Calculate Static Equilibrium: SOH/CAH/TOA?

In summary, when calculating static equilibrium, it is important to consider the angle given in relation to the x or y axis when determining which trigonometric function to use for the x and y components. If the angle is given with respect to the x-axis, cosine would be used for the x-component, and if the angle is given with respect to the y-axis, sine would be used for the y-component. However, if the angle is given in relation to neither axis, a different approach would be needed.
  • #1
Mason98
27
1
Homework Statement
Sin for Y axis and Cos for X axis?
Relevant Equations
Sin = opp/hyp Cos = Adj / hyp
When calculating static equilibrium, i know that you have to split for example, F1 into F1x and F1y. when using soh/cah/toa is it always SIN for the Y axis and always Cos for the X axis? I've been following this method and getting it wrong some times it's really stressing me out, Thanks for any help in advance.
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  • #2
Mason98 said:
when using soh/cah/toa is it always SIN for the Y axis and always Cos for the X axis?
No. It all depends on what angle you are using. If the angle is with respect to the x-axis, then fine: The x-component would use cosine, etc. But if the given angle is with respect to the y-axis, things are reversed.

Remember that sinθ = cos (90° - θ).
 
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  • #3
so that is how in the picture Fax is sin because the angle given is in respect to the y-axis which would mean to use sin?
 
  • #4
Mason98 said:
so that is how in the picture Fax is sin because the angle given is in respect to the y-axis which would mean to use sin?
Exactly!
 
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  • #5
Doc Al said:
Exactly!
Thank you very much! I appreciate your help :)
 
  • #6
But if you adopt this as a new rule-of-thumb, you'll still be in a pickle when the problem gives you an angle which is relative to neither the x nor y axis.
 

1. What is static equilibrium?

Static equilibrium refers to a state in which all forces acting on an object are balanced, resulting in no net acceleration or movement of the object.

2. What is the significance of SOH/CAH/TOA in calculating static equilibrium?

SOH/CAH/TOA are trigonometric ratios that are commonly used in calculating forces and angles in static equilibrium problems. They provide a way to relate the forces and angles in a right triangle, making it easier to solve for unknown values.

3. How do you use SOH/CAH/TOA to calculate static equilibrium?

First, identify the forces acting on the object and draw a free body diagram. Then, use the appropriate trigonometric ratio (SOH/CAH/TOA) to solve for the unknown force or angle. Repeat this process for each unknown value until all forces and angles are known and the object is in a state of static equilibrium.

4. What are some common mistakes when using SOH/CAH/TOA to calculate static equilibrium?

One common mistake is using the wrong trigonometric ratio for the given problem. It is important to carefully identify the sides and angles in the right triangle and use the corresponding ratio. Another mistake is not properly considering the direction of the forces, which can result in incorrect calculations.

5. Can SOH/CAH/TOA be used to calculate static equilibrium in non-right triangles?

No, SOH/CAH/TOA are only applicable to right triangles. In non-right triangles, other trigonometric functions such as sine, cosine, and tangent must be used to calculate forces and angles in static equilibrium.

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