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Zorluk: KolayWheel and Axle

A manual boat winch is used to pull a small boat onto a trailer. The crank handle travels in a circle with a radius of 15 inches15 \text{ inches}, turning a central spool (the axle) with a radius of 3 inches3 \text{ inches}.

What is the Ideal Mechanical Advantage (IMA) of this winch?

Cevap: 5

Cevap

The Ideal Mechanical Advantage is 5.
The Ideal Mechanical Advantage of a wheel and axle is calculated by dividing the radius of the wheel by the radius of the axle. Here, the wheel's radius is 15 inches15 \text{ inches} and the axle's radius is 3 inches3 \text{ inches}, which gives 15÷3=515 \div 3 = 5.

Adım Adım Çözüm

1
Identify the given dimensions of the wheel and the axle.
Rwheel=15 inchesR_{wheel} = 15 \text{ inches}, Raxle=3 inchesR_{axle} = 3 \text{ inches}
These are the required variables for the IMA equation.
2
Apply the Ideal Mechanical Advantage formula for a wheel and axle.
IMA=RwheelRaxleIMA = \frac{R_{wheel}}{R_{axle}}
IMA represents the ratio of the effort distance to the resistance distance.
3
Calculate the final value.
IMA=153=5IMA = \frac{15}{3} = 5
Dividing the wheel radius by the axle radius yields the mechanical advantage.

Anahtar Kavram

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

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