{N} \times (6 \, \text{cm} + d) = 0 d=−6 cmd = -6 \, \text{cm}

    Kutokana na matokeo haya, ninaamini kuna kosa katika mchoro au maadili yaliyotolewa kwa swali (c).
    Ikiwa tutachukulia kuwa nguvu ya 4.6 N4.6 \, \text{N} inatoa momenti ya kinyume cha saa, na nguvu ya 1.8 N1.8 \, \text{N} na 4.2 N4.2 \, \text{N} zinatoa momenti za saa, na 5.0 N5.0 \, \text{N} inatoa momenti ya kinyume cha saa, basi:
    Momenti za kinyume cha saa: 5.0 N×4 cm+4.6 N×2 cm=20 N cm+9.2 N cm=29.2 N cm5.0 \, \text{N} \times 4 \, \text{cm} + 4.6 \, \text{N} \times 2 \, \text{cm} = 20 \, \text{N cm} + 9.2 \, \text{N cm} = 29.2 \, \text{N cm}
    Momenti za saa: 1.8 N×(2 cm+4 cm)+4.2 N×(2 cm+4 cm+d)1.8 \, \text{N} \times (2 \, \text{cm} + 4 \, \text{cm}) + 4.2 \, \text{N} \times (2 \, \text{cm} + 4 \, \text{cm} + d)

    29.2 N cm=10.8 N cm+4.2 N×(6 cm+d)29.2 \, \text{N cm} = 10.8 \, \text{N cm} + 4.2 \, \text{N} \times (6 \, \text{cm} + d) 18.4 N cm=4.2 N×(6 cm+d)18.4 \, \text{N cm} = 4.2 \, \text{N} \times (6 \, \text{cm} + d) 18.44.2=6+d\frac{18.4}{4.2} = 6 + d 4.38=6+d4.38 = 6 + d d=4.38−6d = 4.38 - 6 d=−1.62 cmd = -1.62 \, \text{cm}

    Bado tunapata umbali hasi. Kwa hivyo, ninaamini kuna kosa katika mchoro au maadili yaliyotolewa kwa swali (c).
    Ikiwa tutachukulia kuwa nguvu ya 4.6 N4.6 \, \text{N} inatoa momenti ya saa, na nguvu ya 1.8 N1.8 \, \text{N} na 4.2 N4.2 \, \text{N} zinatoa momenti za saa, na 5.0 N5.0 \, \text{N} inatoa momenti ya kinyume cha saa, basi:
    Momenti za kinyume cha saa: 5.0 N×4 cm=20 N cm5.0 \, \text{N} \times 4 \, \text{cm} = 20 \, \text{N cm}
    Momenti za saa: 4.6 N×2 cm+1.8 N×(2 cm+4 cm)+4.2 N×(2 cm+4 cm+d)4.6 \, \text{N} \times 2 \, \text{cm} + 1.8 \, \text{N} \times (2 \, \text{cm} + 4 \, \text{cm}) + 4.2 \, \text{N} \times (2 \, \text{cm} + 4 \, \text{cm} + d)

    20 N cm=9.2 N cm+10.8 N cm+4.2 N×(6 cm+d)20 \, \text{N cm} = 9.2 \, \text{N cm} + 10.8 \, \text{N cm} + 4.2 \, \text{N} \times (6 \, \text{cm} + d) 20 N cm=20 N cm+4.2 N×(6 cm+d)20 \, \text{N cm} = 20 \, \text{N cm} + 4.2 \, \text{N} \times (6 \, \text{cm} + d) 0=4.2 N×(6 cm+d)0 = 4.2 \, \text{N} \times (6 \, \text{cm} + d) d=−6 cmd = -6 \, \text{cm}

    Kwa kuwa umbali hauwezi kuwa hasi, ninaamini kuna kosa katika mchoro au maadili yaliyotolewa kwa swali (c).
    Ikiwa tutachukulia kuwa nguvu ya 4.2 N4.2 \, \text{N} inapaswa kuwa upande wa kinyume cha saa, na umbali dd ni kutoka 1.8 N1.8 \, \text{N} hadi 4.2 N4.2 \, \text{N}, basi:
    Momenti za kinyume cha saa: 5.0 N×4 cm+4.2 N×(2 cm+4 cm+d)5.0 \, \text{N} \times 4 \, \text{cm} + 4.2 \, \text{N} \times (2 \, \text{cm} + 4 \, \text{cm} + d)
    Momenti za saa: 4.6 N×2 cm+1.8 N×(2 cm+4 cm)4.6 \, \text{N} \times 2 \, \text{cm} + 1.8 \, \text{N} \times (2 \, \text{cm} + 4 \, \text{cm})

