# How to graph Fc=mv^2/r so that the gradient = velocity

## Homework Statement

Fc = mv^2/r represents the motion of a simple pendulum. Describe how this data could be graphed so that the gradient of a straight line could be used to determine the velocity of the object.

Fc = mv^2/r

## The Attempt at a Solution

I'm kinda stumped. I tried graphing Fc vs r and got nowhere. Kinda attempted @ m =0.5, r =1, Fc = v^2/2 and thus when you derive Fc with respect to v, the gradient function = v, and thus the gradient of any tangent through the curve would give the value of the velocity at that point. Didn't really make sense to me
UPDATE: tried graphing Fc vs v^2 and got a straight line. realised the slope gives m/r. not sure if this is any helpful info but pls need help on the ASAP :) thankssss

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BvU
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Hi Lachtal, Unclear to me what you measured. If you can graph Fc vs v2 it seems to me that you already have the velocity of the object as observations ?
So: what did you vary, what did you measure ?

And "Fc = mv^2/r represents the motion of a simple pendulum" ? More like a circular motion, I would say.

Hi, this is an exam question. It was at the end of a practical exam in which we evaluated an experimental value of gravity on Earth using simple pendulum motion. So we found the period of the pendulum and plotted length of string vs period squared; the gradient gave us the experimental value of g. Not sure if this last question was a bit of a mix up by the examiner, which is probable as my teacher isnt the best, but either way that is the question we were given and for the life of me I've no clue of the answer. Also, im sorry i didnt answer your qn bc quite frankly im not sure

BvU
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Sounds a lot clearer to me !
For a mathematical pendulum there is an expression for the period as a function of the length. Looks a lot like what you posted, But it seems to me a plot of T2 versus l is more sensible ...

yes I have plotted the T^2 vs l, it's just that the this question makes specific reference to the velocity and not gravity... I think it's an incorrect question. Thanks!

haruspex