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Vector Components

Vector Components. Just as two vectors can be combined to form a single vector, a single vector can be separated into vectors that are perpendicular to each other. These component vectors show the effect of the original vector in different directions.

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Vector Components

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  1. Vector Components • Just as two vectors can be combined to form a single vector, a single vector can be separated into vectors that are perpendicular to each other. • These component vectors show the effect of the original vector in different directions. • Example: When a tow truck is pulling a car, the lift on the tow truck exerts an upward (vertical) force to raise the car’s front end while, as the truck drives, it exerts a horizontal force as the car is pulled forward.

  2. Vector Components Vertical Component Actual Force Horizontal Component

  3. Vector Vector Components • Consider the original vector as the diagonal of a rectangle.

  4. Vector Vertical Component Horizontal Component Vector Components • The vector components would be the sides of the rectangle adjacent to the vector.

  5. Vector Vertical Component Horizontal Component Vector Components • To find the value of the vector components you will need know the direction of the original vector (expressed as an angle). q

  6. Vector Components • The vertical component of the vector can be temporarily moved to the opposite side of the rectangle for the purpose of calculation. Vector Vertical Component q Horizontal Component

  7. Vector Vertical Component q Horizontal Component Vector Components • The altered figure now forms a right triangle. Use trigonometric functions on right triangles to find the values of the components.

  8. V VV q VH Vector Components Label the original vector V, the vertical component VV, and the horizontal component VH. Applying trigonometric functions for right triangles: VV = V sin q VH = V cos q

  9. VV V q VH Vector Components • It’s important to remember that the vertical vector component hasn’t actually moved. It still acts at its original location.

  10. 600 Vector Components Find the horizontal and vertical components of a 50 N vector that acts at a 600 angle above horizontal. V = original vector VV = vertical component = V sin 600 VV = (50 N)(sin 600) = 43.3 N VH = horizontal component = V cos 600 VH = V cos 600 = 25 N VV V VH

  11. Components of Muscle Force FM FRO FS The force or tension produced by a muscle (FM) can be broken into components, a component that produces torque which is called the rotary force (FRO) and a component which acts directly on the joint called the stabilizing force (FS). These components are directly related to the effect a muscle produces at the joint.

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