How Do I Split This Vector into Components?

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SUMMARY

The discussion focuses on the process of splitting a force vector into its x and y components in the context of inclined planes and centripetal acceleration. The user struggles with understanding how to apply the 60-degree angle to determine these components. It is established that the force vector makes a 90-degree angle with the slope, and through vector addition, the blue angle is identified as 30 degrees. This geometric relationship is crucial for solving the problem effectively.

PREREQUISITES
  • Understanding of vector addition
  • Knowledge of trigonometric functions (sine, cosine)
  • Familiarity with inclined planes in physics
  • Basic geometry concepts, including angles
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  • Study vector decomposition techniques in physics
  • Learn how to apply trigonometric functions to resolve forces
  • Explore inclined plane problems in classical mechanics
  • Review the concept of centripetal acceleration and its applications
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Students studying physics, particularly those focusing on mechanics and vector analysis, as well as educators looking for teaching strategies related to force components.

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Homework Statement


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The Attempt at a Solution



I'm doing a question on inclined planes and centripetal acceleration. I understand the question and what it's asking for, I'm just having trouble splitting F into it's x and y components and how 60 degrees related to it. Any help would be appreciated.
I've drawn multiple diagrams I just can't figure out how to use the 60 degrees to find the x and y components, which would help me finished this question.
Thanks.
 
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The force makes 90 degree angle with the slope. F is the sum of a horizontal and vertical component, drawn according to vector addition. The purple angle is 60° (why?) So what is the blue angle?

splitforce.JPG
 
ehild said:
The force makes 90 degree angle with the slope. F is the sum of a horizontal and vertical component, drawn according to vector addition. The purple angle is 60° (why?) So what is the blue angle?

View attachment 75290
Ohh the Z pattern.
Blue would be 30.

OMG thank you. Not very good at geometry. :P
 

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