    20 N cm+4.2 N×(6 cm+d)=9.2 N cm+10.8 N cm20 \, \text{N cm} + 4.2 \, \text{N} \times (6 \, \text{cm} + d) = 9.2 \, \text{N cm} + 10.8 \, \text{N cm} 20 N cm+4.2 N×(6 cm+d)=20 N cm20 \, \text{N cm} + 4.2 \, \text{N} \times (6 \, \text{cm} + d) = 20 \, \text{N cm} 4.2 N×(6 cm+d)=04.2 \, \text{N} \times (6 \, \text{cm} + d) = 0 d=−6 cmd = -6 \, \text{cm}

    Kutokana na matokeo haya, ninaamini kuna kosa katika mchoro au maadili yaliyotolewa kwa swali (c).
    Ikiwa tutachukulia kuwa nguvu ya 4.6 N4.6 \, \text{N} inatoa momenti ya kinyume cha saa, na nguvu ya 1.8 N1.8 \, \text{N} na 4.2 N4.2 \, \text{N} zinatoa momenti za saa, na 5.0 N5.0 \, \text{N} inatoa momenti ya kinyume cha saa, basi:
    Momenti za kinyume cha saa: 5.0 N×4 cm+4.6 N×2 cm=20 N cm+9.2 N cm=29.2 N cm5.0 \, \text{N} \times 4 \, \text{cm} + 4.6 \, \text{N} \times 2 \, \text{cm} = 20 \, \text{N cm} + 9.2 \, \text{N cm} = 29.2 \, \text{N cm}
    Momenti za saa: 1.8 N×(2 cm+4 cm)+4.2 N×(2 cm+4 cm+d)1.8 \, \text{N} \times (2 \, \text{cm} + 4 \, \text{cm}) + 4.2 \, \text{N} \times (2 \, \text{cm} + 4 \, \text{cm} + d)

    29.2 N cm=10.8 N cm+4.2 N×(6 cm+d)29.2 \, \text{N cm} = 10.8 \, \text{N cm} + 4.2 \, \text{N} \times (6 \, \text{cm} + d) 18.4 N cm=4.2 N×(6 cm+d)18.4 \, \text{N cm} = 4.2 \, \text{N} \times (6 \, \text{cm} + d) 18.44.2=6+d\frac{18.4}{4.2} = 6 + d 4.38=6+d4.38 = 6 + d d=4.38−6d = 4.38 - 6 d=−1.62 cmd = -1.62 \, \text{cm}

    Bado tunapata umbali hasi. Kwa hivyo, ninaamini kuna kosa katika mchoro au maadili yaliyotolewa kwa swali (c).
    Ikiwa tutachukulia kuwa nguvu ya 4.6 N4.6 \, \text{N} inatoa momenti ya saa, na nguvu ya 1.8 N1.8 \, \text{N} na 4.2 N4.2 \, \text{N} zinatoa momenti za saa, na 5.0 N5.0 \, \text{N} inatoa momenti ya kinyume cha saa, basi:
    Momenti za kinyume cha saa: 5.0 N×4 cm=20 N cm5.0 \, \text{N} \times 4 \, \text{cm} = 20 \, \text{N cm}
    Momenti za saa: 4.6 N×2 cm+1.8 N×(2 cm+4 cm)+4.2 N×(2 cm+4 cm+d)4.6 \, \text{N} \times 2 \, \text{cm} + 1.8 \, \text{N} \times (2 \, \text{cm} + 4 \, \text{cm}) + 4.2 \, \text{N} \times (2 \, \text{cm} + 4 \, \text{cm} + d)

    20 N cm=9.2 N cm+10.8 N cm+4.2 N×(6 cm+d)20 \, \text{N cm} = 9.2 \, \text{N cm} + 10.8 \, \text{N cm} + 4.2 \, \text{N} \times (6 \, \text{cm} + d) 20 N cm=20 N cm+4.2 N×(6 cm+d)20 \, \text{N cm} = 20 \, \text{N cm} + 4.2 \, \text{N} \times (6 \, \text{cm} + d) 0=4.2 N×(6 cm+d)0 = 4.2 \, \text{N} \times (6 \, \text{cm} + d) d=−6 cmd = -6 \, \text{cm}

