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Vector Resolution

Vector Resolution. a single vector can be separated into 2 perpendicular vectors. These component vectors are mathematically independent of each other.

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Vector Resolution

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  1. Vector Resolution • a single vector can be separated into 2 perpendicular vectors. • These component vectors are mathematically independent of each other. • Example: When a tow truck is pulling a car, the lift on the tow truck exerts an upward (vertical) force raising the car’s front end while (as the truck drives) it exerts a horizontal force pulling the car forward.

  2. Vector Resolution Actual Force Vertical Component Horizontal Component

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

  4. Vector Vertical Component q Horizontal Component Vector Resolution • Need direction of the original vector (expressed as q). y x

  5. Vector Vertical Component q Horizontal Component Vector Resolution • Use right triangle trig. to solve (ex, sin q, cos q) y x

  6. Vector Resolution inBiomechanics • (1) muscle forces (movement and stability) • Rotary (normal or force) Fro • Stabilizing/dislocating (tangential) Fm Fro a joint Fs

  7. Vector Resolution - Muscle Forces • Given: Fm = 300 N a (angle of pull) = 37° • Find: Fro, Fs Fm Fro a joint Fs

  8. Vector Resolution - Muscle Forces • Formula: sin a = Fro/Fm • cos a = Fs/Fm • Fro= Fm • sin a = 300 N • sin 37° = 300 • 0.602 • Fro=180.54 N • Fs= Fm • cos a = 300 N • cos 37° = 300 • 0.799 • Fs= 239.59 N Fm Fro a joint Fs

  9. Vector Resolution inBiomechanics • (1) Projectile motion • x (horizontal) • y (vertical) vnet vy Gravity acts only on the y direction! vx Solve using right triangle trig.

  10. Vnet Vy q Vx Vector Resolution Label the original vector Vnet, the vertical component Vy, and the horizontal component Vx. Applying trigonometric functions for right triangles: Vy = Vnet sin q Vx = Vnet cos q

  11. 600 Vector Resolution Find the horizontal and vertical components of a 50 m/sec vector that acts at a 600 angle above horizontal. Vnet = original vector Vy= vertical component = Vne sin 600 Vy = (50 m/sec)(sin 600) = 43.3 m/sec Vx = horizontal component = Vnet cos 600 Vx = Vnet cos 600 = 25 m/sec Vy Vnet Vx

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