Basic question about coplanar forces

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SUMMARY

The discussion centers on understanding the decomposition of coplanar forces, specifically the transition from a force magnitude of 15.0N to its x-component of 7.5N when analyzed at an angle of 60 degrees. The user is working through Schaum's Outline of College Physics and seeks clarification on how to calculate the x-component using trigonometric functions. The x-component is derived using the cosine function, where 7.5N equals (15.0N) cos 60 degrees, illustrating the fundamental principles of vector resolution in physics.

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  • Basic understanding of trigonometric functions (sine and cosine)
  • Familiarity with vector resolution in physics
  • Knowledge of force components in two-dimensional space
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This discussion is beneficial for beginners in physics, hobbyists exploring basic mechanics, and students seeking to understand the principles of force decomposition and vector analysis.

Elevenses
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Summary:: Adult brand new to maths and physics and starting from the bottom, just for a hobby. I'm working my way through Schaum's Outline of College Physics and cannot understand why the N unit in the below table goes from 15.0N to 7.5N. Total beginner here, and help appreciated :)

I have written this out rather than copy-and-pasted from the textbook in case of copyright reasons. The question is to find the resultant of these five coplanar forces. I have just given the first two forces here because I cannot understand where the 7.50N is coming from although this issue is repeated for the following forces.

Force - - - - x-Component - - - - - - - - - - - - - - - - - - - y-Component

19.0N - - - - 19.0N - - - - - - - - - - - - - - - - - - - - - - - - - 0N
15.0N - - - - (15.0N) cos 60.0 degrees = 7.50N - - - - (15.0N) sin 60.0 degrees = 13.0N

I start off from origin and go along x-axis with the first force, 19.0N. So far so good. Then I move around 60.0 degrees and draw in the second force, 15.0N, only then this becomes 7.50N. Not getting that when Rx = ΣFx, the 15.0N is 7.50N? Thanks!
 
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Elevenses said:
the second force, 15.0N, only then this becomes 7.50N.
15N is the magnitude, 7.5N is the x-component
 
A.T. said:
15N is the magnitude, 7.5N is the x-component

Thanks for this. Like with so many things, the second it's pointed out it seems so obvious. Now it makes sense why the first Force and x-Component were both 19.0N. 👍:smile:
 

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