Trig problems (relating to FBD)

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SUMMARY

The discussion focuses on resolving a trigonometric misunderstanding related to a free body diagram (FBD) of a car being towed up a 20-degree incline. The participant struggles with the relationship between the weight vector and its components, specifically why the y-component of weight is expressed as -w * cos(theta). The correct interpretation involves recognizing that the weight vector acts vertically downward, making the angle with the negative y-axis equal to the incline angle. This leads to the conclusion that the adjacent side of the triangle formed is the weight vector, and the hypotenuse is the vertical component of the weight.

PREREQUISITES
  • Understanding of basic trigonometry, including sine and cosine functions.
  • Familiarity with free body diagrams (FBD) and their components.
  • Knowledge of vector decomposition in physics.
  • Basic principles of forces acting on inclined planes.
NEXT STEPS
  • Review vector decomposition techniques in physics.
  • Study the relationship between angles and sides in right triangles using trigonometric identities.
  • Practice drawing and analyzing free body diagrams for various inclined plane scenarios.
  • Learn about the effects of friction on inclined planes and how it alters force calculations.
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Students studying physics, particularly those focusing on mechanics and inclined planes, as well as anyone needing to strengthen their understanding of trigonometric applications in real-world scenarios.

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Homework Statement



Car being towed up incline. It makes 20deg angle to the horizontal. Goes at constant velocity. No friction. Tow rope rated at 6000N max..
will it break?

Homework Equations



I don't need help in whole question, its just the trig which i keep getting wrong. (i have taken trig).
The answer is actually worked out in book but i don't understand why the trig is as it is.



The Attempt at a Solution


So in my FBD i orientate axis so that normal force points along pos y-axis, tension points along pos x-axis.
I know that if incline angle is 20deg, then the angle weight makes with neg y-axis will also be 20deg

The book says that wsuby = -w cos theta.
This is messing me up on a lot of problems so here's what I understand, in very basic trig terms:

The weight vector, neg y-axis and horizontal make up a triangle.
Theta is the angle (20deg) between the neg y-axis and the weight.

Therefore weight is the adgacent side
Neg y-axis is the Hyp side
the horizontal is the opposite side (to the angle).

So, ,based on the triangle i have chosen, the y-component of the weight = the hyp side of the triangle and the adjacent side is the weight vector.

To sum up, I have the adjacent, and the angle, and I want the hyp.
So, according to trig, because cos theta = adj / hyp,
then hyp = adj / cos theta.

So why does the book say that the y component of the weight is -w * cos theta?
Thanks for any help.
 
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Why do you say that the weight is the adjacent side? And that the y-axis is the hypotenuse? Draw your diagram again.
 
Along an inclined plane, the incline is the x-axis and the y-axis is perpendicular to it.
 

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