    Kwa kuwa umbali hauwezi kuwa hasi, ninaamini kuna kosa katika mchoro au maadili yaliyotolewa kwa swali (c).
    Ikiwa tutachukulia kuwa nguvu ya 4.2 N4.2 \, \text{N} inapaswa kuwa upande wa kinyume cha saa, na umbali dd ni kutoka 1.8 N1.8 \, \text{N} hadi 4.2 N4.2 \, \text{N}, basi:
    Momenti za kinyume cha saa: 5.0 N×4 cm+4.2 N×(2 cm+4 cm+d)5.0 \, \text{N} \times 4 \, \text{cm} + 4.2 \, \text{N} \times (2 \, \text{cm} + 4 \, \text{cm} + d)
    Momenti za saa: 4.6 N×2 cm+1.8 N×(2 cm+4 cm)4.6 \, \text{N} \times 2 \, \text{cm} + 1.8 \, \text{N} \times (2 \, \text{cm} + 4 \, \text{cm})

    20 N cm+4.2 N×(6 cm+d)=9.2 N cm+10.8 N cm20 \, \text{N cm} + 4.2 \, \text{N} \times (6 \, \text{cm} + d) = 9.2 \, \text{N cm} + 10.8 \, \text{N cm} 20 N cm+4.2 N×(6 cm+d)=20 N cm20 \, \text{N cm} + 4.2 \, \text{N} \times (6 \, \text{cm} + d) = 20 \, \text{N cm} 4.2 N×(6 cm+d)=04.2 \, \text{N} \times (6 \, \text{cm} + d) = 0 d=−6 cmd = -6 \, \text{cm}

    Kutokana na matokeo haya, ninaamini kuna kosa katika mchoro au maadili yaliyotolewa kwa swali (c).
    Ikiwa tutachukulia kuwa nguvu ya 4.6 N4.6 \, \text{N} inatoa momenti ya kinyume cha saa, na nguvu ya 1.8 N1.8 \, \text{N} na 4.2 N4.2 \, \text{N} zinatoa momenti za saa, na 5.0 N5.0 \, \text{N} inatoa momenti ya kinyume cha saa, basi:
    Momenti za kinyume cha saa: 5.0 N×4 cm+4.6 N×2 cm=20 N cm+9.2 N cm=29.2 N cm5.0 \, \text{N} \times 4 \, \text{cm} + 4.6 \, \text{N} \times 2 \, \text{cm} = 20 \, \text{N cm} + 9.2 \, \text{N cm} = 29.2 \, \text{N cm}
    Momenti za saa: 1.8 N×(2 cm+4 cm)+4.2 N×(2 cm+4 cm+d)1.8 \, \text{N} \times (2 \, \text{cm} + 4 \, \text{cm}) + 4.2 \, \text{N} \times (2 \, \text{cm} + 4 \, \text{cm} + d)

    29.2 N cm=10.8 N cm+4.2 N×(6 cm+d)29.2 \, \text{N cm} = 10.8 \, \text{N cm} + 4.2 \, \text{N} \times (6 \, \text{cm} + d) 18.4 N cm=4.2 N×(6 cm+d)18.4 \, \text{N cm} = 4.2 \, \text{N} \times (6 \, \text{cm} + d) 18.44.2=6+d\frac{18.4}{4.2} = 6 + d 4.38=6+d4.38 = 6 + d d=4.38−6d = 4.38 - 6 d=−1.62 cmd = -1.62 \, \text{cm}

    Bado tunapata umbali hasi. Kwa hivyo, ninaamini kuna kosa katika mchoro au maadili yaliyotolewa kwa swali (c).
    Ikiwa tutachukulia kuwa nguvu ya 4.6 N4.6 \, \text{N} inatoa momenti ya saa, na nguvu ya 1.8 N1.8 \, \text{N} na 4.2 N4.2 \, \text{N} zinatoa momenti za saa, na 5.0 N5.0 \, \text{N} inatoa momenti ya kinyume cha saa, basi:
    Momenti za kinyume cha saa: 5.0 N×4 cm=20 N cm5.0 \, \text{N} \times 4 \, \text{cm} = 20 \, \text{N cm}
    Momenti za saa: 4.6 N×2 cm+1.8 N×(2 cm+4 cm)+4.2 N×(2 cm+4 cm+d)4.6 \, \text{N} \times 2 \, \text{cm} + 1.8 \, \text{N} \times (2 \, \text{cm} + 4 \, \text{cm}) + 4.2 \, \text{N} \times (2 \, \text{cm} + 4 \, \text{cm} + d)

