Table of contents

0. Math Review31m
- Math Review
  31m
1. Intro to Physics Units1h 29m
2. 1D Motion / Kinematics3h 56m
3. Vectors2h 43m
4. 2D Kinematics1h 42m
5. Projectile Motion3h 6m
6. Intro to Forces (Dynamics)3h 22m
7. Friction, Inclines, Systems2h 44m
8. Centripetal Forces & Gravitation7h 26m
9. Work & Energy1h 59m
10. Conservation of Energy2h 54m
11. Momentum & Impulse3h 40m
12. Rotational Kinematics2h 59m
13. Rotational Inertia & Energy7h 4m
14. Torque & Rotational Dynamics2h 5m
15. Rotational Equilibrium3h 39m
16. Angular Momentum3h 6m
17. Periodic Motion2h 9m
18. Waves & Sound3h 40m
19. Fluid Mechanics4h 27m
20. Heat and Temperature3h 7m
21. Kinetic Theory of Ideal Gases1h 50m
22. The First Law of Thermodynamics1h 26m
23. The Second Law of Thermodynamics3h 11m
24. Electric Force & Field; Gauss' Law3h 42m
25. Electric Potential1h 51m
26. Capacitors & Dielectrics2h 2m
27. Resistors & DC Circuits3h 8m
28. Magnetic Fields and Forces2h 23m
29. Sources of Magnetic Field2h 30m
30. Induction and Inductance3h 38m
31. Alternating Current2h 37m
32. Electromagnetic Waves2h 14m
33. Geometric Optics2h 57m
34. Wave Optics1h 15m
35. Special Relativity2h 10m

3. Vectors

Vector Composition & Decomposition

Physics

3. Vectors

Vector Composition & Decomposition

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Problem 7c

Textbook Question

Draw each of the following vectors. Then find its x- and y-components. F = (50.0 N, 36.9 degrees counterclockwise from the positive y-axis)

Verified step by step guidance

Step 1: Understand the problem. The vector F has a magnitude of 50.0 N and is oriented at an angle of 36.9 degrees counterclockwise from the positive y-axis. We need to find its x- and y-components.

Step 2: Recognize the coordinate system. Since the angle is given counterclockwise from the positive y-axis, we need to adjust the angle to fit the standard convention where angles are measured counterclockwise from the positive x-axis. The adjusted angle is θ = 90° - 36.9°.

Step 3: Use trigonometric functions to find the components. The x-component of the vector is given by Fₓ = F * cos(θ), and the y-component is given by Fᵧ = F * sin(θ). Substitute the magnitude of F and the adjusted angle θ into these formulas.

Step 4: Write the expressions for the components. Using the formulas: Fₓ = 50.0 * cos(90° - 36.9°) and Fᵧ = 50.0 * sin(90° - 36.9°). Simplify the trigonometric expressions if needed.

Step 5: Conclude the process. Once the trigonometric calculations are performed, the x- and y-components of the vector F will be determined. Ensure the signs of the components are consistent with the vector's direction in the coordinate system.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Vector Representation

Vectors are quantities that have both magnitude and direction. In this context, the force vector F is represented by its magnitude (50.0 N) and its direction (36.9 degrees counterclockwise from the positive y-axis). Understanding how to graphically represent vectors is essential for visualizing their components.

Components of a Vector

The components of a vector are its projections along the axes of a coordinate system, typically the x-axis and y-axis. For a vector given in polar form, such as F, the x-component can be found using F_x = F * cos(θ) and the y-component using F_y = F * sin(θ), where θ is the angle from the positive x-axis.

Trigonometric Functions

Trigonometric functions, specifically sine and cosine, are fundamental in resolving vectors into their components. These functions relate the angles of a triangle to the ratios of its sides, allowing us to calculate the x- and y-components of a vector based on its angle and magnitude. Mastery of these functions is crucial for solving problems involving vector decomposition.

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Textbook Question

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Textbook Question

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Textbook Question

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Textbook Question

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Textbook Question

Two vectors, $V ⃗ sub 1$ and $V ⃗ sub 2$ , add to a resultant ${\vec{V}}_{R} = {\vec{V}}_{1} + {\vec{V}}_{2}$ . Describe $V ⃗ sub 1$ and $V ⃗ sub 2$ if $V_{R}^{2} = V_{1}^{2} + V_{2}^{2}$ .