I'm doing a prac at school at the moment and it involved creating circular motion using string with a weight on the bottom and a rubber stopper being spun around. I know that T^2 should be directly proportional to r but from my results, T is directly proportional to r. ITS A STRAIGHT LINE! i know that its wrong but i dont know what i did wrong in the experiment. PLEASE HELP!
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centripetal acceleration: a = v^2 / r
distance = rate * time
2 pi r = v * T :: the circumference is traversed in one period
T = 2 pi r / v
if mg = m a = m v^2 / r, then v^2 = r g
v = sqrt(r g)
T = 2 pi r / sqrt(r g)
T = 2 pi sqrt(r/g) :: T^2 should be proportional to r and independent of mass.
Given your theoretical assertion seems reasonable, then perhaps your parameter space is too small.
Guessing that you measured T and r to throw them up on a graph.
2 pi is about 6, 1/g is about 1/10, so T^2 ~ 360 r. or T ~ 6 sqrt(10) sqrt(r) ~ 18 sqrt(r)
you'd have to use a pretty wide range of r to see any significant curvature in a T v r curve. near the origin (r=0), it is not unreasonable to approximate the graph with a straight line (linear approximation to the curve.)
A better bet would be to plot T^2 v r, do a least squares fit to the data, get the R value, then see how well the slope of that best fit line matches the theoretical slope. That's a better measure than trying to use the data to infer a quadratic/sqrt relationship if your range of r is not large. [range of r will be limited to lab space available -- suspect your biggest r may be about 3 feet (1 meter). otherwise, the experiment becomes dangerous. With r limited to less than 3 feet (1 meter), you may be in the limit where a linear approximation to the curve provides a good fit -- so your result would not be entirely unexpected.)
distance = rate * time
2 pi r = v * T :: the circumference is traversed in one period
T = 2 pi r / v
if mg = m a = m v^2 / r, then v^2 = r g
v = sqrt(r g)
T = 2 pi r / sqrt(r g)
T = 2 pi sqrt(r/g) :: T^2 should be proportional to r and independent of mass.
Given your theoretical assertion seems reasonable, then perhaps your parameter space is too small.
Guessing that you measured T and r to throw them up on a graph.
2 pi is about 6, 1/g is about 1/10, so T^2 ~ 360 r. or T ~ 6 sqrt(10) sqrt(r) ~ 18 sqrt(r)
you'd have to use a pretty wide range of r to see any significant curvature in a T v r curve. near the origin (r=0), it is not unreasonable to approximate the graph with a straight line (linear approximation to the curve.)
A better bet would be to plot T^2 v r, do a least squares fit to the data, get the R value, then see how well the slope of that best fit line matches the theoretical slope. That's a better measure than trying to use the data to infer a quadratic/sqrt relationship if your range of r is not large. [range of r will be limited to lab space available -- suspect your biggest r may be about 3 feet (1 meter). otherwise, the experiment becomes dangerous. With r limited to less than 3 feet (1 meter), you may be in the limit where a linear approximation to the curve provides a good fit -- so your result would not be entirely unexpected.)