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+clc;
+//Force exerted by track at point 2
+//kinetic energy
+T1=0;//J
+//T2=1/2*m*v2^2 m/s
+
+//Work
+//U12=W*12m;//J
+m=1000;//kg mass of car
+//principle of work and energy we get v2^2=24*g
+g=9.81;//m/s^2
+W=m*g;//N, weight of car
+v2=sqrt(24*g);// m/s
+
+//Newtons second law at point 2
+p=6;//m radius of curvature at 2
+//sum(Fn)=m*an gives N=W*5
+N=W+m*v2^2/p;//N Force exerted by track on car
+N=N/1000;//kN conversion to kN
+printf("Force exerted by track on car where radius of curvature is 6 m N= %.2f kN \n",N);
+
+//Minimum value of rho at point 3
+
+//Work and energy principle gives
+v3=sqrt(2*g*(12-4.5));//m/s
+
+//Newtons second law at point 3
+//sum(Fn)=m*an
+p=v3^2/g;//m
+printf("Minimum safe value radius of curvature at point 3 is %.1f m\n",p);