DeviledEgg24
- 1
- 0
I'm having trouble solving the following problem:
An 80cm string with a mass attached to the end is rotated at a rate of one revolution per second. Assuming the force of gravity is 9.8 m/s^2, what is the angle made with the vertical by the string? [My words, but these were all the variables given].
As for my attempt to solve it: The rotating string will obviously make a cone, with the downward force of gravity at 9.8 m/s2 pulling down and the inward force of centripetal acceleration pulling 'out'. Since the period is one, the centripetal acceleration can be defined as 4 * pi^2 * R, where R is the radius of the circle in meters. Unfortunately, I'm having a hard time figuring out what the radius of the bottom of the cone is when the slant height is .8m. The problem is easy to solve if I just cheat and use .8m for the radius, but that would leave the length of the string (the slant height of the cone) greater then .8m.
I went through a long series of geometric calculations to try and get an equation to relate radius, slant height, and gravity, and I ended up getting a radius of .7605m, which may or may not be correct. That radius gave me an angle of 71.92 degrees with the vertical, but the process I went through to get it was so convoluted I can barely follow it, and I can't even begin to type it out.
Is there a simple way to solve this problem that I'm missing? I'm bad at typing out math problems, so I scanned in this diagram of how I set up the problem to hopefully make it more obvious:
http://i.imgur.com/Lob0B.png
To solve for theta with a radius of .8, I simply plugged it into the formula: tan^-1((4 * pi^2 * .8)/9.8) = 72.76 degrees. But again, the length of the rope would be something greater then .8m, and I'm not sure how to solve it using the length of the rope (hypotenuse of my triangle) instead of the radius.
Thanks for the help.
An 80cm string with a mass attached to the end is rotated at a rate of one revolution per second. Assuming the force of gravity is 9.8 m/s^2, what is the angle made with the vertical by the string? [My words, but these were all the variables given].
As for my attempt to solve it: The rotating string will obviously make a cone, with the downward force of gravity at 9.8 m/s2 pulling down and the inward force of centripetal acceleration pulling 'out'. Since the period is one, the centripetal acceleration can be defined as 4 * pi^2 * R, where R is the radius of the circle in meters. Unfortunately, I'm having a hard time figuring out what the radius of the bottom of the cone is when the slant height is .8m. The problem is easy to solve if I just cheat and use .8m for the radius, but that would leave the length of the string (the slant height of the cone) greater then .8m.
I went through a long series of geometric calculations to try and get an equation to relate radius, slant height, and gravity, and I ended up getting a radius of .7605m, which may or may not be correct. That radius gave me an angle of 71.92 degrees with the vertical, but the process I went through to get it was so convoluted I can barely follow it, and I can't even begin to type it out.
Is there a simple way to solve this problem that I'm missing? I'm bad at typing out math problems, so I scanned in this diagram of how I set up the problem to hopefully make it more obvious:
http://i.imgur.com/Lob0B.png
To solve for theta with a radius of .8, I simply plugged it into the formula: tan^-1((4 * pi^2 * .8)/9.8) = 72.76 degrees. But again, the length of the rope would be something greater then .8m, and I'm not sure how to solve it using the length of the rope (hypotenuse of my triangle) instead of the radius.
Thanks for the help.
Last edited: