Calculating Speed from Energy Arguments?

In summary, the purpose of the lab is to measure the speed of a steel marble rolling down a course with a hill and a loop. The measured velocity is then compared to the predicted velocity using the conservation of energy. The predicted velocity is found using the equation mgh=0.7mv^2, taking into account the rotational kinetic energy of the marble. The "actual" value is the speed measured in the experiment, and the comparison between the two velocities can determine the efficiency of energy transformation. The potential and total mechanical energy calculations may also be useful in interpreting the results.
  • #1
harujina
77
1
I'm doing a lab where I measure the speed of a steel marble rolling down a course with a hill and a loop. I measured distance and time in order to roughly calculate the velocity at a certain position.

My teacher wants me to compare this measured velocity with what the speed should be from energy arguments. I'm not sure what that means... I've been trying to figure it out all day but I'm stuck. What equation would I have to use?
 
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  • #2
You need to consider the conservation of energy. The ball starts with a certain amount of potential energy, which is converted to kinetic energy as the ball rolls down the hill, then back to PE as it goes around the loop.
 
  • #3
nickbob00 said:
You need to consider the conservation of energy. The ball starts with a certain amount of potential energy, which is converted to kinetic energy as the ball rolls down the hill, then back to PE as it goes around the loop.

Yes, I understand that. And I also know that the total mechanical energy should be the same throughout according to the law of conservation of energy but this isn't the case due to loss of energy caused by friction and such.

I was just confused... how does this relate to the speed/velocity that I calculated?
I'm supposed to compare the predicted and actual (speed) to determine how efficient potential energy is transformed into kinetic energy. I found the predicted, I suppose, but how do I found the "actual"?
 
  • #4
The "actual" value is the speed you measured in the experiment (maybe you did distance over time to find it indirectly), while the predicted speed is one you find by doing mgh= 1/2 mv^2. The idea is that you can then compare the two numbers and see how well the theoretical calculation (ignoring friction) matches to the motion of the ball in real life.
 
  • #5
nickbob00 said:
The "actual" value is the speed you measured in the experiment (maybe you did distance over time to find it indirectly), while the predicted speed is one you find by doing mgh= 1/2 mv^2. The idea is that you can then compare the two numbers and see how well the theoretical calculation (ignoring friction) matches to the motion of the ball in real life.

EDIT:
mgh = 1/2 mv^2 ? PE = KE?
Just wondering, I calculated Potential energy and total mechanical energy as well. What could these be of use for? I feel like they should be included but I'm not sure how I could interpret them in a useful/meaningful way.
 
Last edited:
  • #6
mgh=1/2mv2 will not work here. This is because the marble has a tendency to roll. You need to take the rotational kinetic energy into account. The marble is a solid sphere so assuming that it rolls without slipping,

[itex]mgh=1/2mv^2+1/2Iω^2[/itex]

where I is moment of inertia of the marble about its center = 0.4mr2 and ω is its angular velocity about its center = v/r.

Which comes to

[itex]mgh=0.7mv^2[/itex]

We are still ignoring air resistance. It is possible to get a better theoretical result if we take Stokes Law into account. But since a marble is so small, the effect of air resistance is probably negligible anyway.
 
  • #7
consciousness said:
mgh=1/2mv2 will not work here. This is because the marble has a tendency to roll. You need to take the rotational kinetic energy into account. The marble is a solid sphere so assuming that it rolls without slipping,

[itex]mgh=1/2mv^2+1/2Iω^2[/itex]

where I is moment of inertia of the marble about its center = 0.4mr2 and ω is its angular velocity about its center = v/r.

Which comes to

[itex]mgh=0.7mv^2[/itex]

We are still ignoring air resistance. It is possible to get a better theoretical result if we take Stokes Law into account. But since a marble is so small, the effect of air resistance is probably negligible anyway.

Excellent point, rolling completely slipped my mind.
 

1. What is the equation for calculating speed from energy arguments?

The equation for calculating speed from energy arguments is speed = √ (2 x energy/mass). This equation is derived from the principle of conservation of energy, where the total energy of a system remains constant.

2. How do you determine the energy and mass values needed for the calculation?

The energy and mass values needed for the calculation can be determined through experiments or by using known values. For example, if an object's kinetic energy and mass are known, they can be directly substituted into the equation. Alternatively, experiments can be conducted to measure the energy and mass of the object in question.

3. Can this equation be used for all types of energy?

Yes, this equation can be used for all types of energy, as long as the energy is in the form of kinetic energy. This includes mechanical energy, thermal energy, and electrical energy, among others. However, it is important to note that the mass used in the equation should correspond to the type of energy being considered.

4. Are there any limitations to using this equation?

There are a few limitations to using this equation. Firstly, it assumes that all the energy in the system is in the form of kinetic energy. If there are other forms of energy present, the calculated speed may not be accurate. Additionally, this equation does not take into account external factors such as air resistance, which can affect the object's speed.

5. Can this equation be used to calculate the speed of objects in motion?

Yes, this equation can be used to calculate the speed of objects in motion, as long as the energy and mass values are known. It is often used in physics and engineering to analyze the motion of objects, including vehicles, projectiles, and particles.

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