How to Use Euler's Method to Approximate Velocity in a Quarter Circle Motion

[joman138]

I have an assigned project in Physics with numerical modeling, to which I am supposed to use Euler's method to approximate the velocity of a "mass sliding down a frictionless in the shape of a quarter circle of radius 2.00 m."

The assignment also states: "Do three trials: t = 0.2s, t = 0.02s, and t =
0.002 s. Compare the predicted speed at the bottom for each case to the accepted value
of 6.261 m/s."

I know how to use Euler's method to approximate the velocity as time changes, but I am not sure how to find the position, velocity, and acceleration at the first time. Also, I was given a formula for the acceleration at the first time, Ef(T0)/m or the sum of the forces of t0 divided by the mass, but I am not sure how to use this formula.

The problem also states: "Assume it starts from rest" and "Hint: Define the position and acceleration of the mass in terms of the angle."

Thanks in advance for anyone's help. I can also post the actual assignment as a .pdf or word file if further clarification is necessary.

 

[joman138]

I figured out the entire solution to this crazy problem. I'll post it to let you guys look at it tomorrow.