Problem 1. Pancakes are a wonderful food whose texture gives the essence of the concept of this week, elasticity. When you chew a pancake, the mouthfeel of the food is very much affected by its elastic modulus. This is particularly interesting when you compare different pancake recipes, which try to achieve the same consistency with very different ingredients. In thinking through this problem, think about two recipes--a recipe for Normal Pancakes (e.g. this recipe from Joy of Cooking (https://dinersjournal.blogs.nytimes.com/2008/12/24/recipeof-the-day-everyday-pancakes/?_r=0)), and a recipe for Gluten Free Pancakes (e.g. this recipe from detoxinista.com. (https://detoxinista.com/2012/09/almondbutter-pancakes-grain-free/) )
(a) Consider a stack of five pancakes. Assume that each pancake is made of 1/4 cup (60 mL) of batter and that the density of batter is about 1.2g/ml . Consider the pancake at the bottom of the stack. What is the total weight (as a force in N) of pancakes sitting on top of it? Express your answer in Newtons.
(b) This is not a lot of weight. Assume that pancakes have an elastic modulus of 20 kPa ( i.e. 20 x 103 Pa), that they are circular and the radius of each pancake is identical (approximately 5 cm), and that the stack of 5 pancakes has a height of 50 mm. Compute how much the pancake at the bottom of the stack is compressed by the weight of the pancakes on top of it.
(c) This is a very small compression, so instead you place a 6 kg weight on the pancakes. Now you see that the stack noticeably compresses. Assume the area of each pancake is identical. What is the stress on the pancakes? Express your answer in Pascals.
(d) Your observation of the normal pancakes shows that when the 6kg weight is placed on the pancakes, the height of the pancake stack decreases from its initial value of 50 mm to a final value of 30mm. Use these measurements to calculate the elastic modulus of the pancakes. Express your answer in Pascals.
(e) Given your measurement of the elastic modulus, what is the cross link distance in the normal pancakes? Assume that the interaction energy between the glutenin molecules is Uint = 100 kBT= 4 x 10-19 J
(f) The gluten-free pancakes are much softer. For that reason you only use a 0.7kg weight. Now the height of the pancake stack decreases from its initial value of 50 mm to a final value of 39mm. Use these measurements to calculate the elastic modulus of the pancakes. Express your answer in Pascals (g) Using the elastic modulus for the gluten free pancakes and assuming that without the glutenin the interaction energy is ten times larger Uint = 10 (100 kBT) = 4 x 10-18 J what do you conclude regarding the crosslink distance in the gluten free pancakes compared to the normal pancakes-does it increase or decrease? Explain your answer ( if you want to you can also calculate it.