(adsbygoogle = window.adsbygoogle || []).push({}); Physics 101 (forces), Rock on Strings: driving me crazy!

okay, this problem is DRIVING ME CRAZY!! please help me out here, it's a TYCHO homework:

1. The problem statement, all variables and given/known data

A 540 gram rock is held by two strings of 45 cm with ends 57 cm apart (distance d in the picture), any string will break under a tension of 32 N. The rock is whirled in a circle between them. Neglecting gravity: what is the maximum speed the rock can have before one of the string breaks?

the value I got is V = 5.164 m/s but it's WRONG and I cannot find any mistake.

the picture of this problem would be the following one (picture d):

[PLAIN]https://wug-s.physics.uiuc.edu/cgi/courses/shell/common/showme.pl?cc/DuPage/phys2111/summer/homework/Ch-06-Forces/rock_on_strings/13.gif [Broken]

3. The attempt at a solution

1* First I calculated the radius of the circle (R in the picture): r = 0.3482 m

2* Then I found the angle between the radius and one of the strings: angle = 39.30 degrees.

3* I calculated what the max. value of the acceleration in the opposite direction of the tension would be using the formula F = m x a, this is:

32N = 0.54kg x Ay

32N / 0.54kg = Ay

59.26m/s^2 = Ay

(Ay would be acceleration in the Y direction, the direction of the tension)

4* since I got the Y component of the acceleration, I used angle in point 2* to calculate the value of the total acceleration:

cos(39.30) = Ay / A

A = Ay / cos(39.30)

A = 59.26 / cos(39.30)

A = 76.58m/s^2

5* Okay so now I have the maximum acceleration that one string could handle. To calculate the velocity I simply use the formula A = V^2 / r:

V = sqr(A x r)

V = sqr(76.58 x 0.3482)

V = 5.164 m/s

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please let me know if you see any mistake in my calculations or if I didnt set the problem out properly!!

many thanks in advance!

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# Homework Help: Rock on Strings driving me crazy!

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