What is the most accurate way to measure the velocity of a rolling marble?

[MacFanBoy]

Well this isn't really a homework problem, just was curious behind the reasoning.

In a lab we rolled a marble off the edge of a table, and measured the velocity using: Energy and Free fall trajectory. But when comparing the two there was something like a 60% error, between the two.

My Physics teacher doesn't do much, so when I asked him he just shrugged off the question. I think that Free Fall Trajectory is more accurate, but not sure why, its practically a guess.

 

[Hootenanny]

Could you be more specific, what did you actually measure here?

 

[MacFanBoy]

Oh sorry about that, we measured velocity.

Energy using PE=KE

Free fall trajectory d=.5*g*t^2

Is that what you were asking?

 

[Hootenanny]

When you say you "measured" velocity, how did you practically "measure" the velocity?

 

[LowlyPion]

Oh sorry about that, we measured velocity.

Energy using PE=KE

Free fall trajectory d=.5*g*t^2

Is that what you were asking?

Unfortunately missing from the energy calculation was the effect that the friction had on the marble rolling down your ramp if I recall correctly.

Since the ball was rolling without slipping there was some portion of the downward rolling that went into increasing angular velocity of the marble.
Your equation for PE = KE was incomplete then because not only was there the horizontal v from the mv²/2 as it left the table
but there was the energy contained in the rotational kinetic energy I*w²/2
which is the moment of inertia of the marble times the angular velocity squared.

 

[MacFanBoy]

Oh alright:

I attached some images of the work. Seemed easier than typing it out.

 

[LowlyPion]

When you say you "measured" velocity, how did you practically "measure" the velocity?

I think the measurement was of the distance from the edge of the table given the measured height of the table.

The marble that was measured had been released down a ramp, and the horizontal velocity was calculated on that basis.

 

[MacFanBoy]

I think the measurement was of the distance from the edge of the table given the measured height of the table.

The marble that was measured had been released down a ramp, and the horizontal velocity was calculated on that basis.

Yea, sorry. lowlypion is correct. The marble was rolled down a curved ramp, which was on a table. we measured the horizontal velocity when it was at the edge of the ramp, before it rolled off of the table. In the trajectory equation, v_x=d/t "d" is the distance that we measured when the marble hit the ground (measurement by Carbon Paper).

 

[MacFanBoy]

Unfortunately missing from the energy calculation was the effect that the friction had on the marble rolling down your ramp if I recall correctly.

Since the ball was rolling without slipping there was some portion of the downward rolling that went into increasing angular velocity of the marble.
Your equation for PE = KE was incomplete then because not only was there the horizontal v from the mv²/2 as it left the table
but there was the energy contained in the rotational kinetic energy I*w²/2
which is the moment of inertia of the marble times the angular velocity squared.

Ok, that makes sense. I was thinking friction. But I had no idea on how to explain it. Thanks.

 

[Hootenanny]

I think the measurement was of the distance from the edge of the table given the measured height of the table.

The marble that was measured had been released down a ramp, and the horizontal velocity was calculated on that basis.

Ahh, I was labouring under the impression that they were measuring the velocity and then either infering the energy from their measurements or comparing their measurements to theoretical predictions.

 

[LowlyPion]

Ok, that makes sense. I was thinking friction. But I had no idea on how to explain it. Thanks.

Note that the moment of inertia of a sphere is 2/5*m*r² and of course w = v/r, making 1/2*I*w² = 1/5*m*v²

Hence a better expression might have been

m*g*h = 1/2*m*v² + 1/5*m*v²

with v = (10*g*h/7)^1/2 as opposed to the more inexact (2*g*h)^1/2