Finding little g using an inclined plane

[Ahmed Mutaz]

Homework Statement

Is it possible to find the value of g by rolling a wheel (I=mr^2) down an incline and plotting v^2 vs h(vertical length of the incline) by varying the angle? Assuming you can find the final velocity? I think it might work because mgh=0.5mv^2+0.5Iw^2 gives v^2=gh

Relevant Equations

Energy Conservation with rolling without slipping

The slope of the v^2 vs h graph is g

 

[haruspex]

mgh=0.5mv^2+0.5Iw^2 gives v^2=gh

Not quite. What is I in this case?

 

[Ahmed Mutaz]

Not quite. What is I in this case?

I=mr^2

 

[haruspex]

I=mr^2

Ah, sorry, didn't notice you specified that. But you would never quite achieve it. Better to specify a uniform disc.

 

[Ahmed Mutaz]

Ah, sorry, didn't notice you specified that. But you would never quite achieve it. Better to specify a uniform disc.

I meant a hoop/wheel thing idk how to describe it but it has a moment of inertia of I=mr^2. So assuming that is true, would you be able to obtain a value close to 9.8 for g?

 

[haruspex]

I meant a hoop/wheel thing idk how to describe it but it has a moment of inertia of I=mr^2. So assuming that is true, would you be able to obtain a value close to 9.8 for g?

I understand, but to be literally mr² it would have to be very thin radially, so could easily get bent out of round. I'm just saying it would be easier to arrange for a uniform disc.

 

[Ahmed Mutaz]

I understand, but to be literally mr² it would have to be very thin radially, so could easily get bent out of round. I'm just saying it would be easier to arrange for a uniform disc.

I figured as much; I’m only saying that assuming we have a shape that can be approximated to mr^2 does plotting v^2 against h give a decent value of g? I don’t really see any other problems besides the mr^2 approximation so forget about it for now. Also, I believe it is possible to get really thin hoops.

 

[haruspex]

I figured as much; I’m only saying that assuming we have a shape that can be approximated to mr^2 does plotting v^2 against h give a decent value of g? I don’t really see any other problems besides the mr^2 approximation so forget about it for now. Also, I believe it is possible to get really thin hoops.

Yes, the principle is fine.

 

[Ahmed Mutaz]

Yes, the principle is fine.

Thanks for confirming the theory. Now another hypothetical, last question lol, because of air resistance wouldn’t you get an under approximation of g? Or do you think there are other sources of error that may cause it to be an overestimation?

 

[haruspex]

Thanks for confirming the theory. Now another hypothetical, last question lol, because of air resistance wouldn’t you get an under approximation of g? Or do you think there are other sources of error that may cause it to be an overestimation?

Yes, air resistance and rolling resistance will lead to underestimates. Other errors, like timing offset and granularity, could go either way.
Might be a good idea to have three photo timers (I forget the technical term) so you don't have to worry about starting from rest.