Varying mass- finding centripetal force

[HexRei]

Homework Statement

I have another problem with a similar thread title but they are not the same, I'd love help with either or both.

Ran trials with varying mass, but radius and centripetal force as constants. Must find experimental radius from the best fit slope. I have already finished the graph and found the slope. I know the slop is T^2/M, but I don't know how to use that.

Radius = .15
calibration weight 0.050
slope = 5.07

Homework Equations

F=4pi^2rM/T^2

The Attempt at a Solution

T^2=(4pi^2rM)/F I've tried rearranging it many ways but I can't figure out how to use this to determine radius from the slope.

4pi^2*.15M=1/F/T^2
5.92M= 1/F/T^2F*T^2=4pi^2rM
(F*T^2)M=4pi^2r
((F*T^2)M)/4pi^2=r
(.490*T^2)M) /39.47=r

Will subbing in mg for F do anything useful?

 

[BvU]

Must find experimental radius from the best fit slope

of which plot ? You vary ##m## and measure ##T## so with the relationship ##T^2 = {4\pi^2mr\over F}## with fixed values for ##r## and ##F## you expect a slope ##T^2\over m## of ##{4\pi^2r\over F}##.

If you know either ##F## or ##r## you can determine the other; you can't determine both from one single slope...

 

[haruspex]

Ran trials

Please describe the experiment.

best fit slope

What did you plot against what? If you plotted y against x, rearrange your equation into the form y=cx. Whatever that gives for c is what the slope represents.

 

[HexRei]

Experiment was centripetal apparatus rotating with calibration weight representing Centripetal force (mg) and known mass M (calibration weight removed after calibration). Plot was T^2 vs mass. In this case we weren't looking for F (we know it from mg), just deriving r experimentally and seeing how it compares to our known measured r.

 

[HexRei]

Taking the equation T^{^2}=4π^{^2}rM/F

Can I just calculate 4π²r/F? When I plug in numbers I get 5.92M/F. Can I divide 5.92 by the known F of 4.90? When I do that I get 12.085 but M is still floating up there and the 12.085 isn't very close to my measured slope of 5.07.

And how do I get from here to F?

Thank you so much for the help!

 

[haruspex]

When I plug in numbers I get 5.92M/F.

Not sure what you mean by M/F there. If you plug in numbers for r and F in 4π²r/F I would expect units s²/kg.