Calculating Speed from Energy Arguments?

[harujina]

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?

 

[nickbob00]

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.

 

[harujina]

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"?

 

[nickbob00]

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.

 

[harujina]

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.

 

[consciousness]

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,

$mgh=1/2mv^2+1/2Iω^2$

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

$mgh=0.7mv^2$

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.

 

[nickbob00]

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,

$mgh=1/2mv^2+1/2Iω^2$

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

$mgh=0.7mv^2$

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.