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Subject: A physics teacher begs for his subject back
Armchair Private    9/22/2007 11:23:16 AM
h*tp://www.civitas.org.uk/blog/2007/06/a_physics_teacher_begs_for_his.html Some of you may have seen this elsewhere, it's been around a bit. The teacher argues that physics has become a media studies class at GCSE with pupils taught to debate about issues of the day, based on their opinions. The actual science has been removed. You have to read it to get the full gist, so please do. If this is true it's horrific, with all the Government's talk of a knowledge economy, and the tractor-production-like incessant increase in education results too.
 
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Nichevo       9/23/2007 11:19:43 PM
tissapherenes       9/23/2007 10:48:17 PM
ball going on Rail B finishes earlier due to increase in velocity during the portion of the ramp that is lower.
And this is how the Chinese are going to win the space race!
 
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John G    Mith is correct.   9/24/2007 8:36:42 AM
Sorry Nichevo... You had ought to read Asymmetrics answer it is correct.
 
From this simple diagram:
 
      V1                                                   V1
__________a                               d_________  
                      \        V2               /
                        \b___________/c
 
 
V1 is the constant Velocity the ball is released at.
V2 is V1 plus the potential energy of a-b (which is equal to the loss of potential energy c-d in this case as friction is NEGLIGIBLE)
 
And of course this is assuming that the increase in speed makes up for the increase in distance.
 
 
 
 
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Armchair Private       9/24/2007 9:01:34 AM



Displacement is the same for both, but (b)'s average velocity is greater.

So answer b)?




 

So we have Armchair going for b) and Nichevo going for c).


Well Armchair is correct b) will arrive significantly earlier because its mean velocity is faster. Seems so simple when you say it like that doesn’t it? But it is amazing how many people will conclude that they should arrive at the same time and choose c) due to the kinetic energy of the ball equalling the start and the finish in both cases. It is not immediately apparent the answer just by looking at it and requires a certain amount of logic.


Now this questions mark could be increased by asking for further understanding like deducing the velocity increases by v= square root (2gh) where h is the depth of the of the dip. Furthermore you could provide measurements for the length and the initial velocity and ask how long (a) and (b) actual took.



Do I win a prize?
 
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EW3       9/24/2007 12:18:54 PM
 
Have you accounted for the increased distance traveled by the lower ball? 
 
 
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Armchair Private    EW3 - Distance   9/24/2007 1:29:14 PM
Imagine a 'V' shape, not a trapezoid.

In a 'V' shape both balls arrive at the same time as although distance is higher in (b) so is speed.

But in a 'V' shape overall displacement, and Velocity (Vector - heh heh) remain the same.

The extra distance travelled is caused by gravity, it is a new force acting on the ball, perpendicular to the overall displacement.

Delete the rails from your minds eye and imagine the same experiment carried out in space with a magnet (acting at 90 degrees to the direction of travel) turned on for 1 second's attraction, then for 1 second's worth of repelling.

You can see it's Newton's first law then.
 
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Armchair Private    EW3 - Distance   9/24/2007 1:41:24 PM
Imagine a 'V' shape, not a trapezoid.

In a 'V' shape both balls arrive at the same time as although distance is higher in (b) so is speed.

But in a 'V' shape overall displacement, and Velocity (Vector - heh heh) remain the same.

The extra distance travelled is caused by gravity, it is a new force acting on the ball, perpendicular to the overall displacement.

Delete the rails from your minds eye and imagine the same experiment carried out in space with a magnet (acting at 90 degrees to the direction of travel) turned on for 1 second's attraction, then for 1 second's worth of repelling.

You can see it's Newton's first law then.
 
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FJV       9/24/2007 2:01:27 PM
I would say B, though it wouldn't suprise me if the bearing didn't lift from the rail and follow a parabolic path with sufficient speed. Also the direction of the bearing at B changes rather abruptly (collision like), so some energy would be transferred into heat when at point b and c because of this.

Now what would happen if the speed of the bearing is fast enough to hit ramp c-d after travelling through the frictionless vacuum, it might bounce back.

As for the problems in education, one of the major factors is that the money doesn't reach the right people. Most of the money gets taken by managers and consultants who have never taugh a class not even for a day. Then there is also a lot of money wasted on incompetents who are favored by those managers and consultants, because they leave their BS unchallenged.
 
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flamingknives       9/24/2007 2:19:12 PM
The only way that this will work for all cases is if the dip is set up such that no forward velocity is lost, so there is a limit to the steepness of the ramps (a parabola) Otherwise one could have an infinitely deep dip. (in the wonderful world of limits)

So a sharp 'V' path will be dependent on dimensions. A parabola, such as that seen in free space, is dimensionally independent.
 
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Armchair Private    yup.   9/24/2007 3:45:00 PM
Lies, damned lies, statistics and assumptions!
 
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Nichevo       9/24/2007 4:08:37 PM

Sorry Nichevo... You had ought to read Asymmetrics answer it is correct.

 

From this simple diagram:

 

      V1                                                   V1

__________a                               d_________  

                      \        V2               /

                        \b___________/c

 

 

V1 is the constant Velocity the ball is released at.

V2 is V1 plus the potential energy of a-b (which is equal to the loss of potential energy c-d in this case as friction is NEGLIGIBLE)

 

And of course this is assuming that the increase in speed makes up for the increase in distance.

 

 

 

That's what I SAID!!!

No - v0=v0b=v0a ...then drops, +v to v1b and it covers the low track at v1 then decelerates to v0...

i.e. they both start at v0, b (v0b) accels to v1b along the trough...then reverts to v0b, the same speed as a!
 
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