Simple Machines: Wrenches and Wheels
Lee Falin, PhD
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Simple Machines: Wrenches and Wheels
Today we’ll continue with our series on simple machines. We’ve already discussed pulleys, levers, and ramps, so please check out those episodes if you haven’t yet. And since we’re still in this mode, I started wondering: What’s the most common type of simple machine?
It’s difficult to calculate something like that because simple machines are virtually everywhere, and sometimes they’re in forms that you don’t recognize. Take the wheel and axle for example. When you think of a wheel and axle, your first thought is probably the wheels of your car or bike. However, wheels and axles show up in all sorts of places that you might not expect. Let’s talk about the wheel and axle in detail and look at some examples of this simple machine.
Size Does Matter
If you grab a screwdriver out of your toolbox, chances are that the handle of the screwdriver is fatter than the shaft, or the part that you put into the screw. Screwdriver designers don’t just do this because they think it looks nice, the screwdriver is a type of wheel and axle and the mechanical advantage of a wheel and axle depends upon the size of the wheel compared with the size of the axle.
To calculate the mechanical advantage of a wheel and axle, you take the radius of the wheel, (which is the distance from the center of the wheel to the outside edge), and divide it by the radius of the axle.
So if your screwdriver’s handle has a 2 inch radius, and the shaft has a radius of 0.25 inches, the mechanical advantage of your screw driver is: 2 divided by 0.25, which equals 8. This means for every newton of force you apply to the screwdriver, you get 8 newtons of force applied to the screw.
See also: Newton’s 3 Laws of Motion
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The Right Tool for the Job
Have you ever seen a nut driver? Nut drivers are those tools that come in toolsets that look like a screwdriver but with a large socket attached to the end instead of a narrow tip for screws. They are designed to let you reach bolts in deep recesses, but compared to a wrench, nut drivers are actually pretty weak. That’s because wrenches have bigger wheels. Wait, since when do wrenches have wheels?
Actually, a wrench is a wheel. When you attach a wrench to a bolt and start to turn it, the wrench and bolt together act just like a wheel and axle. As you spin the wrench around, it turns the bolt (hopefully), just like any other spinning wheel turns its axle.
To calculate the mechanical advantage that a wrench gives you, just take the length of the wrench (which serves as the radius of the wheel) and divide it by the radius of the bolt you’re trying to turn. So if you have wrench that is 6 inches long and you’re using it to remove a bolt with a radius of 0.5 inches, you get a mechanical advantage of 12.
You might notice that if your wrench were 8 inches long, you would get a mechanical advantage of 16, because 8 inches divided by 0.5 inches is 16. In fact, the longer the wrench, the more mechanical advantage you get, making it even easier to loosen that bolt. But as always with simple machines, there’s a price to be paid for that power.
No Such Thing as a Free Wrench
Remember that simple machines allow you to trade force for distance. In order for you to turn the bolt all the way around, you have to spin the wrench all the way around. You probably know that the measurement all the way around the outside of a circle is called the circumference. To calculate the circumference, we take the radius and multiply it by 2 times pi.
So in order to turn our bolt once with a 6-inch wrench, we have to turn the wrench 6 inches x 2 pi, which is about 37.6 inches. However to spin the bolt once with an 8-inch wrench, we have to turn the wrench 8 inches x 2 pi, which is about 50.2 inches. So while the 8-inch wrench gives us more force, we have to turn that wrench further in order to accomplish the same amount of work.
Conclusion
So now you know why wrenches work better than fingers for loosening bolts, and that the longer the wrench, the higher the mechanical advantage. You also know that like all simple machines, a wheel and axle gives you more force, but requires you to turn the wheel a greater distance than the axle has to turn.
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Screwdriver and Wrench images from Shutterstock
