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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5:54 minutes

Problem 27

Textbook Question

Compute the x- and y-components of the vectors A, B, C, and D in Fig. E1.24.

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Identify the vectors and their respective angles with the positive x-axis: Vector N (14 cm, 13°), Vector M (21 cm, 62°), Vector P (17 cm, 40°), and Vector O (25 cm, 45°).

For each vector, use the trigonometric functions to find the x-component: x-component = magnitude * cos(angle).

For each vector, use the trigonometric functions to find the y-component: y-component = magnitude * sin(angle).

Apply the formulas to Vector N: x-component = 14 * cos(13°), y-component = 14 * sin(13°).

Apply the formulas to Vector M: x-component = 21 * cos(62°), y-component = 21 * sin(62°).

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Key Concepts

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

Vector Components

Vectors can be broken down into their x- and y-components, which represent the vector's influence in the horizontal and vertical directions, respectively. This is done using trigonometric functions: the x-component is found using the cosine of the angle, and the y-component is found using the sine of the angle, both multiplied by the vector's magnitude.

Trigonometric Functions

Trigonometric functions, such as sine and cosine, are essential for resolving vectors into components. For a vector at an angle θ from the positive x-axis, the cosine function helps find the adjacent side (x-component), while the sine function helps find the opposite side (y-component) of the right triangle formed by the vector.

Reference Angles and Quadrants

Understanding the quadrant in which a vector lies is crucial for determining the signs of its components. Angles are typically measured from the positive x-axis, and the sign of the components depends on the vector's direction: positive in the first quadrant, negative in the second for x, and so on. This helps in correctly applying trigonometric functions to find vector components.

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Multiple Choice

The figure shows vectors

\overset{⇀}{A}

and

\overset{⇀}{B}

. What are the x and y components of

\overset{⇀}{A}

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Multiple Choice

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Textbook Question

Vector A is 2.80 cm long and is 60.0° above the x-axis in the first quadrant. Vector B is 1.90 cm long and is 60.0° below the x-axis in the fourth quadrant (Fig. E1.35). Use components to find the magnitude and direction of A - B In each case, sketch the vector addition or subtraction and show that your numerical answers are in qualitative agreement with your sketch.

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Textbook Question

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