Coaster Dynamics: Coaster Lab #1



Coaster Dynamics
Coaster Lab

Lesson #1:   Velocity and Acceleration:   The Need for Speed

TOPICS:   Velocity and acceleration, conversion of units.

1.   Starting with the default track configuration in Coaster Dynamics, use the Coaster Lab feature to determine the x and y coordinates, and the x and y components of the velocity at each of the 11 Watchpoints of the Lift Hill (ie., the first hill).


1 2 3 4 5 6 7 8 9 10 11
x
y
vx
vy





2.   Because the slope of the Lift Hill is nonlinear, the acceleration of the roller coaster car as it travels down the hill is not constant. However, to estimate the approximate instantaneous acceleration, let us assume that the acceleration is constant for each track sub-section between the Watchpoints.

If acceleration is constant, the change in velocity will be linear. From this fact, it can easily be shown that for 2 points in time, t1 and t2, the velocity and position will be equal to:

(1)         vx2 = vx1 + (ax)(t)
(2)         x2 = x1 + (1/2)(vx1 + vx2)(t)

(3)         vy2 = vy1 + (ay)(t)
(4)         y2 = y1 + (1/2)(vy1 + vy2)(t).

By using equations (1) and (2), eliminate the variable, t, and derive an equation for the average acceleration, ax. Similarly, using equations (3) and (4), eliminate t and derive an equation for ay.




















3.   Using the data you collected from Part 1, and the equations you derived in Part 2, calculate the average accelerations (ax, ay, and the magnitude of a) for each sub-section of the Lift Hill between Watchpoints.


S1-2 S2-3 S3-4 S4-5 S5-6 S6-7 S7-8 S8-9 S9-10 S10-11
ax
ay
|a|




4. A really hot sports car I would like to own can accelerate from 0-60 mph in 6.0 seconds. Convert the car's acceleration to m/s², and compare it to the largest acceleration you calculated in Part 3.































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