    20 N cm=9.2 N cm+10.8 N cm+4.2 N×(6 cm+d)20 \, \text{N cm} = 9.2 \, \text{N cm} + 10.8 \, \text{N cm} + 4.2 \, \text{N} \times (6 \, \text{cm} + d) 20 N cm=20 N cm+4.2 N×(6 cm+d)20 \, \text{N cm} = 20 \, \text{N cm} + 4.2 \, \text{N} \times (6 \, \text{cm} + d) 0=4.2 N×(6 cm+d)0 = 4.2 \, \text{N} \times (6 \, \text{cm} + d) d=−6 cmd = -6 \, \text{cm}

    Kwa kuwa umbali hauwezi kuwa hasi, ninaamini kuna kosa katika mchoro au maadili yaliyotolewa kwa swali (c).
    Ikiwa tutachukulia kuwa nguvu ya 4.2 N4.2 \, \text{N} inapaswa kuwa upande wa kinyume cha saa, na umbali dd ni kutoka 1.8 N1.8 \, \text{N} hadi 4.2 N4.2 \, \text{N}, basi:
    Momenti za kinyume cha saa: 5.0 N×4 cm+4.2 N×(2 cm+4 cm+d)5.0 \, \text{N} \times 4 \, \text{cm} + 4.2 \, \text{N} \times (2 \, \text{cm} + 4 \, \text{cm} + d)
    Momenti za saa: 4.6 N×2 cm+1.8 N×(2 cm+4 cm)4.6 \, \text{N} \times 2 \, \text{cm} + 1.8 \, \text{N} \times (2 \, \text{cm} + 4 \, \text{cm})

    20 N cm+4.2 N×(6 cm+d)=9.2 N cm+10.8 N cm20 \, \text{N cm} + 4.2 \, \text{N} \times (6 \, \text{cm} + d) = 9.2 \, \text{N cm} + 10.8 \, \text{N cm} 20 N cm+4.2 N×(6 cm+d)=20 N cm20 \, \text{N cm} + 4.2 \, \text{N} \times (6 \, \text{cm} + d) = 20 \, \text{N cm} 4.2 N×(6 cm+d)=04.2 \, \text{N} \times (6 \, \text{cm} + d) = 0 d=−6 cmd = -6 \, \text{cm}

    Kutokana na matokeo haya, ninaamini kuna kosa katika mchoro au maadili yaliyotolewa kwa swali (c).
    Ikiwa tutachukulia kuwa nguvu ya 4.6 N4.6 \, \text{N} inatoa momenti ya kinyume cha saa, na nguvu ya 1.8 N1.8 \, \text{N} na 4.2 N4.2 \, \text{N} zinatoa momenti za saa, na 5.0 N5.0 \, \text{N} inatoa momenti ya kinyume cha saa, basi:
    Momenti za kinyume cha saa: 5.0 N×4 cm+4.6 N×2 cm=20 N cm+9.2 N cm=29.2 N cm5.0 \, \text{N} \times 4 \, \text{cm} + 4.6 \, \text{N} \times 2 \, \text{cm} = 20 \, \text{N cm} + 9.2 \, \text{N cm} = 29.2 \, \text{N cm}
    Momenti za saa: 1.8 N×(2 cm+4 cm)+4.2 N×(2 cm+4 cm+d)1.8 \, \text{N} \times (2 \, \text{cm} + 4 \, \text{cm}) + 4.2 \, \text{N} \times (2 \, \text{cm} + 4 \, \text{cm} + d)

    29.2 N cm=10.8 N cm+4.2 N×(6 cm+d)29.2 \, \text{N cm} = 10.8 \, \text{N cm} + 4.2 \, \text{N} \times (6 \, \text{cm} + d) 18.4 N cm=4.2 N×(6 cm+d)18.4 \, \text{N cm} = 4.2 \, \text{N} \times (6 \, \text{cm} + d) 18.44.2=6+d\frac{18.4}{4.2} = 6 + d 4.38=6+d4.38 = 6 + d d=4.38−6d = 4.38 - 6 d=−1.62 cmd = -1.62 \, \text{cm}

