Driving me crazy: Physics problem?

Question

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, 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.

1* First I calculated the radius of the circle: 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!

Answer 1

the acceleration is centripetal acceleration in the horizontal direction not along the line of the string

so Force does not = 32 N



A 540 gram rock is held by two strings of 45 cm with ends 57 cm apart, 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?



On the left side of your paper, draw a 13 cm vertical line to represent the distance between the ends of the string that are 57 cm apart.

Draw a 3.5 cm horizontal line from the center of the vertical line to the right.



Draw 2 lines from the top and bottom of the vertical line to end of the horizontal line.

You should see 2 right triangles that are mirror images.

Each of these 2 lines represents the tension in 1 string.



The rock is whirled in a horizontal circle.

The horizontal line represents the represents the centripetal force needed to hold the rock in its circular path.

Looking only at the top right triangle, label the horizontal line Fc, force centripetal.

Label the hypotenuse T, tension. The hypotenuse is the 45 cm string. The top half of the vertical line is the side opposite the angle made by the hypotenuse and the horizontal line.

Side opposite = 57 ÷ 2 = 28.5 cm



Sin θ = side opposite / hypotenuse = 28.5 / 45

θ = 39.3°



Fc / T = cos 39.3°



Fc = 32 * cos 39.3°



Fc = 24.7 N



Looking at the bottom triangle, label the hypotenuse 45 cm, label the bottom half of the vertical line 28.5 cm.

Fc = (mass * velocity^2) ÷ radius

Mass = 540g = 0.54 kg

Radius = length of side adjacent to 39.3° angle = horizontal line

Radius = (45^2 – 28.5^2)^0.5

Radius = 34.8 cm = 0.348 m





24.7 = (0.54 * v^2) ÷ 0.348

Multiply both sides by 0.348



24.7 * 0.348 = 0.54 * v^2



v^2 = (24.7 * 0.348) ÷ 0.54



v = 4 m/s

Answer 2

it fairly works out to be the correlation of two motions. One is horizontal action, defined by employing x=vt, the different is vertical action, defined by employing y=(gt^2)/2, the place g = 9.8 m/s^2. you're employing the valuables that t is equivalent in the two equations. Use t = x/v, plug into the equation for y, use x = 13.5 m and y = a million.40 m, then sparkling up for v, which could be the speed which you're fixing for.

Answer 3

when you ignore gravity and the fact that the two cables are 45cm length, i would assume that the path would be part of circles of 45 cm radius. the shape would be more like () . the point of intersection would then be the point of maximum force encountered. quite complex i assume.