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Vectors Revisited

Learn how to resolve vectors into horizontal and vertical components using trigonometry, understanding forces in multiple dimensions.

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Vectors Revisited

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  1. Vectors Revisited Physics Chapter 6 D

  2. Net Force • Net force is the sum of all forces on an object • If net force is zero, the object will not accelerate

  3. Net Force • In the real world, forces don't exist in one dimension! • We must be able to resolve vectors into vertical and horizontal components.

  4. Vector Resolution

  5. Vector Resolution • Here is the vector we will work with. • First draw the horizontal and vertical component of this vector • This forms a right triangle

  6. Vector Resolution • This right triangle will allow us to do calculation of the vertical and horizontal components using trigonometry

  7. Trigonometry • The sine of angle A is the opposite side over the hypotenuse • The cosine of angle A is the adjacent side over the hypotenuse • The tangent of angle A is the opposite side over the adjacent side

  8. Vector Resolution • Now we can find the vertical component: Vertical/Hypotenuse = ?

  9. Vector Resolution • Now we can find the vertical component: Vertical/Hypotenuse = sin 35 • So Vertical = 316N * sin35 • Vertical: Fy=181 N

  10. Vector Resolution • Now we can find the horizontal component: Horizontal/Hypotenuse = ?

  11. Vector Resolution • Now we can find the horizontal component: Horizontal/Hypotenuse = cos 35 • So Horiz = 316N * cos 35 • Horiz: Fx=259 N

  12. Vector Resolution • We now know both the vertical and horizontal components of this vector • We also know that the vertical doesn't care what the horizontal is doing, and vice versa

  13. Vector Resolution • We now know both the vertical and horizontal components of this vector • Fx=259 N

  14. Vector Resolution • We now know both the vertical and horizontal components of this vector • Fx=259 N • Fy=181 N

  15. Vector Resolution • Sometimes we can't make a right triangle

  16. Vector Resolution • Sometimes we can't make a right triangle • We can use the law of cosines: R2 = A2 + B2 -- 2ABcosΘ (R is the side opposite the angle you know)‏

  17. Vector Resolution • Even with many vectors, if we resolve them into components, we can add them all to get a final result

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