SHS General Physics 1 | Lesson 3: VECTOR ADDITION

Summary

In this lesson, students will learn about vectors, including differentiating vectors and scalar quantities, performing vector addition, and rewriting vectors in component form. The lesson begins with a review of trigonometric functions and the law of cosines. It covers vector representation, addition of parallel and non-parallel vectors, and methods like the tip-to-tail and parallelogram methods for finding resultant vectors. The lesson also includes numerical analysis for calculating resultant forces and introduces unit vectors and their calculations. Practical examples and problems are provided for better understanding. Students are assigned activities to reinforce the concepts learned.

Takeaways

• 📚 The lesson covers vectors, including differentiation between vectors and scalars, vector addition, and writing vectors in component form.
• 📐 Quick review of SOHCAHTOA: sine is opposite over hypotenuse, cosine is adjacent over hypotenuse, and tangent is opposite over adjacent.
• 🔢 Example problem solving: For a 30-degree triangle with given sides, calculating sine, cosine, and tangent.
• 🔺 Law of cosines: Useful for finding a third side of a triangle when two sides and the angle between them are known, or finding angles when all three sides are known.
• 🛠️ Scalars are quantities described by magnitude only, such as speed, volume, mass, and time.
• ➡️ Vectors have both magnitude and direction, important in motion studies; examples include force, velocity, acceleration, and momentum.
• 📏 Representation of vectors: Typically a letter with an arrow above or in boldface, and the magnitude is shown without an arrow or with vertical bars.
• ➕ Vector addition: Adding corresponding components of vectors to find the resultant vector.
• 🔄 Adding parallel and non-parallel vectors: Use direction consideration for parallel vectors and tip-to-tail or parallelogram methods for non-parallel vectors.
• 📊 Numerical analysis: Law of cosines and Pythagorean theorem can be used for calculating resultant forces in non-graphical methods.

Q & A

What are the objectives of today's lesson on vectors?

The objectives are to differentiate vectors and scalar quantities, perform addition of vectors, and rewrite a vector in component form.

What is SOHCAHTOA and how is it used?

SOHCAHTOA is a mnemonic to remember the definitions of sine, cosine, and tangent: Sine is opposite over hypotenuse, cosine is adjacent over hypotenuse, and tangent is opposite over adjacent.

How do you solve for sine, cosine, and tangent in a 30-degree triangle with given side lengths?

For sine, divide the opposite side (1) by the hypotenuse (2) to get 0.5. For cosine, divide the adjacent side (√3) by the hypotenuse (2) to get 0.866. For tangent, divide the opposite side (1) by the adjacent side (√3) to get 0.577.

What is the law of cosines and when is it useful?

The law of cosines is useful for finding the third side of a triangle when two sides and the angle between them are known, or for finding the angles when all three sides are known. The formula is c² = a² + b² - 2ab * cos(C).

What is the difference between a scalar and a vector quantity?

A scalar quantity is described by a magnitude only, while a vector quantity has both a magnitude and a direction.

How are vectors typically represented?

Vectors are usually represented by a letter with an arrow above it or in boldface. The magnitude of a vector can be represented by a lightface letter without an arrow or the vector symbol with vertical bars on both sides.

How do you add two vectors in component form?

To add two vectors in component form, you add their corresponding components. For example, vector A (2, 4) + vector B (-1, 6) results in vector C (1, 10).

How do you add parallel vectors?

For parallel vectors in the same direction, you add their magnitudes. For vectors in opposite directions, you subtract their magnitudes.

What methods can be used to add non-parallel vectors?

The tip-to-tail method and the parallelogram method can be used to add non-parallel vectors.

How can you calculate the resultant force using the law of cosines?

Using the law of cosines, you can calculate the resultant force by applying the formula: R² = a² + b² - 2ab * cos(C). Then, solve for R.

What is a unit vector and how is it calculated?

A unit vector has a magnitude of one and is used to indicate direction. It is calculated by dividing each component of the vector by the vector's magnitude.

How can you find the direction of a vector using trigonometry?

The direction of a vector can be found using the arctangent function: θ = arctan(b/a), where b and a are the components of the vector.

What is the process for finding the net force when multiple forces act at different angles?

To find the net force, break each force into its x and y components, sum the components separately, then use the Pythagorean theorem to find the resultant magnitude and arctangent to find the direction.

What activities were assigned at the end of the lesson?

The activities assigned are: Activity 1 on page 13, Activity 2 on page 14, Activity 3 on page 15, and Activity 4 on page 16.