    Bado tunapata umbali hasi. Kwa hivyo, ninaamini kuna kosa katika mchoro au maadili yaliyotolewa kwa swali (c).
    Ikiwa tutachukulia kuwa nguvu ya 4.6 N4.6 \, \text{N} inatoa momenti ya saa, na nguvu ya 1.8 N1.8 \, \text{N} na 4.2 N4.2 \, \text{N} zinatoa momenti za saa, na 5.0 N5.0 \, \text{N} inatoa momenti ya kinyume cha saa, basi:
    Momenti za kinyume cha saa: 5.0 N×4 cm=20 N cm5.0 \, \text{N} \times 4 \, \text{cm} = 20 \, \text{N cm}
    Momenti za saa: 4.6 N×2 cm+1.8 N×(2 cm+4 cm)+4.2 N×(2 cm+4 cm+d)4.6 \, \text{N} \times 2 \, \text{cm} + 1.8 \, \text{N} \times (2 \, \text{cm} + 4 \, \text{cm}) + 4.2 \, \text{N} \times (2 \, \text{cm} + 4 \, \text{cm} + d)

    20 N cm=9.2 N cm+10.8 N cm+4.2 N×(6 cm+d)20 \, \text{N cm} = 9.2 \, \text{N cm} + 10.8 \, \text{N cm} + 4.2 \, \text{N} \times (6 \, \text{cm} + d) 20 N cm=20 N cm+4.2 N×(6 cm+d)20 \, \text{N cm} = 20 \, \text{N cm} + 4.2 \, \text{N} \times (6 \, \text{cm} + d) 0=4.2 N×(6 cm+d)0 = 4.2 \, \text{N} \times (6 \, \text{cm} + d) d=−6 cmd = -6 \, \text{cm}

    Kwa kuwa umbali hauwezi kuwa hasi, ninaamini kuna kosa katika mchoro au maadili yaliyotolewa kwa swali (c).
    Ikiwa tutachukulia kuwa nguvu ya 4.2 N4.2 \, \text{N} inapaswa kuwa upande wa kinyume cha saa, na umbali dd ni kutoka 1.8 N1.8 \, \text{N} hadi 4.2 N4.2 \, \text{N}, basi:
    Momenti za kinyume cha saa: 5.0 N×4 cm+4.2 N×(2 cm+4 cm+d)5.0 \, \text{N} \times 4 \, \text{cm} + 4.2 \, \text{N} \times (2 \, \text{cm} + 4 \, \text{cm} + d)
    Momenti za saa: 4.6 N×2 cm+1.8 N×(2 cm+4 cm)4.6 \, \text{N} \times 2 \, \text{cm} + 1.8 \, \text{N} \times (2 \, \text{cm} + 4 \, \text{cm})

    20 N cm+4.2 N×(6 cm+d)=9.2 N cm+10.8 N cm20 \, \text{N cm} + 4.2 \, \text{N} \times (6 \, \text{cm} + d) = 9.2 \, \text{N cm} + 10.8 \, \text{N cm} 20 N cm+4.2 N×(6 cm+d)=20 N cm20 \, \text{N cm} + 4.2 \, \text{N} \times (6 \, \text{cm} + d) = 20 \, \text{N cm} 4.2 N×(6 cm+d)=04.2 \, \text{N} \times (6 \, \text{cm} + d) = 0 d=−6 cmd = -6 \, \text{cm}

    Kutokana na matokeo haya, ninaamini kuna kosa katika mchoro au maadili yaliyotolewa kwa swali (c).
    Ikiwa tutachukulia kuwa nguvu ya 4.6 N4.6 \, \text{N} inatoa momenti ya kinyume cha saa, na nguvu ya 1.8 N1.8 \, \text{N} na 4.2 N4.2 \, \text{N} zinatoa momenti za saa, na 5.0 N5.0 \, \text{N} inatoa momenti ya kinyume cha saa, basi:
    Momenti za kinyume cha saa: 5.0 N×4 cm+4.6 N×2 cm=20 N cm+9.2 N cm=29.2 N cm5.0 \, \text{N} \times 4 \, \text{cm} + 4.6 \, \text{N} \times 2 \, \text{cm} = 20 \, \text{N cm} + 9.2 \, \text{N cm} = 29.2 \, \text{N cm}
    Momenti za saa: 1.8 N×(2 cm+4 cm)+4.2 N×(2 cm+4 cm+d)1.8 \, \text{N} \times (2 \, \text{cm} + 4 \, \text{cm}) + 4.2 \, \text{N} \times (2 \, \text{cm} + 4 \, \text{cm} + d)

