The position and velocity of the object as a function of time can then be approx

Question

The position and velocity of the object as a function of time can then be approximated by a series of calculations as follows Velocit Step Time 0 Position Acceleration To Fu.) Vo FG1) F(t.) You may work in groups of up to three students if you desire. Turn in one assignment per group y ? a) (5 pts) 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 takes to reach the bottom of the curve and its speed at the bottm. You may either use a spreadsheet like MS Excel or you may write and execute a computer program in the language of your choice. Do three trials: -02s,At = 0.02s, and At = 0.002 s. Compare the predicted 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 At becomes smaller?

Explanation / Answer

s=r

t_n=t_(n-1)+t

x_n=x_(n-1)+v_(n-1) t

v_n=v_(n-1)+a_(n-1)t

a_n=F(tn)/m

V0=0

V1=0+9.8*0.2=1.96

X0=0

X1=0+0(0.2)=0

X2=0+1.96(0.2)=.392

V2=1.96+9.8(0.2)=3.92

V3=3.92+9.8*cos(X3/2)=5.842473

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