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da/dt = jerk?



I've read Arons book on Teaching Introductory Physics and I've always been
bothered by a particular paragraph in there. Perhaps someone can
enlighten me about it.

The particular paragraph is 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 nuetral 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.

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| Robert Cohen Department of Physics |
| East Stroudsburg University |
| bbq@esu.edu East Stroudsburg, PA 18301 |
| http://www.esu.edu/~bbq/ (570) 422-3428 |
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