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please helppppp:((( Computer Assignment Nr. 1 Due Noon Friday, March 6th Consider a system of ten particles P., i = 1,2,..., 10, as in Figure

please helppppp:"(((

Computer Assignment Nr. 1 Due Noon Friday, March 6th Consider a system of ten particles P., i = 1,2,..., 10, as in Figure 1(a). The cartesian components of the position vectors of the particles are given in Figure 1(b). Each particle Phas forces F, exerted on it by each of the other nine particles P and each such force lies along the line defined by particles P, and P. Further, by convention, the force F., is positive if it is attractive between the two particles and negative if it is repulsive. The magnitudes of the inter-particle forces are included in Table 1 P 0.1291 1 -0.3952 P -1.4960 P -4.0195 B -0.6633 2.0924 -3.8403 -4.2192 B -1.3075 Po -4.6637 -3.0785 -1.3918 -0.2864 -1.6352 -3.5505 -3.2673 2.1784 -4.1388 1.6171 -1.0666 -0.6813 3.0437 -0.5397 -4.8892 0.0833 -2.6689 0.2809 4.3385 0.7288 -2.7320 Figure 1: (a) The system of particles. (6) The cartesian coordinates of the particles For the given system of particles, we will use MATLAB to compute the resultant force acting on each particle P due to the other nine particles, as well as the moment of this force about the origin O with coordinates (0,0,0) and about the point T with coordinates (1,2,3). In addition, we want to confirm that the resultant force for the entire system, as well as the sum of the moments of all the forces about points 0 and T are equal to zero. The MATLAB code particlesystem provided on Courses was developed to per- form the above tasks. However, it is missing some steps that you will have to code as compl CEC30/MECS5 in the areas denoted by % ADD CODE". Procedure The script first creates the position vectors in a 10 x 3 matrix P) and the inter- particle forces shown in Table 1 in a 10 x 10 matrix Ful Complete the following steps: 1. Compute the unit vector between particle pairs (PP). This will be used by the code to calculate the three components of the resultant force at each particle, which is stored in the 10 x 3 matrix (F_Prie) 2. Compute the 10 x 3 matrices (M_0) and M_T..), which contain the three components of the resultant moments of each particle about points 0 and T, respectively. 3. If each particle is not individually in equilibrium, determine the components of the external forces necessary to equilibrate each particle and store them in a 10 x 3 matrix FE 4. Check the force equilibrium of the entire system. Is it satisfied? 5. Check the moment equilibrium of the entire system by considering both points O and T. Is equilibrium satisfied? The MATLAB code will also provide a plot of the resultant force at each particle. To Submit Submit on Courses a PDF file (lastname-firstname.CAI) containing the com- pleted m-file and the outputs requested. Your final PDF file should be less than 5 pages for this assignment. A good way of presenting the code and results is by using the publish command, which can be found under "File'. 0.00001.0534 1.0534 0.0000 -2.6365 -0.2971 -0.0617 1.0213 0.6077 0.1834 -0.0215 1.4618 0.7822 -0.2388 -0.3871-1.2029 0.4466 -1.7173 -0.06650.2002 -2.6365 -0.2971 0.0000 0.0144 1.8676 0.3647 -1.3845 1.6571 0.2077 -0.8231 -0.0617 1.0213 0.0144 0.0000 1.5520 -0.4121 -0.1447 0.4662 0.1484 -1.9719 7 0.6077 -0.0215 0.7822 0.1834 1.4618 -0.2388 1.8676 0.3617 -1.38 15 1.5520 -0.4121 -0.1447 0.00001.0968 -2.15.10 1.09680.00.00 .1.6281 -2.1540 -1.6281 0.0000 -1.5109 1.7112 -0.8910 -0.8345 1.13881.5033 -1.5307 0.6163 -1.9832 8 9 10 -0.3871 0.4466 -0.0665 -1.2029 -1.7173 0.2002 1.6571 0.2077 -0.8231 0.4662 0.1484 -1.9719 -1.5109 -0.8345 -1.5307 1.71121.1388 0.6163 -0.89101.5033 -1.9832 0.0000 1.76-120.5628 1.7642 0.0000 -0.3741 0.5628 -0.3741 0.0000 10 Table 1: Inter-particle force matrix [F]. close all % Generate ten particle positions P = (x,y,z) in a X,Y,Zeb a = -5; b = 5; m 10; % Number of particles n 3: Dimension of vector rand('seed', 1); P = a + (b-a). rand(m,n,1); % Generate inter-particle forces in A F CB A = -1.5; B = 1.5; FEA (B-A). rand(a,m, 1); Inter-particle force matrix for i = 1: F(1, 1) = 0; end % Compute resultant force at particle Pi u_PiPj - zeros(1,3); Unit vector between particle pairs (Pi, Pj) (directed Pi to Pj) F Pi = zeros(m, 3); Force vector at particle Pi for i = 1:m Fix particle Pi for j = 1:m Range through all other particles Pj if( i--)) % Compute