Circular motion

A stone of mass 0.5kg performs complete vertical circles on the end of a string of length 1m. Show that the string must be strong enough to support a tension of at least 29.4N.

Surely as we aren't given a speed the maximum tension on the string is just the weight of the mass - 4.9N?

Reply 1

user2020user

16

Original post by Europa192

A stone of mass 0.5kg performs complete vertical circles on the end of a string of length 1m. Show that the string must be strong enough to support a tension of at least 29.4N.

Surely as we aren't given a speed the maximum tension on the string is just the weight of the mass - 4.9N?

That's what I would've thought as well. Is this question from the Edexcel M3 book by any chance?

Reply 2

ghostwalker

17

To perform a complete circle it needs a certain minimum velocity at the top of the circle.
Hence the minimum velocity at the bottom of the circle must be ...
Hence it must support a tension of ....

Reply 3

Europa192

OP

Original post by Khallil

That's what I would've thought as well. Is this question from the Edexcel M3 book by any chance?

Nope, AQA M2. I keep rereading it to see if maybe I missed any information out. But even if it did give a speed this would mean the force resulting from the particles acceleration would decrease the tension needed. So how its meant to be 29.4N...

Reply 4

user2020user

16

Original post by Europa192

...

Oh wait. I just assumed that the velocity at the highest point of the circle must be greater than 0. That's not the case. You'd need to find the lowest possible velocity by considering the conservation of energy!

Edit: That would then lead you to the lowest possible tension that could support such movement.

Reply 5

Europa192

OP

Thanks to both of you :smile:

Reply 6

maggiehodgson

14

Original post by ghostwalker

To perform a complete circle it needs a certain minimum velocity at the top of the circle.
Hence the minimum velocity at the bottom of the circle must be ...
Hence it must support a tension of ....

I had started this question and was having trouble when I found these postings. I had a go and am posting my workings.

The answer I'm looking for is the one I get minus the mg acting away from the centre. If the stone was part way round the circle then we would use T -mgcosTheta = ma so why don't we do T- mg at the bottom of the loop?

Original post by maggiehodgson

I had started this question and was having trouble when I found these postings. I had a go and am posting my workings.

The answer I'm looking for is the one I get minus the mg acting away from the centre. If the stone was part way round the circle then we would use T -mgcosTheta = ma so why don't we do T- mg at the bottom of the loop?