How Do Trig Ratios Solve Equilibrium Problems in Physics?

[planauts]

Homework Statement

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

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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,

 

[SammyS]

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?

 

[planauts]

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;

 

[Fewmet]

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.

 

[SammyS]

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.