Physics Energy - how fast ball is moving from certain height

[astru025]

Homework Statement

You let a ball roll from rest from the top of a ramp sitting on a table. If the top of the ramp is 12 cm above the top of the table, how fast is it moving when it reaches the bottom? Use g=9.8m/s/s

Homework Equations

Convert 12 cm to meters an you get .12. Then multiply that by 9.8 m/s.

The Attempt at a Solution

My answer was 1.176 which was incorrect. I think my equation and solving is wrong but I'm not sure what to change. Any help would be appreciated! Thanks!

 

[nasu]

You forgot to show your equation. And why do you thing it applies here.

 

[astru025]

I don't know the mass of the ball so I took an educated guess and used the equation v= gh

 

[nasu]

What equation is this? Where does it come from? It is dimensionaly inconsistent, for one thing.

What would you do if you knew the mass? What equation will you apply then?

 

[astru025]

If I knew the mass I would do mgh as an equation

 

[Panphobia]

Is this your whole question? It does not even give you an angle of the ramp, or the length of the ramp with the height so you could at least calculate the angle. Is there any more information from the question that you left out? Also mgh = gravitational potential energy

 

[astru025]

No this is all it gives me. Its an intro question to a lab that I am doing... I don't understand it but the lab is on energy.. In the lab it says that "you should be able to use conservation of energy to find speed of ball at the bottom of the incline."

 

[Panphobia]

Ebefore = Eafter so you need to find the equation that sums up all energy.

 

[astru025]

Conservation of energy= total energy of an isolated system does not change. So would It be 0?

 

[Panphobia]

just because it doesn't change doesn't mean there is 0 energy.

 

[astru025]

I don't know if this is relevant but kinetic energy= 1/2 mv^2

 

[Panphobia]

that is one half of it

 

[astru025]

How do I find the energy then?

 

[astru025]

Sorry I am just really struggling with this problem. I'm doing this class online through a university and the book I'm using is not very helpful. It's very heavy on concepts and light on math

 

[Panphobia]

If I give you the answer, then it would be like you cheating. But let's just say you had a quarter of the right idea at the beginning. Remember Etot = Etot' and Etot is the total energy in a system

 

[astru025]

Is this the correct equation? E total=( mv^ / 2) / mgh

 

[astru025]

Can you give me your equation? That's not cheating..

 

[Panphobia]

if i remember correctly from high school it is Etot = mv^2/2 + mgh

 

[astru025]

How do I do this if I don't know the mass?! Do I cancel the masses?

 

[Panphobia]

I basically gave you the answer, from then on it is pretty simple. Just do the math.

 

[astru025]

Wow I feel really dumb right now. Why am I not seeing it...

 

[Panphobia]

You have all the numbers you need.

 

[astru025]

Okay so taking 1/2mv^2 + mgh I simplify to get v^2 = 2gh...

 

[nasu]

If I knew the mass I would do mgh as an equation

This is not an equation. It has no equal sign in it.
But this formula represents the potential energy of the body at height h. It's a good start.
What is the kinetic energy of the same body at the height h? What is his speed?

 

[astru025]

Okay so it's mass is 1.176 ? M=gh

 

[nasu]

You don't need the mass. And cannot calculate it from the given information.
You already wrote the answer above. Even though you got it by chance and not by solving corectly, what you wrote in post 23 is the right expression for velocity squared.

 

[astru025]

This problem is due by midnight tonight and even after all your help I am not even close to finding the right answer... :(

 

[astru025]

Okay so I take 2 x 9.8 x .12 and then square that?

 

[nasu]

Your equation (you wrote it) is
v^2=2gh

So what do you get if you multiply 2 x 9.8 x 0.12?
Isn't v squared? How do you get v is v squared is given by the above multiplication?

 

[astru025]

2 x 9.8 x .12 is 2.352... That is the wrong answer though

 

[nasu]

This is v^2. You did not read the previous post?
How do you find v if v^2 is 2.352?

 

[astru025]

Yes so I take the square root of 2.532 to get what v is? Which would be 1.5

 

[nasu]

Yes, take the square root.

 

[astru025]

Ugh I entered this and it said it was incorrect. Is 1.5 m/s not the right answer?!

 

[nasu]

It may be a rounding error.
Or it may be a little more complicated. Depends on the level of your class.

Have you learned about moment of inertia and rotational kinetic energy?
They say that the ball is rolling so you may be supposed to consider the rotation of the ball too.
In this case the kinetic energy will have two terms,
KE=1/2mv^2 + 1/2 I ω^2
where I is the moment of inertia of the ball and ω is the angular speed. For rolling without slipping, ω is v/R where R is the radius of the ball.
Have you seen any of these?

 

[NihalSh]

It may be a rounding error.
Or it may be a little more complicated. Depends on the level of your class.

Have you learned about moment of inertia and rotational kinetic energy?
They say that the ball is rolling so you may be supposed to consider the rotation of the ball too.
In this case the kinetic energy will have two terms,
KE=1/2mv^2 + 1/2 I ω^2
where I is the moment of inertia of the ball and ω is the angular speed. For rolling without slipping, ω is v/R where R is the radius of the ball.
Have you seen any of these?

The question specifically mentions that the ball rolls. That means:

change in gravitational potential energy = (translation kinetic energy)+(rotational kinetic energy)

assuming ball is a solid sphere, you should know the moment of inertia of sphere. and as nasu already mentioned for pure rolling ω= \frac{v}{r}
mgh = \frac{1}{2}mv^2 + \frac{1}{2}Iω^2
mgh = \frac{1}{2}mv^2 + \frac{1}{2}\frac{2mr^2}{5}ω^2
mgh = \frac{1}{2}mv^2 + \frac{1}{2}\frac{2mr^2}{5}(\frac{v}{r})^2

the final equation would come out to be mgh = \frac{7}{10}mv^2