In years past, steam locomotive wheels were driven by a connecting rod attached to a cylinder. Open the Geometer's Sketchpad file below. You will see a simulation representing a toy locomotive wheel. By clicking and dragging the point on the wheel you can see that the motions of the wheel and cylinder can be modeled using trigonometric functions.
Your task is to create an equation in the form y = a sin k(θ - c) + d modeling the motion of the cylinder with respect to the rotational angle of a point on the wheel. To do this, rotate the point, and double click on the data table on the left to collect data.
a) Use this information to create an equation.
b) If you are told that the speed of rotation is 150o/sec, change the equation to represent the motion of the cylinder in terms of time.
c) For the equation, describe how the various factors (a, k, c, and d) relate to the motion the cylinder.
d) Suppose the train started out with the cylinder at the far right end. How far along the track does the train travel before the cylinder reaches the original position?
e) What position (in terms of angle) would the point on the cylinder be in after the train traveled 200 cm?
f) What would the effect of introducing a larger wheel be on the equation?
g) What would the effect of introducing a longer connecting rod be on the equation (assume the wheel stays in the same location)?
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