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Zorluk: KolayGears and Gear Ratios

Inside a wind-up toy, a main spring rotates a driving gear with 60 teeth at a speed of 10 RPM. This gear directly meshes with a smaller driven gear that powers the toy's legs. If the legs require the driven gear to spin at 40 RPM to function properly, how many teeth must the driven gear have?

Cevap: 15 teeth

Cevap

15 teeth
The correct answer is derived using the principle that the product of the number of teeth and rotational speed must be equal for two meshed gears (60×10=15×4060 \times 10 = 15 \times 40). This confirms the driven gear must have 15 teeth to rotate at 40 RPM.

Adım Adım Çözüm

1
Identify the relationship between gear teeth and rotational speed.
The governing formula is T1×S1=T2×S2T_1 \times S_1 = T_2 \times S_2, where T represents the number of teeth and S represents the speed in RPM.
Gear speed is inversely proportional to the number of teeth.
2
Substitute the given numerical values into the equation.
60×10=T2×4060 \times 10 = T_2 \times 40
Applying the known driving gear parameters (60 teeth, 10 RPM) and the target speed for the driven gear (40 RPM).
3
Calculate the unknown number of teeth for the driven gear.
600=T2×40600 = T_2 \times 40, which gives T2=15T_2 = 15
Isolating the variable T2T_2 yields the required tooth count for the mechanism to function correctly.

Anahtar Kavram

Gear Ratio and Speed Calculations
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Konular

Gears and Gear Ratios

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