QUESTION: Hello! I am trying to a buy citrus press, but I am not sure which one delivers the greatest leverage. Does the Chef'n Fresh Force Lemon Squeezer really provide more leverage, or is it just some marketing trick? I understand it's second class lever, but how does the additional metal piece help? Thank you.
ANSWER: While this is more of a question for someone who's actually used one and not a physicist, I googled it. The lever design looks relatively clever, but I don't see anything really extraordinary about it. I also, upon googling "citrus juicer" see many stand-up varieties with much larger levers for even less money...why don't you try one of those?
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QUESTION: How would you calculate the mechanical advantage of the dual lever and gear assembly?
ANSWER: I'd have to actually see a schematic to be able to do that with any precision. Do you happen to have one? I looked at a youtube video of it to get a better idea than still pictures can provide. Basically, instead of just using a lever with a hinge and calculating the mechanical advantage that way (the length of the lever to the point where you're pushing on from the hinge divided by the length from the hinge to the fruit), you need to figure out the distance to the gear. You're providing torque on the handle one way, the gear is pressing back the other. Therefore, the mechanical advantage should be the lever arm from the gear axle to your hand divided by the gear radius. Simple enough. Believe it or not, the length of that second lever is immaterial to the pressing process (it will not appear in the torque equations because I used the axle of the geared lever as a rotation point). It does look like it would be possible to break this device relatively easily, I saw the hinged part flexing somewhat as it was being used. Keep that in mind for safety, when large forces are involved device failures can have consequences.
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QUESTION: Why do you claim the following:
Believe it or not, the length of that second lever(what is the second lever?) is immaterial to the pressing process (it will not appear in the torque equations because I used the axle of the geared lever as a rotation point).
This is a little more than a claim, it's physics! Seriously, this is the way I would instruct students to set up a similar problem, so perhaps I can explain why the length of the second lever doesn't matter...though this is a tricky one. Yes, the second lever is necessary for this to work, it's needed to provide tension or compression. The lever applies torque to rotate the gear at the end of the handle. The gear teeth apply the counter torque in a steady state (like maximum juice compression). This a torque problem, you *have* to be able to find equations that make sense, no matter what point you choose for rotation. We choose points for rotation to eliminate the unknown forces in such a problem. The best choice here is the gear axle, around which the gear and handle rotate. That eliminates forces that center on the axle in the rotation, but obviously the force on the fruit is important! Now consider the second lever itself. If you choose the second lever's end away from the gear axle, there's only one force. Since, at maximum compression (works when it's moving, too, but it's harder to explain), you have a stationary second small lever, you can only have tension or compression at the gear axle end. If you had any other forces, that tiny second lever would spin wildly. It's physically wrong to have anything aside from tension or compression on the second lever, its length really doesn't matter as long as it's long enough to accommodate the corresponding gear on the body of the juicer. Even when it's in motion, the transverse forces that make it rotate are comparatively tiny. Now the length they have is the simplest configuration (you can also do this with an asymmetric gear and a lever of different length), where the axle appears to be equal to the radius of the corresponding gear on the body of the device **correction, the combined radii of both gears**. I'm pretty sure I would design it the same way, but make sure it was made out of some kind of really durable metal.