In this article we will take an interesting question on theoretical work done while eating a cookie. We will apply the basic concepts of Physics to answer it. We will see that the answer predicted by Physics varies drastically to what we experience in our daily life. In actuality though, the two answers are not very different. We just need to change our perspective to actually see that they are essentially the same.
Question: How much work is involved in eating a 27-gram cookie, if it can be eaten in 6 bites and the distance from hand to mouth is 24 centimeters? The cookie is raised to the mouth at a 45° angle and is put down after each bite. Assume that each bite of cookie has the same mass. (If you need to eat a cookie in order to visualize this problem better, feel free to do so!)
Answer: Assuming that we move the cookie slowly to our mouth, the force applied by our hand must equal to the weight of the cookie. Whether we are lifting up or moving it down, the force applied by hand is always in the upward direction so as to counter the weight of the cookie. When we are moving up the work done by our hand is positive as the force applied and motion are in the same direction.
When we are moving down, the work done by our hand is negative as the force applied by hand and the motion of cookie is in opposite direction. So we can say that the if we move the cookie to our mouth for the first time; we lifted a mass of m*1=27 grams to a height of h=24cm*sin 45= 17 cm (approx). Our bite was just 27/6=4.5 grams. So the remaining m2=27-4.5= 22.5 grams was shifted downward. So in this first trip of upward and downward motion, the total work done was w= (m1*gh – m2*gh)=(m1 – m2)*g*h= 4.5 grams*9.8m/s^2*17cm=0.0075 Joules. Similarly for the next trip, work done will be same. So when we add all the 6 trips, we will get a net work done of W= 6 times of 0.0075 joules. Hence W= 0.0045 Joules. Here we note that the theoretical net work done is simply m*g*h where m is the total mass of the cookie. So whether we eat it in 6 bites or 60 bites does not make any difference as far as the theoretical work done by the hand is concerned.
In real life though if we eat that cookie in say 60 bites, we feel more tired. The reason is simple. Our hand has to lift its own mass as well so for every trip it does work just to move itself up or down. This work is not useful though. So even though Physics might say that its only the mass of the cookie that matters and not the number of bites, but in real life we need to do more work than simply m*g*h. Here it must be noted that h= perpendicular height of 17cm which was obtained by the formula h= 24*cos 45=17 cm.
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