Calculating Tension in a Vertical Circle

[jasonbans]

1. A string 1.5 m long is used to whirl a 1.5 kg stone in a vertical circle to that its velocity at the top is 6 m/s. What if tension in the string when it is horizontal? (g = 9.8 m/s2)



2. Centripetal acceleration = mv^2/r



3. i don't get what they mean by vertical circle...

 

[Delphi51]

Welcome to PF, jason.
"Vertical circle" means it is going around the way a car tire goes, not the way a merry-go-round goes. The string will be horizontal then swing up to vertical and back down to horizontal, then straight down and back up to horizontal. When at the top of the swing, gravity provides part of the centripetal force so the tension will be less. At the bottom of the swing, the tension must overcome mg and provide the centripetal force. Gravity is not involved when the string is horizontal.

 

[jasonbans]

does tension alway act towards the centripetal ?

 

[Delphi51]

Yes, the string can only pull toward the center of the circle.

 

[jasonbans]

i see, is it possible to tell me which equation to use?

 

[Delphi51]

Fc = m*v²/R

I am having some doubts upon re-reading the question. "velocity at the top is 6 m/s" suggests that the speed is different when the string is horizontal. If so, the question is more complex than it appears. I suggest you work it out with constant speed and check the answer if possible. If the answer is too small, use conservation of energy to figure out how fast it will be going when the string is horizontal and has lost some potential energy by falling distance R from the top.

 

[jasonbans]

is the radius 1.5? cau it say " length "

 

[Delphi51]

Yes, R = 1.5.