Assignment
You may work in groups of up to three students if you desire. Turn in one assignment per group.
a) Consider a mass sliding down a frictionless curve in the shape of a quarter circle of radius 2.00 m as in the diagram. Assuming it starts from rest, use Euler's method to approximate both the time it takes to reach the bottom of the curve and its speed at the bottom. You may either use a speed sheet like a MS excel or you may write and execute a computer program in the language of your choice. Do three trials: Δt = 0.2s, Δt = 0.02s and Δt = 0.002s. Compare the predicated speed at the bottom for each case to the accepted value of 6.261 m/s. (calculate a percent error.)
Does the approximation improve as t becomes smaller?
b) Repeat (a), but this time assume a constant kinetic friction coefficient of μk= 0.200. Again determine the time to the bottom and the speed at the bottom. You need only run one trial; Δt = 0.200. As you do not have a "correct" value to compare, do not calculate a percent error.