Understanding Forces in 3D Space: Solving Problems and Formulas Explained

Click For Summary

Discussion Overview

The discussion revolves around understanding the application of trigonometric formulas to resolve forces in three-dimensional space, specifically in the context of a problem from a textbook. Participants explore the calculations involved in determining the components of a force vector using trigonometric principles.

Discussion Character

  • Technical explanation
  • Mathematical reasoning
  • Homework-related

Main Points Raised

  • One participant expresses confusion about applying the formula Fx=Fcosθ in a 3D context and questions whether a specific formula for 3D needs to be memorized.
  • Another participant clarifies that the calculation involves projecting the force vector onto the x-y plane and then determining the x-component using cos(40°), suggesting that it is a matter of applying 2-D trigonometry.
  • A participant seeks clarification on finding Fz, questioning the use of sin(30°) and its relation to the geometry of the problem.
  • Another participant explains the relationship between the sine and cosine functions in the context of right triangles, indicating how they relate to the projections of the force vector.

Areas of Agreement / Disagreement

Participants generally agree on the application of trigonometric principles to resolve the components of the force vector, but there is some uncertainty expressed regarding the understanding of these concepts, particularly in the context of 3D forces.

Contextual Notes

Some participants indicate a need for further clarification on the geometric interpretation of the angles and the projections involved, suggesting that the understanding of the problem may depend on the specific diagram provided.

Who May Find This Useful

Students studying physics or engineering who are working on problems involving forces in three-dimensional space and those seeking to reinforce their understanding of trigonometric applications in vector resolution.

jdawg
Messages
366
Reaction score
2
2.61_Pic.jpg

I'm having trouble number 2.61. I have the answers, but I don't understand why they are doing what they're doing.

They have this for (Fx)1:(Fx)1=(80 lb)*cos(30)*cos(40)=53 lb
I'm familiar with the formula Fx=Fcosθ , but I'm confused about using it in 3D. Is there a formula that I need to memorize specifically for 3D?
 
Physics news on Phys.org
jdawg said:
View attachment 84239
I'm having trouble number 2.61. I have the answers, but I don't understand why they are doing what they're doing.

They have this for (Fx)1:(Fx)1=(80 lb)*cos(30)*cos(40)=53 lb
I'm familiar with the formula Fx=Fcosθ , but I'm confused about using it in 3D. Is there a formula that I need to memorize specifically for 3D?
Not really. You should study carefully the diagram which is included with the problem.

Calculating (80 lb) * cos 30° gives the projection of the force vector in the x-y plane. Multiplying this projection of the force vector in the x-y plane by cos 40° gives the x-component of the force. Similar calculations can give the components along the y and z axes.

It's just a matter of applying 2-D trigonometry and not being distracted because the force vector is 3-D.
 
  • Like
Likes   Reactions: jdawg
Ohh ok, that makes sense! I'm still a little confused about finding Fz. It says Fz=80*sin(30). I kind of have an idea of why, but I'm not super confident about it. Do you use sin(30) in this situation because the the line on the far left of the triangle is parallel to the z axis?
 
This is just basic trigonometry. Look at this right triangle:
Snapshot.jpg

From trigonometry you know that ##sin\alpha =F_z/F## and ##cos\alpha = F_x/F##.
You can rearrange these to get:
$$F_z=F sin\alpha$$
$$F_x=F cos\alpha$$
These have the intuitive meaning of projections: a vector times cosα means a projection of that vector onto the plane from which the angle alpha is measured, and sinα means a projection onto a plane perpendicular to the previous one.
 
  • Like
Likes   Reactions: jdawg
Perfect! Thanks so much, its been a minute since I had trig! :)
 

Similar threads

Finding the direction of the force knowing the mu static
  • · Replies 3 ·
Replies
3
Views
2K
Calculating Forces & Stress of Vertical Cut Line on Beam
  • · Replies 22 ·
Replies
22
Views
3K
Solving for Alpha in Mechanics: Trig Formulas and Force Components
  • · Replies 1 ·
Replies
1
Views
2K
Mastering 3D Statics: How to Solve Moments and Forces for Bearings A and B
  • · Replies 1 ·
Replies
1
Views
3K
Statics, forces in each memeber of a truss
  • · Replies 5 ·
Replies
5
Views
7K
Horizontal Force in Bottom Member of a Truss
  • · Replies 5 ·
Replies
5
Views
3K
Method of Sections: Solving Truss Moment & Force Equations
  • · Replies 1 ·
Replies
1
Views
3K
Solve Statics Problems: Finding Forces in Members AB, BH, OH"
  • · Replies 3 ·
Replies
3
Views
2K
Undergrad [Questions] Modeling a Baseball Pitch Trajectory in 3D Space
  • · Replies 1 ·
Replies
1
Views
2K
Statics and equilibrium - asking for some guidance
  • · Replies 3 ·
Replies
3
Views
2K