Figure 3 shows a uniform rule balanced horizontally on a pivot. A load of 60 N hangs from the rule at a…

Question

Figure 3 shows a uniform rule balanced horizontally on a pivot. A load of 60 N hangs from the rule at a distance of 12 cm from the pivot. A metal block hangs on the other side at a distance of 30 cm from the pivot. Determine the weight of the metal block.

ScanSolve AI Tutor · Accepted Answer

Ili kutatua swali hili, tutatumia kanuni ya mizani (principle of moments), ambayo inasema kwamba kwa kitu kilicho katika usawa, jumla ya momenti za kinyume na saa ni sawa na jumla ya momenti za saa.

Tambua nguvu na umbali kutoka kwenye egemeo (pivot).
Nguvu ya mzigo (anti-clockwise force), $F_1 = 60 \text{ N}$
Umbali wa mzigo kutoka egemeo (anti-clockwise distance), $d_1 = 12 \text{ cm}$
Umbali wa kizuizi cha chuma kutoka egemeo (clockwise distance), $d_2 = 30 \text{ cm}$
Uzito wa kizuizi cha chuma (clockwise force), $F_2 = ?$
Badilisha umbali kutoka sentimita kwenda mita.
$d_1 = 12 \text{ cm} = 0.12 \text{ m}$
$d_2 = 30 \text{ cm} = 0.30 \text{ m}$
Tumia kanuni ya momenti.
Moment ya kinyume na saa = Moment ya saa
$F_1 \times d_1 = F_2 \times d_2$
Weka thamani zinazojulikana kwenye fomula.
$60 \text{ N} \times 0.12 \text{ m} = F_2 \times 0.30 \text{ m}$ $7.2 \text{ N}\cdot\text{m} = F_2 \times 0.30 \text{ m}$
Tatua kwa $F_2$ .
$F_2 = \frac{7.2 \text{ N}\cdot\text{m}}{0.30 \text{ m}}$ $F_2 = 24 \text{ N}$
Uzito wa kizuizi cha chuma ni $\text{24 N}$ .

Figure 3 shows a uniform rule balanced horizontally on a pivot. A load of 60 N hangs from the rule at a distance of 12 cm from the pivot. A metal block hangs on the other side at a distance of 30 cm from the pivot. Determine the weight of the metal block.

Answer

Step-by-step solution

Tambua nguvu na umbali kutoka kwenye egemeo (pivot).

Badilisha umbali kutoka sentimita kwenda mita.

Tumia kanuni ya momenti.

Weka thamani zinazojulikana kwenye fomula.

Tatua kwa $F_2$ .

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Figure 3 shows a uniform rule balanced horizontally on a pivot. A load of 60 N hangs from the rule at a distance of 12 cm from the pivot. A metal block hangs on the other side at a distance of 30 cm from the pivot. Determine the weight of the metal block.

Answer

Step-by-step solution

Tambua nguvu na umbali kutoka kwenye egemeo (pivot).

Badilisha umbali kutoka sentimita kwenda mita.

Tumia kanuni ya momenti.

Weka thamani zinazojulikana kwenye fomula.

Tatua kwa F2F_2F2​.

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Tatua kwa $F_2$ .