How Do Trig Ratios Solve Equilibrium Problems in Physics?

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Homework Help Overview

The discussion revolves around using trigonometric ratios to analyze equilibrium problems in physics, specifically involving forces exerted by springs and weights. Participants are exploring how to represent these forces graphically and mathematically.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the use of scale diagrams to visualize forces and their relationships. Questions are raised about the forces exerted by the springs and how to determine their components. There is an attempt to calculate angles and components using trigonometric ratios.

Discussion Status

Some participants have provided insights into constructing scale diagrams and interpreting vector components. There is a recognition of the equilibrium conditions of the forces involved, but no consensus has been reached on the complete solution or approach.

Contextual Notes

Participants are working with a specific setup involving springs and a weight, and there are references to an answer key that may influence their reasoning. The original poster expresses confusion about the problem setup and the use of diagrams.

planauts
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Homework Statement



[EDIT]
Spring A got cut off, it is supposed to be on the Right hand side.
http://bit.ly/mkjurm"
http://bit.ly/mkjurm

[URL]http://ploader.net/files/46286976424f22ace6412a9256aee50e.jpg[/URL]

Homework Equations



The Attempt at a Solution


I am not exactly sure how to go about solving this. The answer key says to use a scale diagram but I am still a bit confused.

Thanks,
 
Last edited by a moderator:
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What have you tried?

Where are you stuck?

What can you say about the force exerted by the 10 N weight?

What can you say about the force exerted by Spring A?
 
I got the angle as 53.1 using Trig Ratios for a right angle triangle. The three vectors are in equilibrium. The X-component of Spring B must be equal to the X-component of Spring A (but in opposite direction). Spring A has no vertical component, therefore all of the weight must be supported by Spring B.

The answer key says:
(a)
correct construction of triangle / parallelogram;
reading on spring balance A: 16.0 (+/- 0.5) N;
reading on spring balance B: 12.5 (+/- 0.5) N;
 
A scale diagram is just a drawing of the forces (i.e., showing them as arrows) where the length is proportional to the size of the vector. Star by picking a scale (something like one small box is 0.5 N) and draw the three force vectors parallel to the strings.

Do you know how to arrange the vectors to find the sum? You will find the length of the sum by measuring it directly and converting to Newtons with your scale.
 
planauts said:
I got the angle as 53.1 using Trig Ratios for a right angle triangle. The three vectors are in equilibrium. The X-component of Spring B must be equal to the X-component of Spring A (but in opposite direction). Spring A has no vertical component, therefore all of the weight must be supported by Spring B.

...
Correct.

So the vertical component of the force produced by spring B must be 10 N.

The slope of the string attached to spring B appears to be -4/5, so the horizontal component of the force produced by spring B must be -5/4 times 10 N.
 

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