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+// SAMPLE PROBLEM 6/5

+clc;funcprot(0);

+// Given data

+r=6/12;// ft

+mu_s=0.15;// The coefficients of static friction

+mu_k=0.12;// The coefficients of kinetic friction

+theta=20;// degree

+g=32.2;// The acceleration due to gravity in ft/sec^2

+x=10;// ft

+

+// Calculation

+// SigmaF_x=m*abar_x----> mg*sind(theta)-F=m*abar

+// SigmaF_x=m*abar_y----> N-mg*cosd(theta)=0

+// SigmaM_G=Ibar*alpha---> F*r=m*r^2*alpha

+abar=(g/2)*sind(theta);// ft/sec^2

+// SigmaM_G=Ibar*alpha+m*abar*d----->mgr*sin(theta)=mr^2*(abar/r)+ m*abar*r

+// From the above equations,we solve using the coefficients of mg

+F=sind(theta)-(sind(theta))/2;// N

+N=cosd(theta);// N

+F_max=mu_s*N;// N

+F=mu_k*N;// N

+// SigmaF_x=m*abar_x

+abar=(sind(theta)-F)*g;// ft/sec^2

+alpha=(F*g)/r;// rad/sec^2

+t=sqrt((2*x)/abar);// sec

+printf("\nThe angular acceleration of the hoop,alpha=%1.2f ft/sec^2 \nThe time t for the hoop to move a distance of 10 ft down the incline,t=%1.3f sec",alpha,t);