What bonds are we breaking when we cut potatoes? This might seem like a stupid question, but if you think of it, we are cutting through something and separating the potato molecules, right? I don't think it's covalent bonds...but I have no idea.
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may be the bond between the fat molecules of the potato.
potatoes are mostly starch and water, so it would be covalent bonds of the carbohydrates. @srev98 potatoes don't have much fat content.
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Generally you aren't cutting chemical bonds at all. Keep in mind chemical bonds are extremely strong, and when you truly must cut chemical bonds to divide a sample of a substance -- e.g. when you are cutting diamond or steel -- it takes quite a lot of force, much more than when you are cutting a potato. And keep in mind the bonds in food (e.g. carbon-carbon bonds) aren't any weaker than those in diamond.
What you are actually doing is just dividing the sample on a line that runs *between* molecules, so you are working against the much weaker intermolecular forces, in the case of foodstuffs almost entirely London forces, with a little seasoning of H-bonding and "hydrophobic force." On both sides of your cut you would find almost nothing but intact molecules. (You might well cut a bond or two, here or there, just by luck.)