Forces in Space

1
Forces in Space

• Force F is defined by magnitude F, two angles q
  and f, and point of application (origin).

2
Rectangular Components

• Given the size F and angles q, f obtain
  components Fx, Fy, Fz of force F.
• Step One.
• FFhFy
• Fh F sinq
• Fy F cosq

3
more

• Step Two. Fh Fx Fz , F Fx Fy Fz
• Fx Fh cosf , Fz Fh sinf
• Fx F cosf sinq
• Fy F cosq
• Fz F sinf sinq

4
more

• Given the components Fx, Fy, Fz of force F,
  obtain magnitude F and angles q, f.

5
Direction Cosines

• Direction cosines qx, qy, qz.
• Fx F cosqx
• Fy F cosqy
• Fz F cosqz

6
The Unit Vector k

• F Fxi Fyj Fzk
• Fx, Fy, Fz scalar components
• Fx, Fy, Fz vector components
• F F (cosqxi cosqyj cosqzk)
• F F ? , ? is a unit vector in direction F

7
More on unit vectors.

• F F l
• l cosqxi cosqyj cosqzk

8
Still more on unit vectors.

• Force direction via point coordinates.
• MN dxi dyj dzk
• l MN ? ?MN?

9
Addition of forces in space

• Resolve forces into components sum components.
• R ?F ?
• Rxi Ryj Rzk (?Fx)i (?Fy) j (?Fz) k
• Rx ?Fx Ry ?Fy Rz ?Fz