How Do You Calculate Tension and Speed in Rotating Bead Physics Problems?

AI Thread Summary
To calculate the tension and speed in the rotating bead physics problem, a free body diagram is essential, revealing a right triangle formed by the string and the vertical pole. The vertical side measures 40 cm, while the total length of the string is 80 cm, leading to the equation X^2 + (40)^2 = (80 - x)^2 to find the horizontal side. Once the horizontal length is determined, the tension in the string can be calculated as the force in the horizontal direction. The speed of the bead at point B can then be derived using the formula a = v^2/r. Understanding these relationships is crucial for solving the problem effectively.
Joelseph
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Homework Statement


A 100 g bead is free to slide along an 80 cm long piece of string ABC. The
ends of the string are attached to a vertical pole at A and C, which are 40
cm apart. When the pole is rotated about its axis, AB becomes horizontal.
(a) Find the tension in the string. (b) Find the speed of the bead at B.


Homework Equations


F=ma
a=v^2/r



The Attempt at a Solution


I have drawn a free body diagram, and it is a right angle triangle with the vertical side being 40cm, and the other 2 sides being 80 in TOTAL but I'm not sure how to figure out the angles or sides with that little information.

Please assist. Once I have that information, the tension of the string is the force in the horizontal direction, and the speed will be easy enough to find as well.

Thanks
 
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If x is the length of the horizontal side then X^2 + (40)^2 = (80 - x )^2
Solve for x.
 
Gotcha, thanks for the help that was perfect.
The classic 3-4-5 triangle!
 
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