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authorprashantsinalkar2017-10-10 12:27:19 +0530
committerprashantsinalkar2017-10-10 12:27:19 +0530
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+clc;
+m=60;//kg, mass of package
+k=20;//kN/m, spring constant
+k=k*1000;//N, conversion into N
+xo=120;//mm, initial compression
+xo=xo/1000;//m, conversion into meter
+x1=600;//mm
+x1=x1/1000;//m
+v1=2.5;//m/s , velocity of package
+delx=40;//mm, additional deflectio of spring
+delx=delx/1000;//m, conversion into meter
+
+//Motion from position 1to 2
+// kinetic energy at 1
+T1=1/2*m*v1^2;//N.m or J
+
+//Position 2 maximum spring deflection
+v2=0;//m/s^2
+T2=0;//J
+
+//friction force F=uk*N=uk*W
+W=m*9.81;//N
+x=(x1+delx);//m,
+//work is U12f=-F*x=-uk*w*x
+//spring force
+Pmin=k*xo;//N
+Pmax=Pmin+k*delx;//N
+// By principle of work and energy
+U12e=-1/2*(Pmin+Pmax)*delx;//J
+uk=-(T2-T1-U12e)/(W*x);// coefficient of kinetic friction
+printf("Coefficient of kinetic friction between package and surface is uk= %.2f \n",uk);
+//Motion from position 2 to position 3
+//Position 2
+v2=0;//m/s^2
+T2=0;//J
+//Position 3
+//T3=1/2*m*v3^2;//N.m or J
+U12f=-uk*W*x;//J,
+U23f=U12f;//J
+
+U23e=-U12e;//J, direction changes
+
+U23=U12f+U23e;//J Total work done
+
+//Principle of work and energy
+
+v3=sqrt((T2+U23)*2/m);//m/s,
+printf("Velocity of passage as it again passes through same position is V3= %0.3f m/s \n",v3);