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+clc

+clear

+printf("Example 2.4 | Page number 39 \n\n");

+//(a)Calculate the magnitude and direction of work for air inside the balloon

+//(b)Find the magnitide and direction of work for the atmosphere and the balloon

+

+//Given Data

+p1 = 1.5 * 10^(5) //N/m^2 //initial pressure in ballon

+d1 = 0.25 //m //initial diameter of balloon

+d2 = 0.3 //m //final diameter of balloon

+p_atm = 10^(5) //N/m^2 //atmospheric pressure

+printf("Initial pressure in ballon = %.2f N/m^2\n",p1); 

+printf("Initial diameter of ballon = %.2f m\n",d1);

+printf("Final diameter of ballon = %.2f m\n",d2);

+printf("Atmospheric pressure = %.2f N/m^2\n\n",p_atm);

+

+//Solution

+

+//Part (a)

+printf("Part (a)\n");

+printf("As p is proportional to d, p = k*d, where k is proportionality constant\n");

+printf("Therefore,\n");

+

+k = p1/d1;

+printf("p1 = k*d1 => k = (p1/d1) = (%.2f/%.2f) = %.2f N/m^3\n",p1,d1,k);

+

+p2 = k*d2; //N/m^2 //final pressure in balloon

+printf("p2 = k*d2 = (%.2f*%.2f) = %.2f N/m^2\n\n",k,d2,p2);

+

+W_air = integrate('k*(%pi/2)*(d^3)','d',d1,d2) //Nm //Work done by air on the balloon

+printf("Work done by balloon on air = %.2f Nm\n\n",W_air);

+

+//Part (b)

+printf("Part (b)\n");

+W_atm = integrate('p_atm*(0.5*%pi*(d^2))','d',d2,d1); //Nm //Work done by atmosphere on ballon

+printf("Work done by atmosphere on balloon = %.2f Nm\n",W_atm);

+W_balloon = -1*(W_air+W_atm);

+printf("Work done by balloon = -(Work done by air + Work done by atmosphere) = -(%.2f%.2f) = %.2f Nm\n",W_air,W_atm,W_balloon);