Worksheet 5 Math 126
1. Suppose a train follows a circular path of radius
R
at constant speed. Compute the
acceleration, and show that it is perpendicular to the direction of travel of the train
and points into the circle.
2. Engineers in France observed that high–speed trains will not stay on the tracks if the
tracks are constructed of straight lines and arcs of circles. Use the answer to problem
1 to explain why the trains will tend to leave the tracks at the juncture of a straight
track and a circular track.
Remark:
If the acceleration of a vehicle changes abruptly, the passengers will feel
a sudden push in the opposite direction.
For instance, if the driver steps on the
accelerator, you will be pushed backwards in your seat. Perhaps you have also felt a
sideways jolt when riding in a train or car.
3. Suppose we want the train to make a smooth transition from a straight track along
the line
y
=

x
for
x
≤ 
1 to a straight track along the line
y
=
x
for
x
≥
1. That is,
we seek a new curve (
x, y
(
x
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 Spring '07
 Smith
 Math, straight track, straight segments

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