# Energy conservation used to predict speed?

• chops369
In summary, the conversation discusses using energy conservation to predict the speed of a marble on a rollercoaster at different heights. The equation Vf = √2ghi is derived from energy conservation, but it does not give the correct speed when plugged in. The conversation also addresses the use of angular kinetic energy for a rolling marble and the fact that not all potential energy is converted to kinetic energy.
chops369

## Homework Statement

I don't know if anyone can help me with this without having done the lab, but I thought I'd give it a shot. Ok, so I did a lab in my physics class where we used little rollercoasters to find the PE and KE of a marble at various heights and speeds. Here is the question in my lab write-up that has me stumped.

How can you use energy conservation to predict the speed of the marble from the height?

## Homework Equations

PEi + KEi = PEf = KEf

## The Attempt at a Solution

I know that you can obtain the equation Vf = √2ghi from energy conservation, but that doesn't seem to be working when I plug in the height. It isn't coming out to the correct speed which I already calculated.

Well from the top of the roller coaster it would have 0 KE, and max PE. (At height h1). So the PE here is mgh1.

When it moves from the initial height, h1 to another height, h2. The PE is mgh2. This change in PE, mg(h1-h2). Gives the change in kinetic energy.

EDIT:

So by conservation of energy:

1/2 mv2=mg(h1-h2)

Last edited:
you can use the equation 1/2mv^2+mgh=1/2mv^2+mgh

For one thing you have the angular kinetic energy of the marble.

KE = 1/2*I*ω²

For a sphere - the marble - I = 2/5*m*r²

So the √2gh is really (2gh/(1+2/5*r))1/2

rock.freak667 said:
So by conservation of energy:

1/2 mv2=mg(h1-h2)

Wouldn't that simplify to Vf = √2g(hi - hf) ?

And @ LowlyPion, idk how to do angular KE, you're making it harder than it actually is.

chops369 said:
And @ LowlyPion, idk how to do angular KE, you're making it harder than it actually is.

I understand. But your marble rolls without slipping. That means as the speed increases, some of the PE is going to KEr.

If you are wanting to determine why observation doesn't match the math, that's where some of your error is coming from.

## 1. How does energy conservation help predict speed?

Energy conservation is based on the principle that energy cannot be created or destroyed, only transferred or transformed. This means that the initial energy of a system must be equal to the final energy of the system. By using this principle, we can determine the speed of an object by analyzing its initial and final energy values.

## 2. What types of energy are typically conserved when predicting speed?

The most common types of energy that are conserved when predicting speed are kinetic energy, potential energy, and thermal energy. Kinetic energy is the energy an object possesses due to its motion, potential energy is the energy an object possesses due to its position or height, and thermal energy is the energy associated with the temperature of an object.

## 3. How can energy conservation be applied in real-life scenarios to predict speed?

Energy conservation can be applied in various real-life scenarios to predict speed. For example, in a roller coaster, the initial potential energy of the cart at the top of the hill is converted into kinetic energy as it travels down the track. By using the principle of energy conservation, we can determine the speed of the cart at any point along the track.

## 4. Are there any limitations to using energy conservation to predict speed?

While energy conservation is a useful tool for predicting speed, there are some limitations to its application. For instance, it assumes that there are no external forces acting on the system, which may not always be the case in real-life situations. It also assumes that all forms of energy are conserved, which may not be true in certain scenarios involving energy transfers or transformations.

## 5. How does friction affect the use of energy conservation to predict speed?

Friction is a force that opposes motion and can significantly affect the accuracy of using energy conservation to predict speed. Friction converts some of the initial energy of a system into thermal energy, causing the final energy to be less than the initial energy. This can result in a slower predicted speed compared to the actual speed of the object.

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