Interpreting graphs is a really important
problem-solving skill - well done Sam from Dorset for thinking this
through so carefully, and for leaving us with an excellent question
at the end.
All the graphs start with a rising straight line. That stage is
when the bead falls directly down.
The speed and the vertical velocity will be the same thing.
Next there's a jolt when the bead hits the rail and gets shifted
On graphs 1 and 3 that's a big loss of vertical velocity.
Graph 2 has less of a jolt and graph 4 doesn't seem to have any
Now for the bead moving down the rail : If the rail was flat
(horizontal) vertical velocity would be zero.
So if the bead had some vertical velocity and the rail flattened
out that would show on the graph as vertical velocity falling -
graphs 2 and 4 do that.
Graph 2 actually goes to zero
Graph 4 doesn't continue far enough to say for sure
If the rail was a straight line (sloping down) the bead would get
faster and faster just like something rolling down a hill, and of
course that means the vertical velocity is also increasing.
The rail for graph 1 is nearly a straight slope so the graph shows
a fairly steady increasing vertical velocity but not as steep as
the straight drop right at the start. Things speed up quickly on a
steep hill but only speed up slowly on a gentle slope.
The rail for graph 3 descends more and more steeply so the plot for
vertical velocity becomes more and more steep.
I thought of the rail like lots of very short straight rails each
having a steeper gradient than the one before.
Now for the main challenge :
For the vertical velocity to stay at a fixed level my reasoning
went like this.
I know that a straight line with even the slightest slope makes the
vertical velocity increase steadily and I know that the rail
flattening out can make the vertical velocity decrease so there
must be some shape, just a bit bowed downwards from a straight line
that will make the vertical velocity neither increase or decrease
but stay exactly the same.
I think I've done quite well but I can't help the jolt at the
It seems that I need some flattening out of the rail but not much.
I don't know what sort of curve that is mathematically.
An arc from a circle seems too much curved.
Maybe some kind of big oval ?
That's an excellent question to finish with
Sam - seems a curve isn't just a curve!