- #1
Why Can't I Use Standard Cosine Calculations for Non-Orthogonal Axes Forces?
In summary, it is not possible to find Fu and Fv such that they sum to 600 N without the use of the law of sines.
- #2
SteamKing
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Well, for one thing, it appears that Fu and Fv are not the sides of a right triangle. It's hard to tell from the attached image.goldfish9776 said:
For solving oblique triangles, the law of sines or the law of cosines must be used. For more information, see the article below:
https://en.wikipedia.org/wiki/Solution_of_triangles
- #3
goldfish9776
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SteamKing said:
- #4
goldfish9776
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Why can't I do in this way??SteamKing said:
- #5
SteamKing
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As has already been explained, the forces Fu and Fv are not the sides of a right triangle.goldfish9776 said:
The triangle which contains Fu and Fv has angles of 120°, 30°, and 30°. Do you see any right angles there?
Haven't you learned the difference yet between an oblique triangle and a right triangle?
The solution in your text clearly shows the use of the Law of Sines.
Please study the material I linked to previously. If you have any questions about that, I will be happy to answer them.
- #6
gneill
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As was mentioned already, The u and v axes are not orthogonal (do not meet at a right angle). So you can't treat them as if they do.goldfish9776 said:
If the using the laws of sines or cosines is throwing you off, you could approach the problem as two equations in two unknowns.
Suppose that Fu and Fv are two vectors with the given directions and you need to find Fu and Fv such that they sum to a 600 N horizontal resultant. Impose axes x-y on the image such that the x-axis coincides with the horizontal 600 N force. Then write equations summing the x and y components of Fu and Fv accordingly.
FAQ: Why Can't I Use Standard Cosine Calculations for Non-Orthogonal Axes Forces?
1. What is force along u and v axes?
Force along u and v axes refers to the component of force that acts in the direction of the u and v axes, which are typically used in Cartesian coordinate systems. This means that the force can be broken down into two separate components, one acting along the u axis and one along the v axis.
2. How is force along u and v axes calculated?
Force along u and v axes can be calculated using trigonometric functions in relation to the angle between the force vector and the u and v axes. The magnitude of the force can also be found using the Pythagorean theorem.
3. What is the significance of force along u and v axes in physics?
Force along u and v axes is important in physics because it allows for the analysis and calculation of forces in two-dimensional systems. It also helps to understand the direction and magnitude of forces acting on an object.
4. How does force along u and v axes affect an object's motion?
The force acting along the u and v axes can affect an object's motion by changing its velocity and direction. This is because forces cause acceleration, and the direction of the acceleration is dependent on the direction of the force.
5. Can force along u and v axes be negative?
Yes, force along u and v axes can be negative. This means that the force is acting in the opposite direction of the positive direction of the u and v axes. Negative forces can also be thought of as pulling or pushing in the opposite direction of the positive force.