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!

   🔗
   🔗

🔗

🔗

🔗