# Find the minimum velocity

1. Nov 14, 2014

### james t

1. The problem statement, all variables and given/known data
A ball of mass M is attached to a 1.0m pole that is pivoted on the wall at point (0,0); such that it can take the path of a circle. The ball is initially held up at rest at the point (1,0). It is then pushed with a downward force.

What minimum initial velocity must it have if it is to be able to travel all the way around the circle of radius 1.0m ?
(It must be able to get back to the point (1,0)

2. Relevant equations
Conservation of Energy
Ui + Ki = Uf + Kf
Centripetal Force
F = mv^2/r

3. The attempt at a solution
Due to gravity it will probably move past point (1,0) and make its way down to point (0,-1) at which I have no idea what will exactly happen then.
I guess a way to look at it is that if is able to get past point (0,1) then that is sufficient, as gravity can then take over. So what will be the minimum initial velocity if it is able to get past (0,1)

I am only guessing here but i should probably use conservation of energy, but centripetal force seems like it has something to do with this problem.

So im going to solve for what kinetic energy at point (0,-1) that will allow it to get to point (0,1) although i have no idea if thats even right. The kinetic energy at point (0,-1) should equal the potential plus kinetic energy it has initially at point (1,0)

I set U=0 at y = -1

mgh = 1/2mv^2
2gh = v^2
(2)(9.81)(2) = v^2
6.26= V at (-1,0)

The energy it had initally must equal the energy it has at y = -1

1/2mv^2 = mgh + 1/2mv^2
v^2 = 2gh + v^2
39.2 = 2(9.81)(1) + v^2
v= 4.42 = initial velocity

Last edited: Nov 14, 2014
2. Nov 14, 2014

### Staff: Mentor

This is an unconventional (hence awkward) choice of axes. Did the problem have a diagram to accompany it? Maybe you took readings off it, erroneously?

Can you give us the figure? You have it right, you'll give the ball sufficent K.E. to allow it to overcome g and attain a specific height.

The ball needs to be on the end of a horizontally-held stick if an initial push "downwards" is to set it going. The way your data presents it, the ball starts with the stick held vertically so being pushed "downwards" will achieve nought.

We need the accompanying diagram, I think.

3. Nov 14, 2014

### james t

Im sorry, i was mistaken in my coordinates. The original coordinates are (1,0). It is pushed with a downward force when it is released. .

4. Nov 14, 2014

### james t

We must find the initial velocity such that will be able to get past point (0,1) thus it will be able to get back to ( and past) its original position of (1,0)

5. Nov 14, 2014

### james t

Are you sure thats all there is to it? Because if we give it just enough velocity to reach the top of the circle (0,1) then would it not just stay at rest at that point theoretically? The problem states that it must get past its original position of (1,0). We must find the absolute minimum initial velocity required to achieve this. Is there another way to do this to check that the answer is correct?

6. Nov 14, 2014

### james t

here is a diagram of the situation

7. Nov 14, 2014

### Staff: Mentor

Were you given that diagram?

The Cartesian coordinates of a point are denoted (x,y) where x is the horizontal measure from the origin, y is the vertical measure from the origin.

EDIT: You've attached a diagram you already know is wrong? Why not fix it first? How much help will this be to other students trying to follow along?

8. Nov 14, 2014

### Staff: Mentor

Instead of giving the body a starting K.E. exactly equal to the P.E. involved, you could give it that amount plus just 0.00000001 Joules and that should ensure it makes it past 12 o'clock? Or

9. Nov 14, 2014

### james t

ok here is the corrected diagram. I know about Cartesian coordinates and yes thats what i use but i am a dyslexic so sometimes i get things switched around.

10. Nov 14, 2014

### james t

How about an infinitely small amount of energy? Would that work too

11. Nov 14, 2014

### james t

are you sure that conservation of energy is the correct way to solve the problem? because that just seems a little too easy. Is there another way to do it so we compare the results

12. Nov 14, 2014

### Staff: Mentor

I tried to continue saying, but PF doesn't work so well with tablets. I was trying to say ...

Or, just phrase it as the K.E. given the ball at the start must exceed xx Joules. That neatly takes care of the issue.