# A balls velocity when it reaches the top of the inside of a loop

1. Jul 13, 2013

### jeff.reinecke

1. The problem statement, all variables and given/known data
A tennis ball is a hollow sphere with a thin wall. It is set rolling without slipping at 4.08 m/s on a horizontal section of a track as shown in the figure below. It rolls around the inside of a vertical circular loop of radius r = 45.8 cm.
ω= 4.08

2. Relevant equations
KE1 + GPE1 = KE2 +GPE2
V = Rω

3. The attempt at a solution
I did the algrabra and ended up with Vf = ( (ωR)^2 -4gR)^(1/2)
i end up with a negative number.

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2. Jul 13, 2013

### tiny-tim

hello jeff!

what formula did you use for KE ?

anyway, you need to show us your full calculations if we're to spot your mistake

3. Jul 13, 2013

### jeff.reinecke

i used 0.5mv^2

KE1 + GPE1 = KE2 + GPE2
GPE1 = 0
so then i got
0.5mV1^2 = m(0.5V2^2 + gh) h = 2R (masses cancel each other out)
V1^2 - 2gh = V2^2
V2 = ((ωR)^2 -4gR)^(1/2)
V2= ((4.08(m/s)*0.458m)^2 - 4*9.8(m/(s^2))*0.458m)

4. Jul 13, 2013

### tiny-tim

(try using the X2 button just above the Reply box )

ah, you need to add the rotational kinetic energy

5. Jul 13, 2013

### jeff.reinecke

but wouldn't i need to add inertia to the equation?

6. Jul 13, 2013

### tiny-tim

not following you

7. Jul 13, 2013

### jeff.reinecke

KErot = 0.5Iω^[2]
is that not right
since is do not have the mass of the ball i wouldn't not be able to solve equation
because i would not be able to cancel out inertia

8. Jul 13, 2013

### tiny-tim

yes

call the mass "m", and find the moment of inertia as a multiple of m

(m will cancel out in the end)

and now i'm off to bed :zzz:

9. Jul 13, 2013

### jeff.reinecke

im still getting the wrong answer
V2 = ((ωR)^2 -4gR)^(1/2)
i now have V2 = (((ωR)2 -4gR)/R2)1/2
which ends up with a wrong answer

10. Jul 14, 2013

### jeff.reinecke

11. Jul 14, 2013

### haruspex

I don't know how you get that equation. You need to show all your working.
If the ball has radius r, what is its moment of inertia? Rolling at speed v, what is its rotational KE? What is its total KE?

12. Jul 14, 2013

### jeff.reinecke

I figured it out
I needed my KErot to be 2/5Iw^2 and realized that
Vi = 4.08 not w =4.08
w = V/R

Sorry I typed this on my phone

13. Jul 14, 2013

### haruspex

You mean KErot = (1/2)Iw2 = (1/2)(2/5)mr2w2 = (1/5)mv2, right? Except, that's still wrong. This is a hollow sphere.