Learning Introductory Physics with Activities

Section 4.11 Special-case Analysis

• You will often need to identify an interesting special case. Good cases are special if they are easy to solve or if you have solved them before.
• When you identify a good special case, you should quickly be able to write down the answer in that case. The answer you write down should be specific.
• When you evaluate your answer in the special case, you will need to identify the value that a variable of interest takes on in the case and then evaluate your symbolic equation at that value. Sometimes the value may require you to take a limit!
• At the end, you should compare your two answers; typically, this involves comparing two symbolic equations and checking if they are exactly equal!

Exercises Activities

1. A*R*C*S: The Gymnast.

A gymnast is training using two ropes attached to the ceiling, as shown in the figure. The gymnast is currently suspended at rest. The mass of the gymnast is \(75 \mathrm{~kg}\text{.}\) Your goal is to find the tension in each rope.

1. Analyze and Represent

1. Identify known and unknown quantities with both a symbol and a number.
2. Identify and justify any assumptions.
3. Choose an appropriate system and draw a-free-body diagram for the system.

2. Calculate

1. Identify relevant laws that will help you solve for the tensions.
2. Determine a symbolic equation for each unknown quantity in terms of known variables.
3. Plug numbers into your symbolic answer.

3. Sensemake

1. Check the units of your symbolic answer.
2. Compare your numerical answers to appropriate numerical quantities with the same units.
3. Consider a special case: a simplified version of the physical situation where the answer is easy!