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santi_h87
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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:
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
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
--------------------------------------------------------------
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!
okay, this problem is DRIVING ME CRAZY! please help me out here, it's a TYCHO homework:
Homework Statement
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
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
--------------------------------------------------------------
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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