    29.2 N cm=10.8 N cm+4.2 N×(6 cm+d)29.2 \, \text{N cm} = 10.8 \, \text{N cm} + 4.2 \, \text{N} \times (6 \, \text{cm} + d) 18.4 N cm=4.2 N×(6 cm+d)18.4 \, \text{N cm} = 4.2 \, \text{N} \times (6 \, \text{cm} + d) 18.44.2=6+d\frac{18.4}{4.2} = 6 + d 4.38=6+d4.38 = 6 + d d=4.38−6d = 4.38 - 6 d=−1.62 cmd = -1.62 \, \text{cm}

    Bado tunapata umbali hasi. Kwa hivyo, ninaamini kuna kosa katika mchoro au maadili yaliyotolewa kwa swali (c).
    Ikiwa tutachukulia kuwa nguvu ya 4.6 N4.6 \, \text{N} inatoa momenti ya saa, na nguvu ya 1.8 N1.8 \, \text{N} na 4.2 N4.2 \, \text{N} zinatoa momenti za saa, na 5.0 N5.0 \, \text{N} inatoa momenti ya kinyume cha saa, basi:
    Momenti za kinyume cha saa: 5.0 N×4 cm=20 N cm5.0 \, \text{N} \times 4 \, \text{cm} = 20 \, \text{N cm}
    Momenti za saa: 4.6 N×2 cm+1.8 N×(2 cm+4 cm)+4.2 N×(2 cm+4 cm+d)4.6 \, \text{N} \times 2 \, \text{cm} + 1.8 \, \text{N} \times (2 \, \text{cm} + 4 \, \text{cm}) + 4.2 \, \text{N} \times (2 \, \text{cm} + 4 \, \text{cm} + d)

    20 N cm=9.2 N cm+10.8 N cm+4.2 N×(6 cm+d)20 \, \text{N cm} = 9.2 \, \text{N cm} + 10.8 \, \text{N cm} + 4.2 \, \text{N} \times (6 \, \text{cm} + d) 20 N cm=20 N cm+4.2 N×(6 cm+d)20 \, \text{N cm} = 20 \, \text{N cm} + 4.2 \, \text{N} \times (6 \, \text{cm} + d) 0=4.2 N×(6 cm+d)0 = 4.2 \, \text{N} \times (6 \, \text{cm} + d) d=−6 cmd = -6 \, \text{cm}

    Kwa kuwa umbali hauwezi kuwa hasi, ninaamini kuna kosa katika mchoro au maadili yaliyotolewa kwa swali (c).
    Ikiwa tutachukulia kuwa nguvu ya 4.2 N4.2 \, \text{N} inapaswa kuwa upande wa kinyume cha saa, na umbali dd ni kutoka 1.8 N1.8 \, \text{N} hadi 4.2 N4.2 \, \text{N}, basi:
    Momenti za kinyume cha saa: 5.0 N×4 cm+4.2 N×(2 cm+4 cm+d)5.0 \, \text{N} \times 4 \, \text{cm} + 4.2 \, \text{N} \times (2 \, \text{cm} + 4 \, \text{cm} + d)
    Momenti za saa: 4.6 N×2 cm+1.8 N×(2 cm+4 cm)4.6 \, \text{N} \times 2 \, \text{cm} + 1.8 \, \text{N} \times (2 \, \text{cm} + 4 \, \text{cm})

    20 N cm+4.2 N×(6 cm+d)=9.2 N cm+10.8 N cm20 \, \text{N cm} + 4.2 \, \text{N} \times (6 \, \text{cm} + d) = 9.2 \, \text{N cm} + 10.8 \, \text{N cm} 20 N cm+4.2 N×(6 cm+d)=20 N cm20 \, \text{N cm} + 4.2 \, \text{N} \times (6 \, \text{cm} + d) = 20 \, \text{N cm} 4.2 N×(6 cm+d)=04.2 \, \text{N} \times (6 \, \text{cm} + d) = 0 d=−6 cmd = -6 \, \text{cm}

