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Zorluk: KolayWheel and Axle

A carpenter uses a standard screwdriver to drive a screw into a piece of wood. The screwdriver handle, acting as the wheel, has a radius of 2 cm2 \text{ cm}. The metal shaft, acting as the axle, has a radius of 4 mm4 \text{ mm}. What is the ideal mechanical advantage (IMA) of the screwdriver?

  1. 5Cevap
  2. B
    0.5
  3. C
    2
  4. D
    0.2

Cevap

The ideal mechanical advantage is 5.
The correct answer is 5. To find the ideal mechanical advantage, both radii must first be in the same unit. Converting the 2 cm2 \text{ cm} handle radius yields 20 mm20 \text{ mm}. Dividing the wheel radius (20 mm20 \text{ mm}) by the axle radius (4 mm4 \text{ mm}) gives a mechanical advantage of 5, meaning the screwdriver multiplies the user's turning force by 5 times.

Adım Adım Çözüm

1
Convert the given measurements to the same unit (millimeters).
The handle (wheel) radius is 2 cm2 \text{ cm}, which equals 20 mm20 \text{ mm}.
Units must match before calculating any ratios to ensure accuracy.
2
Identify the values for the wheel and the axle.
Wheel radius = 20 mm20 \text{ mm}; Axle radius = 4 mm4 \text{ mm}.
In a screwdriver, the wider handle functions as the wheel, while the narrower shaft functions as the axle.
3
Calculate the Ideal Mechanical Advantage (IMA) by dividing the wheel radius by the axle radius.
IMA=20/4=5IMA = 20 / 4 = 5.
The formula for the IMA of a wheel and axle system driven by the wheel is the radius of the wheel divided by the radius of the axle.

Anahtar Kavram

Ideal Mechanical Advantage (IMA) of a Wheel and Axle
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Konular

Wheel and Axle

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