ok a person is holding onto a piece of string

Question

at the end of the string is a ball

the person whrils it around in a circle

i've been asked what's the mininum value of at the top of the circle (this is swung around in a verticle circle) what is the mininum value the velocity could be to keep it moving in a circle

ok i found it my only question is why is the speed at the bottom given as twice the mininum speed at the top

then from there it says solv efor the force of tension at the bottom which i know how to do once i know why i can multiply the minninum speed at the top by two

Answer 1

Vertical circle? At the top, tension has to equal the force of centripetal acceleration (minus weight) or

Tension=mv^2/r -mg

IF tension is zero,
v= sqrt (rg) that is the minimum value.

so if v = sqrt(rg), then the KE at the top is 1/2 m rg. the PE at the top is 2mgr

So it falls to the bottom, total energy is 1/2 mrg+2mgr. All that energy is in KE, as PE is zero.

1/2mv^2=1/2mrg+2mgr=2.5 mrg

v=sqrt(5gr) which is slightly more than twice the speed at the top.
hyperphysics.phy-astr.gsu.edu/HBASE/mechanics/cirvert.html
check my thinking and math.

Answer 2

hey wow thanks!!!
I acutally understood
just kind of werid because our book hasn't mentioned energy yet but I know about it from just regualr old physics

I'm taking ap this year and doing the first chapters in order and it hasn't mentioned anything about energy yet just told me it was twice but not why

Thanks =]