Homework 0 is no longer being graded unless you have made special arrangements with Dr. Rees
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| You may submit answers to any problem a maximum of three times during the grading period. It doesn't matter when you submit your answers during this time. Homework will be graded at 8 a.m. each morning of the grading period. |
Submitted Answers will be graded M-F at 8 a.m. from September 8 until September 12.
| Problem 0.1 | |||||||||||||
| What you should learn:
Answers can be algebraic or numerical. The first problem requires an algebraic answer. Sometimes hints are opened in a new window or tab. You may refer to constants and fixed variables by name in both algebraic and numerical solutions. |
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| Problem:
A sphere of radius R has the same volume as a cube of length a on a side. Find R in terms of a. |
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| Constants and fixed variables:
Pi = 3.14159265... (Pi is always defined and won't usually appear in this list.) |
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| Hints:
What is the volume of a sphere? |
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Results of previous submissions:
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| Submit HW answers. | |||||||||||||
| Problem 0.2 | |||||||||||||
| What you should learn:
This is a numerical version of the same problem. Note that there are different values of a given for each submission. |
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| Problem:
Find a numerical value of R for Problem 0.2 if a has the value given below. |
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Variables that must be changed with each submission:
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Results of previous submissions:
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| Answer Range: 3.10 cm3 to 4.40 cm3 | |||||||||||||
| Problem 0.3 | |||||||||||||
| What you should learn:
If you prefer, you can let the program do computation for you. This has the disadvantage that you can't see if the numerical answer is in range; however, it can save you some trouble punching numbers into a calculator. |
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| Problem:
Repeat the same problem as above, but this time enter your answer in terms of variables. |
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Variables that must be changed with each submission:
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| Hints:
Help! I'm lost... |
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Results of previous submissions:
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| Answer Range: 3.10 cm3 to 4.40 cm3 | |||||||||||||
| Problem 0.4 | |||||||||||||||
| What you should learn:
Often coming up with a single number for an answer isn't very instructive. At times I'll have you plot a function or do similar graphical analysis. One way I can check on your graphing is to ask you to describe something about your graph. |
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| Problem:
This is just a mathematical problem that sometimes comes up in physics problems. Find the value of x nearest 0.40 m that satisfies the equation ax = tan (kx) where a and k are given below. To solve this equation, you will need to generate a graph something like that to the right. The solution is given by the intersection of the two curves. You may plot the graph with a graphing calculator or any computer program you want. One option is to use Maple, as we discussed in class. Be sure your graph looks something like that to the the right. Some graphing packages will connect the sections of the tangent function with a vertical line, but this isn't really part of the function. |
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| Constants and fixed variables:
a = 3.00 m-1 |
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Variables that must be changed with each submission:
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| Hints:
How can I generate this plot in MAPLE? How can I generate this plot in Python? How can I find the root with Excel? |
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Results of previous submissions:
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| Answer Range: 0.390 m to 0.460 m | |||||||||||||||