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Re: da/dt = jerk?



At 12:41 11/6/99 -0500, Robert Cohen wrote:
I've read Arons book on Teaching Introductory Physics...
the last paragraph of section 2.12 on page 38.
He describes an experiment where someone drives a car up a gentle slope,
puts the car into neutral and then coasts. At the instant of zero
velocity, the driver abruptly puts on the brake. The result, according to
Arons is "a heavy jolt associated with the "jerk" (an abrupt change in
acceleration)." Arons goes on to say that no jerk is felt on a level road
because there is no abrupt change in acceleration.

It seems to me that the jerk is felt because, for an instant, there is no
longer a net force on the car but there still is a net force on the
driver. That is, while coasting, the force of the chair on the back of
the driver is less than when the car is stopped.

It reminds me of the experiment where a ball is rolled down a curved ramp
and experiences a jerk when it reaches the horizontal surface at the
bottom of the ramp, even if the slope of the ramp is zero at the point at
which it ends. I've heard it explained that this jerk is also due to the
da/dt experienced at the bottom of the ramp. It seems to me, though, that
the jerk is because the rotation rate corresponding to a particular
translation rate is different while on a curved surface as on the straight
surface.

Am I missing something here? If I am, I'd appreciate someone giving me
the appropriate "jerk" vs. da/dt relationship.

Thanks in advance.

| Robert Cohen

Galileo selected sloping boards to roll his test balls down.
Their effect was to dilute gravity which suited his timing equipment,
by making everything go slower.

So a car rolling on a slope sees a diluted acceleration - due to a
diluted force, if you like. A vertical roller coaster sees a REALLY
diluted force (or 'weight')

It was Leigh who pointed out the educational value of discussing just
this scenario, i.e a car freewheeling up hill, and braked when
stationary.
Here the velocity is nil, but the acceleration suddenly changes from
its diluted fraction of g to 1. This is evidently a change of
applied force.
It was reasonable for us to visualize that this changed force
enforces a rapid acceleration of the car body as the g vector rapidly
jumps up to its customary value. In response the car springs deflect
a little more and so do you. jerk = da/dt OK?

brian whatcott <inet@intellisys.net>
Altus OK