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Math Help - Physics experiment results

  1. #1
    Senior Member Paze's Avatar
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    Physics experiment results

    Hi MHF.

    I swung a bucket filled with water in circles and calculated the minimum centripetal force that the bucket had to have in order for the water not to spill.

    I found out that I had to swing the bucket with a maximum of 1.8 seconds but the water started spilling when I was swinging at 1.4 seconds per loop. These calculations are derived from putting a stopwatch on a camera recording.

    My calculations are correct but now I ask...What could be causing this difference? I'm thinking gravitational constant is different in Iceland than simply 9,8 but what other factors could be contributing to the problem other than a difference in swing speed (human error)?
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  2. #2
    Forum Admin topsquark's Avatar
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    Re: Physics experiment results

    Quote Originally Posted by Paze View Post
    Hi MHF.

    I swung a bucket filled with water in circles and calculated the minimum centripetal force that the bucket had to have in order for the water not to spill.

    I found out that I had to swing the bucket with a maximum of 1.8 seconds but the water started spilling when I was swinging at 1.4 seconds per loop. These calculations are derived from putting a stopwatch on a camera recording.

    My calculations are correct but now I ask...What could be causing this difference? I'm thinking gravitational constant is different in Iceland than simply 9,8 but what other factors could be contributing to the problem other than a difference in swing speed (human error)?
    Are you sure that you have a maximum of 1.8 s? The water should stay in the bucket if you move it faster than some minimum. I would say that the minimum period would be 1.8 s and your water spilled at 1.4 s because it wasn't going fast enough.

    -Dan
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  3. #3
    MHF Contributor ebaines's Avatar
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    Re: Physics experiment results

    topsquark - the period of rotation is inversely proportional to rotational velocity. Swinging the bucket with a period of 1.4 seconds creates more centripedal acceleration than swinging it with a period of 1.8s.

    Paze: maybe you're being sarcastic, but the gravitational constant is not different in Iceland - the value of 9.8 m/s^2 is close enough for any location on Earth. Perhaps the speed of rotation isn't constant throughout the entire arc. Or maybe the radius of rotation is less than you think it is - how did you measure it?
    Last edited by ebaines; June 24th 2013 at 09:03 AM.
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  4. #4
    Forum Admin topsquark's Avatar
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    Re: Physics experiment results

    Quote Originally Posted by ebaines View Post
    topsquark - the period of rotation is inversely proportional to rotational velocity. Swinging the bucket with a period of 1.4 seconds creates more centripedal acceleration than swinging it with a period of 1.8s.
    I'm having a moment over here. Thanks for the catch.

    -Dan
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  5. #5
    Senior Member Paze's Avatar
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    Re: Physics experiment results

    Quote Originally Posted by ebaines View Post
    topsquark - the period of rotation is inversely proportional to rotational velocity. Swinging the bucket with a period of 1.4 seconds creates more centripedal acceleration than swinging it with a period of 1.8s.

    Paze: maybe you're being sarcastic, but the gravitational constant is not different in Iceland - the value of 9.8 m/s^2 is close enough for any location on Earth. Perhaps the speed of rotation isn't constant throughout the entire arc. Or maybe the radius of rotation is less than you think it is - how did you measure it?
    I wasn't being sarcastic. You should notice that this is really basic physics and as so I'm not very keen on how much of a difference the gravitational constant has on my calculations.

    My main concern is that the speed of rotation wasn't constant throughout the arc.

    I measured from the bottom of the bucket to the start of my shoulder.
    The bucket had a move-able hinge(?) so that may have affected the experiment as well.
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  6. #6
    MHF Contributor ebaines's Avatar
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    Re: Physics experiment results

    You should measure from the shoulder to the top of the water surface in the bucket, not the bottom of the bucket.

    The constant 'g' does indeed vary depending on your location and altitude. Factors influencing it are:

    1. Centripedal acceleration due to the Earth's rotation - has the effect of decreasing 'g' near the equator by about 0.03% compared to the poles.
    2. Non-spherical shape of the earth (equitorial bulge) - has the effect of also decreasing g near the equator.

    These two factors together make the value for 'g' vary from 9.780 m/s^2 at the equator to 9.832 m/s^2 at the poles. If the results you got were due to 'g' being non-standard, it would only be if 'g' was larger than the 9.8 m/s^2 value you used. So your answer would be off by sqrt(9.832/9.2), or 0.16% if you were at the north pole. This is less than the margin of error in your measurements.

    There may also be local gravitational anomolies caused by geology in your area. Variations may be around 1.15 mm/s^2 depending on the local geology. This is less then 1/10 of 1% of the 9.8 m/s^2 value you used, so again it's inconsequential to your calculations.

    Finally your altitude above sea level has an effect, but it's to lower the value of 'g' by a very small amount, not increase it. So the conclusion is that variations in 'g' don't explain your results. I really think it's the "jerkiness" in motion as you swing the bucket - it's very hard to avoid decelerating on the upswing or accelerating on the down swing. This unevenspeed of rotation not only causes reduced centripedal acceleration at the top of the arc but would also cause sloshing of the water with the result that some could splash out of the bucket.
    Last edited by ebaines; June 24th 2013 at 11:21 AM.
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  7. #7
    Senior Member Paze's Avatar
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    Re: Physics experiment results

    Quote Originally Posted by ebaines View Post
    You should measure from the shoulder to the top of the water surface in the bucket, not the bottom of the bucket.

    The constant 'g' does indeed vary depending on your location and altitude. Factors influencing it are:

    1. Centripedal acceleration due to the Earth's rotation - has the effect of decreasing 'g' near the equator by about 0.03% compared to the poles.
    2. Non-spherical shape of the earth (equitorial bulge) - has the effect of also decreasing g near the equator.

    These two factors together make the value for 'g' vary from 9.780 m/s^2 at the equator to 9.832 m/s^2 at the poles. If the results you got were due to 'g' being non-standard, it would only be if 'g' was larger than the 9.8 m/s^2 value you used. So your answer would be off by sqrt(9.832/9.2), or 0.16% if you were at the north pole. This is less than the margin of error in your measurements.

    There may also be local gravitational anomolies caused by geology in your area. Variations may be around 1.15 mm/s^2 depending on the local geology. This is less then 1/10 of 1% of the 9.8 m/s^2 value you used, so again it's inconsequential to your calculations.

    Finally your altitude above sea level has an effect, but it's to lower the value of 'g' by a very small amount, not increase it. So the conclusion is that variations in 'g' don't explain your results. I really think it's the "jerkiness" in motion as you swing the bucket - it's very hard to avoid decelerating on the upswing or accelerating on the down swing. This unevenspeed of rotation not only causes reduced centripedal acceleration at the top of the arc but would also cause sloshing of the water with the result that some could splash out of the bucket.
    I think this sums it up pretty much. Thank you very much.
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