How to Calculate Minimum Speed for a Ball to Make a Vertical Circle?

[kimjh]

Please help this urgent problem!~

Homework Statement

A ball is tied to a light string L=1.39m . What is the minimum horizontal speed of the ball which will ensutre that the ball makes a full vertical circle?

Homework Equations

I still struggle how this answer is 8.25

The Attempt at a Solution

8.25 <-- this is correct answer from professor but I don't know how it became

 

[pooface]

8.25 m/s?

well what do you mean by full 'vertical' circle? a full circle? meaning one whole rotation right?

Well L=1.39m should equal the radius(r) of this circle right?
So i see that 2*pi*r is the circumference and effectively the distance the ball has to cover. which i get to be 8.734m.

I don't know what do to from here.

 

[kimjh]

I think it is full vertical circle..I still trying another way..Please keep on eye this~

 

[kimjh]

Also L= should equal to r~

 

[learningphysics]

Think centripetal motion... what does the velocity at the top of the loop need to be?

then think conservation of energy... energy at the bottom must equal energy at the top.

 

[kimjh]

I put the mgr=1/2 * m * v**2 but I can't find.. any ideay someone has this?

 

[Anadyne]

Draw yourself a picture. The energy at the top isn't mgr.

 

[learningphysics]

I put the mgr=1/2 * m * v**2 but I can't find.. any ideay someone has this?

First use centripetal acceleration to find what the velocity at the top of the loop needs to be...

Then use conservation of energy. How high above the bottom of the loop is the top of the loop? you also need to consider the kinetic energy at the top of the loop.