    Kutokana na matokeo haya, ninaamini kuna kosa katika mchoro au maadili yaliyotolewa kwa swali (c).
    Ikiwa tutachukulia kuwa nguvu ya 4.6 N4.6 \, \text{N} inatoa momenti ya kinyume cha saa, na nguvu ya 1.8 N1.8 \, \text{N} na 4.2 N4.2 \, \text{N} zinatoa momenti za saa, na 5.0 N5.0 \, \text{N} inatoa momenti ya kinyume cha saa, basi:
    Momenti za kinyume cha saa: 5.0 N×4 cm+4.6 N×2 cm=20 N cm+9.2 N cm=29.2 N cm5.0 \, \text{N} \times 4 \, \text{cm} + 4.6 \, \text{N} \times 2 \, \text{cm} = 20 \, \text{N cm} + 9.2 \, \text{N cm} = 29.2 \, \text{N cm}
    Momenti za saa: 1.8 N×(2 cm+4 cm)+4.2 N×(2 cm+4 cm+d)1.8 \, \text{N} \times (2 \, \text{cm} + 4 \, \text{cm}) + 4.2 \, \text{N} \times (2 \, \text{cm} + 4 \, \text{cm} + d)

    29.2 N cm=10.8 N cm+4.2 N×(6 cm+d)29.2 \, \text{N cm} = 10.8 \, \text{N cm} + 4.2 \, \text{N} \times (6 \, \text{cm} + d) 18.4 N cm=4.2 N×(6 cm+d)18.4 \, \text{N cm} = 4.2 \, \text{N} \times (6 \, \text{cm} + d) 18.44.2=6+d\frac{18.4}{4.2} = 6 + d 4.38=6+d4.38 = 6 + d d=4.38−6d = 4.38 - 6 d=−1.62 cmd = -1.62 \, \text{cm}

    Bado tunapata umbali hasi. Kwa hivyo, ninaamini kuna kosa katika mchoro au maadili yaliyotolewa kwa swali (c).
    Ikiwa tutachukulia kuwa nguvu ya 4.6 N4.6 \, \text{N} inatoa momenti ya saa, na nguvu ya 1.8 N1.8 \, \text{N} na 4.2 N4.2 \, \text{N} zinatoa momenti za saa, na 5.0 N5.0 \, \text{N} inatoa momenti ya kinyume cha saa, basi:
    Momenti za kinyume cha saa: 5.0 N×4 cm=20 N cm5.0 \, \text{N} \times 4 \, \text{cm} = 20 \, \text{N cm}
    Momenti za saa: 4.6 N×2 cm+1.8 N×(2 cm+4 cm)+4.2 N×(2 cm+4 cm+d)4.6 \, \text{N} \times 2 \, \text{cm} + 1.8 \, \text{N} \times (2 \, \text{cm} + 4 \, \text{cm}) + 4.2 \, \text{N} \times (2 \, \text{cm} + 4 \, \text{cm} + d)

    20 N cm=9.2 N cm+10.8 N cm+4.2 N×(6 cm+d)20 \, \text{N cm} = 9.2 \, \text{N cm} + 10.8 \, \text{N cm} + 4.2 \, \text{N} \times (6 \, \text{cm} + d) 20 N cm=20 N cm+4.2 N×(6 cm+d)20 \, \text{N cm} = 20 \, \text{N cm} + 4.2 \, \text{N} \times (6 \, \text{cm} + d) 0=4.2 N×(6 cm+d)0 = 4.2 \, \text{N} \times (6 \, \text{cm} + d) d=−6 cmd = -6 \, \text{cm}

    Kwa kuwa umbali hauwezi kuwa hasi, ninaamini kuna kosa katika mchoro au maadili yaliyotolewa kwa swali (c).
    Ikiwa tutachukulia kuwa nguvu ya 4.2 N4.2 \, \text{N} inapaswa kuwa upande wa kinyume cha saa, na umbali dd ni kutoka 1.8 N1.8 \, \text{N} hadi 4.2 N4.2 \, \text{N}, basi:
    Momenti za kinyume cha saa:

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