Particle statistics- Three forces on force table

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Homework Help Overview

The discussion revolves around a problem in particle statics involving three forces in equilibrium on a force table. The forces have magnitudes of 10, 25, and 30 dynes, and the original poster seeks to find the angles between these forces both algebraically and graphically.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • The original poster attempts to establish a reference force along the x-axis and set up equations for the x and y components of the forces to find the angles. They express confusion over the resulting equations involving sine and cosine functions.
  • Some participants note that the resultant of the forces must equal zero, suggesting a geometric interpretation where the forces form a triangle.
  • Others suggest using the Law of Cosines in the context of a triangle formed by the forces.

Discussion Status

The discussion is active, with participants exploring different interpretations of the problem. There is an acknowledgment of the need to solve the problem both algebraically and graphically, and some guidance has been offered regarding the use of trigonometric principles.

Contextual Notes

The original poster mentions a challenge in their approach due to the equations involving multiple unknowns, which raises questions about the assumptions made in setting up the problem.

shogunultra
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Particle statics- Three forces on force table

I have the following problem:

Three forces of magnitude 10, 25, 30 dynes are in equilibrium on a force table.

a) find the angles between the forces algebraicly.

b) find the angles graphically

Here is how I attempted to solve a):

I considered one force to be my "force of reference", making it parallel to the x-axis and its vector pointing towards positive x.

Then I tried to find the angles that the other forces make with the x-axis by means of a two equation system, one for the X and one for the Y components of the forces, from which I know that their sum must equate 0.

Im stumped here, equation contains the angles in their sin form and the other contains them as cos, so not knowing any angle doesn't really give me two unknowns, but four.

Thankyou.
 
Last edited:
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The resultant of the three forces need to be zero. Which means that the three vectors will form the sides of a triangle.
 
That would be the graphic way, but a) requests you to solve it algebraeicly.
 
I would think carefully about what andrevdh said, and dust off the old trig. textbook.
Think of the problem as a SSS triangle, and then think Law of Cosines.
Good Luck!
 

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