Calculating the Mass of a Ball with F = 9.5 N and θ = 28°

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SUMMARY

The discussion focuses on calculating the mass of a ball subjected to a horizontal force of 9.5 N at an angle of 28°. The key equation used is ƩF=ma, which relates the net force to mass and acceleration. The participant correctly identifies the need to resolve the tension into vertical and horizontal components and equate them to the gravitational force (mg) and the applied force (F). The final solution requires drawing a free body diagram (FBD) and applying vector resolution techniques to find the mass of the ball.

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  • Understanding of Newton's second law (ƩF=ma)
  • Knowledge of vector resolution and free body diagrams (FBD)
  • Familiarity with trigonometric functions, specifically tangent
  • Ability to calculate gravitational force (mg)
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  • Study vector resolution techniques in physics
  • Learn how to draw and analyze free body diagrams (FBD)
  • Explore the application of trigonometric functions in physics problems
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Students in physics courses, particularly those studying mechanics, as well as educators looking for practical examples of force analysis and vector resolution in problem-solving.

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Homework Statement


In the diagram below, the horizontal force, F, holds the ball steady. Given F = 9.5 N, and θ = 28°, calculate the mass of the ball. (I think I attached the picture, or well I hope I did)



Homework Equations


ƩF=ma



The Attempt at a Solution


So I know I have to find the angle between the two vectors, which is just 28°+90°=118°. Then I know the force from the tension must be equal to the horizontal force, I just can't seem to figure out the formula. I also think I need to find the hypotenuse, which is : 9.5 *Tan(118°)≈17.867 I think...

Well any help would be awesome, thanks for everything in advanced :)
 

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The resultant of forces in any direction is equal to zero.
Take any reference of frame for easy calculation.
Vectors in opposite or same direction can be added or substracted directly.
A vector can be resolved or replaced with 2 component vectors.

Finally draw a vector or fbd diagram.
 
Resolve the tension T in two vertical and horizontal components. Equate them to mg and F. From that find the required result.
 

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