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A typical car has an axle with 1.10 cm radius driving a tire with a radius of 27.5 cm . What is its mechanical advantage assuming the very simplified model in Figure 9.24(b)?
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<b>Figure 9.24b</b> A car axel driving a wheel. Radii, and input and output forces are shown to illustrate mechanical advantage.
Figure 9.24b A car axel driving a wheel. Radii, and input and output forces are shown to illustrate mechanical advantage.
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Final Answer
$0.0400$
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OpenStax College Physics Solution, Chapter 9, Problem 22 (Problems & Exercises) (1:37)

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Video Transcript

This is College Physics Answers with Shaun Dychko. This axle is driving the wheel of the car and we are told that the axle has a radius of 1.10 centimeters. The wheel radius, which is the output radius, you could say, is 27.5 centimeters. I am gonna leave the units as centimeters; normally, I would convert things into meters, kilograms and seconds and so on... <i>mks</i> units for our formulas but in this case since we are going to be dividing these radii, the units will cancel and the only important thing is that they are the same and they are both centimeters so that's fine. So the output torque at this edge of the wheel is going to equal the input torque on the edge of this axle. and we can calculate the mechanical advantage by dividing both sides by <i>F input</i> and also divide by <i>r output</i> and that leaves us with this line here: the mechanical advantage, which is the output force divided by the input force, is the input radius divided by the output radius. So that's 1.10 centimeters divided by 27.5 centimeters which is the mechanical advantage of 0.0400 and it's not really an advantage but it still gets the same term, same name—mechanical advantage— even though there's a big disadvantage to having a big output radius versus a small input radius.