In this article, we will take an interesting question on theoretical work done while eating a cookie. 

To answer that, we’ll use basic physics concepts. We will see that the Quantum theory answer differs dramatically from what we observe in our daily lives. In essence, the two responses aren’t that dissimilar. All we have to do is shift our perspective to realize that they are essentially the same.

Question: How much effort is required to consume a 27-gram cookie in six bits at a distance of 24 centimeters between hand and mouth? The cookie is held at a 45° angle to the mouth and then lowered after each mouthful. Assume that each cookie bite is the same size. (If you need to eat a cookie to visualize this situation more clearly, go ahead!)

Answer: If we move the cookie slowly to our mouth, the force used by our hand must be equivalent to the cookie’s weight. Whether we’re pulling it up or pushing it down, the force we apply with our hands is always upward to oppose the cookie’s weight. Because the force applied and the motion is in the same direction when we move up, the work done by our hands is positive.

Because the force produced by the hand and the motion of the cookie are in opposite directions as we move down, the work done by our hand is negative. 

So, if we lift a mass of m*1=27 grams to a height of h=24cm*sin 45=17 cm the first time we take the cookie to our lips, we have lifted a mass of m*1=27 grams to a height of h=24cm*sin 45=17 cm (approx). The weight of our bite was 27/6=4.5 grams. As a result, the remaining m2=27-4.5= 22.5 grams were moved lower. So the total effort done in this first upward and downward motion was w= (m1*gh – m2*gh)=(m1 – m2)*g*h= 4.5 grams*9.8m/s2*17cm=0.0075 Joules. Work will be done in the same way on the following trip. 

As a result, when all six trips are added together, we get a net work done on W= 6 times 0.0075 joules. As a result, W= 0.0045 Joules.

We can see that the theoretical net work is just m*g*h, where m is the cookie’s total mass. So, in terms of the theoretical labor done by hand, whether we eat it in 6 bites or 60 nibbles makes no difference. 

In reality, if we devour that cookie in 60 bites, we will be exhausted. The reason is straightforward. Our hand must also lift its own mass. Thus each journey requires effort only to move up or down. However, this work is ineffective. So, even though physics may state that only the mass of the cookie matters, not the number of bites, in reality, we need to do more than just m*g*h.

It’s worth noting that h= perpendicular height of 17cm, which was calculated using the formula h= 24*cos 45=17 cm.

This article is made up of live extracts from a real Mytutorhub session between a student and a tutor. 

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