Re: AP PROBLEM

[brian whatcott <inet@INTELLISYS.NET>]

At 20:16 11/10/00 -0500, you wrote:
> I wonder if someone can head me in the right direction on an old AP C
> question?
>
> A car door is open an acute angle theta when the car begins accelerating
> constantly forward.  At what time after the start of the acceleration
> will the door close. I believe we are ignoring frictional effects and
> are treating the door as a rod.
>
> Any help would be appreciated, it has been a while since I have done
> this type of problem.
>
>     Dave Abineri
> David Abineri   dabineri@choice.net

Perhaps some slight transformation would be helpful.
Visualize a mass swinging on the end of a string whose length is
the radius of gyration, and whose mass is that of the car door.

 A stick pivoted at one end has a moment of inertia I =  (m L^2)/3
which can be equated to the concentrated mass at radius k whose
Moment I = m k^2      We find the desired radius of gyration
by equating the two expressions for I
So k^2 = L^2/3 and k is then L/sqrt(3)

We now appear to have an equivalent simple pendulum deflected
by angle theta, of length 0.58 L    (L being the width of the car door.)

 The centralising force is due to some acceleration a rather than g
but we are familiar with the expression for periodic time of the
simple pendulum (approximate though it is) and this appears to scale
with acceleration simply.

We notice that this reasonable if approximate approach fails if
the car door is of the type known as a 'suicide door' - more popular
on cars of 50 years ago - though making a come back by all accounts.
In that case, the answer is 'never'; after snapping open, it may break
its restraint - and the unfortunate passenger may be rolling away.


brian whatcott <inet@intellisys.net>  Altus OK
                Eureka!