🔖 Topics

  • Practice With Vectors
  • Practice With Dimensional Analysis
  • Introduction to Excel and PhET Lab

🎯 Objectives

  • Perform mathematical operations on vectors with greater confidence.
  • Perform dimensional analysis with greater confidence.
  • Learn how to work with PhET and Excel.

📋 Sequence

  • Wrap up any lecture topics from Math Review: Part 1
  • Additional practice problems
  • Pre-lab discussion
    • What is an equation of best fit?
    • What is \(R^2\)?
    • How does the slope of a line of best fit relate to dimensional analysis?
    • How does the area under a line of best fit relate to dimensional analysis?

🖥️ Animations, Simulations, Activities

N/A

📝 Practice Problems

Vector Operations: Consider vector \(\vec{D} = 3 \hat{i} - 4\hat{j} + 2\hat{k}\) and vector \(\vec{E} = 4 \hat{i} - 2\hat{j} - 2\hat{k}\)

  • Sketch out a diagram of the setup.
  • What is \(\vec{D} + \vec{E}\) ?
  • What is \(\vec{D} - \vec{E}\) ?
  • What is \(\vec{D} \cdot \vec{E}\) ?
  • What is \(\vec{D} \times \vec{E}\) ?

Moving Car: A car moves 150 meters at 63\(^\circ\) north of east. It then moves 300 meters at 34\(^\circ\) south of west. What is the final position of the car?

Vectors on a Pentagon: Suppose I construct a regular pentagon with side length equal to one using five vectors. The five vectors all lie tip to tail.

  • Sketch out a diagram of the setup.
  • Write out each vector in array or \(\hat{i}\), \(\hat{j}\), \(\hat{k}\) format.
  • What is the sum of the five vectors?
  • How does the sum change if you double the length of each vector?
  • How does the sum change if you reverse the direction of each vector?

✅ Partial Solutions

N/A

📘 Connected Resources

  • Giambattista, Alan, et al. College Physics With an Integrated Approach to Forces and Kinematics. 5th ed., McGraw-Hill Education, 2020.