Dimensional Analysis Word Problems

You must use the formal method of dimensional analysis as taught in this class to receive credit for these solutions. (One point for each correct solution.) Later in the course, you may use any method of dimensional analysis to solve this type of problem.

1. Every three times I clean my bedroom, my mother makes me an apple pie. I cleaned my bedroom 9 times. How many apple pies does she owe me?

2. A chemistry teacher working at a golf camp during the summer found a liquid that caused him to slice ball after ball into the water without disturbing him. He thought this was an important liquid to identify, so he set out to determine its density. He found that a sample of the liquid had a mass equal to 455 golf balls and occupied a volume of 620 water cups that he obtained at the 7th hole. Each golf ball had a mass of 50 g, and the water cups at the 7th hole of the golf course held 45 mL each. What is the density of the unknown liquid?

3. A Wilton High School senior was applying to college and wondered how many applications she needed to send. Her counselor explained that with the excellent grade she received in chemistry, she would probably be accepted to one school out of every three to which she applied. She immediately realized that for each application she would have to write 3 essays, and each essay would require 2 hours of work. For each hour of serious essay writing, she would need to expend 500 calories, which she could derive from her mother's apple pies (1 pie = 1000 calories). How many times would she have to clean her room in order to gain acceptance to 10 colleges?

4. How much force, in g·cm/s², is exerted by a golf ball described in problem 2 striking a tree while accelerating at 20 cm/s²? Show how you can solve this problem without knowing that \(F=ma\). Explain your solution.

5. Because you never learned dimensional analysis, you have been working at a fast-food restaurant for the past 35 years wrapping hamburgers. Each hour, you wrap 184 hamburgers. You work 8 hours per day, 5 days a week, and get paid every 2 weeks with a salary of $840.34. How many hamburgers will you have to wrap to make your first one million dollars?

(Note: This is a closed-loop problem. If you can solve it, you have learned dimensional analysis and can get a better job. However, since you won't be working there any longer, your solution will be wrong. If you can't solve it, you can continue working, which means the problem is solvable, but you can't solve it. We have decided to overlook this impasse and allow you to solve the problem as if you had continued to wrap hamburgers.)