Solving Force Problems: Finding F with Trig and Components

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SUMMARY

This discussion focuses on solving force problems using trigonometry and component analysis. The specific scenario involves a sphere with a mass of 3.0 x E-4 kg suspended by a cord at a 34-degree angle due to a horizontal breeze. Participants emphasize the use of the equation F=ma and the necessity of breaking down the tension in the cord into horizontal and vertical components to find the magnitude of the push and the tension itself. Key insights include the importance of analyzing net forces in both the x and y directions to achieve a solution.

PREREQUISITES
  • Understanding of Newton's Second Law (F=ma)
  • Basic knowledge of trigonometric functions
  • Ability to resolve forces into components
  • Familiarity with equilibrium conditions in physics
NEXT STEPS
  • Study how to resolve forces into horizontal and vertical components
  • Learn about equilibrium conditions in physics
  • Practice problems involving tension in strings and cords
  • Explore the application of trigonometric functions in force analysis
USEFUL FOR

This discussion is beneficial for physics students, educators, and anyone seeking to enhance their problem-solving skills in mechanics, particularly in analyzing forces and tension in static systems.

rt525600
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I'm having a lot of trouble solving force problems even though I understand the concepts (or, at least I think I do). This is a specific example:

A sphere of mass 3.0 x E-4 kg is suspended from a cord. A steady horizontal breeze pushes the sphere so that the cord makes an angle of 34 degrees with the vertical when at rest.

Find the a) magnitude of that push and b) the tension in the cord.


The only equation that I know of to solve force problems is F=ma. We have m.


I think that I can use trig to find F, but I can't figure out how.
I tried to solve for F by using components: I found the downward force by finding mg (= -2.94 E-3). I'm kind of stuck now. Any suggestions?
 
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Divide the tension in the cord into 2 compoennts... horizontal and vertical. If T is the tension, what is the horizontal component of tension? what is the vertical component of tension?

net force in x direction = max... however ax = 0

net force in the x direction = 0

same way

net force in the y direction = 0

What are the forces acting vertically... what are the forces acting horizontally?
 

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