Varying mass- finding centripetal force

If you then multiply by M I would expect units of s2.In summary, the conversation involves a student seeking help with a physics problem involving centripetal force and experimental radius. The student has completed a graph and found the slope, but is unsure how to use it to determine the radius. The expert suggests rearranging the equation and plotting T^2 against mass to find the slope. The experiment involves a centripetal apparatus rotating with a calibration weight representing centripetal force and a known mass M. The student is unsure how to calculate 4π2r/F and how to get from there to F.
  • #1
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?
 
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  • #2
HexRei said:
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...
 
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  • #3
HexRei said:
Ran trials
Please describe the experiment.
HexRei said:
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.
 
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  • #4
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.
 
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  • #5
Taking the equation T^2=4π^2rM/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!
 
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  • #6
HexRei said:
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.
 

Related to Varying mass- finding centripetal force

1. What is centripetal force?

Centripetal force is the force that acts towards the center of a circular motion. It is responsible for keeping an object moving in a circular path.

2. How does mass affect centripetal force?

The centripetal force is directly proportional to the mass of the object. This means that as the mass of an object increases, the centripetal force required to keep it in circular motion also increases.

3. What is the formula for calculating centripetal force?

The formula for calculating centripetal force is Fc = mv^2/r, where Fc is the centripetal force, m is the mass of the object, v is its velocity, and r is the radius of the circular path.

4. How does changing the mass affect the centripetal force in an object?

As the mass of an object increases, the centripetal force required to keep it in a circular path also increases. This is because a larger mass requires a greater force to maintain the same velocity and radius of the circular motion.

5. Can centripetal force be measured?

Yes, centripetal force can be measured using a force sensor or a spring scale. The force sensor measures the force required to keep the object in circular motion, while the spring scale measures the tension in the string or rope that is providing the centripetal force.

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