- #1
shyta
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Homework Statement
A particle moves in a plane according to
x= Rsin(wt) = wRt
y= Rcos(wt) + R
where w and R are constants. This curve, called a cycloid, is the path traced out by a point on the rim of a wheel which rolls without slipping along the x-axis.
Question:
(a) Sketch the path.
(b) Calculate the instantaneous velocity and acceleration when the particle is at its maximum and minimum value of y.
Homework Equations
x= Rsin(wt) = wRt
y= Rcos(wt) + R
The Attempt at a Solution
I drew up the path of the particle, as a cycloid of course. No problem with that.
I am having problems understand part b, with relation to the curve.
I differentiated the given equations wrt to x.
i.e.
dy/dt = -Rw sin (wt)
dx/dt= Rw cos (wt) + wR
then i proceed to find dy/dx = [Rw sin (wt)]/[Rw cos (wt) + wR]
Ymaximum should be 2R (diameter of the rim of the wheel)
I also went ahead to find values of x which corresponds to the maximum and minimum values of y.
Values of X for maximum Y = 0, 2pie, ...
Values of X for minimum Y = pie, 3pie, ...
Instantaneous velocity is tangent of the curve of a position time graph, which is it the same as the graph i drew out?
Then back to the original question, the instantaneous velocity at maximum y is therefore 0? and instantaneous velocity at minimum y is infinity?
I know I have a conceptual error somewhere but I just can't figure it out.