unit vector between particle pairs (Pi, Pj) (directed from Pit u PiPj = ADD CODE % Convert unit vector into force vector at particle Pi and sum F_Pili,:) = F_Pii, :) + F(1,3) "u_PiPj; end end end % Calculate moment about a point (origin O =(0,0,0) and point T = (1,2,3)] MO - zeros(m, 3); MT - zeros(m, 3); for 11: M0(1,:) = ADD CODE MT(1,:) ADD CODE end % Calculate external force to equilibrate each particle FE = ADD CODE % Check force equilibrium of the entire system F_resultant = ADD CODE % Check moment equilibrium MO_resultant = ADD CODE MT_resultant = ADD CODE % Create force plot plot 3(P(:,1),P(1,2),P(:,3),'., 'MarkerSize', 29) hold on grid axis equal quiver 3(P(:,1),P(:,2),P(:,3), F_Pi(:,1),F_P1(3,2).F_P:(:,3),-) Computer Assignment Nr. 1 Due Noon Friday, March 6th Consider a system of ten particles P., i = 1,2,..., 10, as in Figure 1(a). The cartesian components of the position vectors of the particles are given in Figure 1(b). Each particle Phas forces F, exerted on it by each of the other nine particles P and each such force lies along the line defined by particles P, and P. Further, by convention, the force F., is positive if it is attractive between the two particles and negative if it is repulsive. The magnitudes of the inter-particle forces are included in Table 1 P 0.1291 1 -0.3952 P -1.4960 P -4.0195 B -0.6633 2.0924 -3.8403 -4.2192 B -1.3075 Po -4.6637 -3.0785 -1.3918 -0.2864 -1.6352 -3.5505 -3.2673 2.1784 -4.1388 1.6171 -1.0666 -0.6813 3.0437 -0.5397 -4.8892 0.0833 -2.6689 0.2809 4.3385 0.7288 -2.7320 Figure 1: (a) The system of particles. (6) The cartesian coordinates of the particles For the given system of particles, we will use MATLAB to compute the resultant force acting on each particle P due to the other nine particles, as well as the moment of this force about the origin O with coordinates (0,0,0) and about the point T with coordinates (1,2,3). In addition, we want to confirm that the resultant force for the entire system, as well as the sum of the moments of all the forces about points 0 and T are equal to zero. The MATLAB code particlesystem provided on Courses was developed to per- form the above tasks. However, it is missing some steps that you will have to code as compl CEC30/MECS5 in the areas denoted by % ADD CODE". Procedure The script first creates the position vectors in a 10 x 3 matrix P) and the inter- particle forces shown in Table 1 in a 10 x 10 matrix Ful Complete the following steps: 1. Compute the unit vector between particle pairs (PP). This will be used by the code to calculate the three components of the resultant force at each particle, which is stored in the 10 x 3 matrix (F_Prie) 2. Compute the 10 x 3 matrices (M_0) and M_T..), which contain the three components of the resultant moments of each particle about points 0 and T, respectively. 3. If each particle is not individually in equilibrium, determine the components of the external forces necessary to equilibrate each particle and store them in a 10 x 3 matrix FE 4. Check the force equilibrium of the entire system. Is it satisfied? 5. Check the moment equilibrium of the entire system by considering both points O and T. Is equilibrium satisfied? The MATLAB code will also provide a plot of the resultant force at each particle. To Submit Submit on Courses a PDF file (lastname-firstname.CAI) containing the com- pleted m-file and the outputs requested. Your final PDF file should be less than 5 pages for this assignment. A good way of presenting the code and results is by using the publish command, which can be found under "File'. 0.00001.0534 1.0534 0.0000 -2.6365 -0.2971 -0.0617 1.0213 0.6077 0.1834 -0.0215 1.4618 0.7822 -0.2388 -0.3871-1.2029 0.4466 -1.7173 -0.06650.2002 -2.6365 -0.2971 0.0000 0.0144 1.8676 0.3647 -1.3845 1.6571 0.2077 -0.8231 -0.0617 1.0213 0.0144 0.0000 1.5520 -0.4121 -0.1447 0.4662 0.1484 -1.9719 7 0.6077 -0.0215 0.7822 0.1834 1.4618 -0.2388 1.8676 0.3617 -1.38 15 1.5520 -0.4121 -0.1447 0.00001.0968 -2.15.10 1.09680.00.00 .1.6281 -2.1540 -1.6281 0.0000 -1.5109 1.7112 -0.8910 -0.8345 1.13881.5033 -1.5307 0.6163 -1.9832 8 9 10 -0.3871 0.4466 -0.0665 -1.2029 -1.7173 0.2002 1.6571 0.2077 -0.8231 0.4662 0.1484 -1.9719 -1.5109 -0.8345 -1.5307 1.71121.1388 0.6163 -0.89101.5033 -1.9832 0.0000 1.76-120.5628 1.7642 0.0000 -0.3741 0.5628 -0.3741 0.0000 10 Table 1: Inter-particle force matrix [F]. close all % Generate ten particle positions P = (x,y,z) in a X,Y,Zeb a = -5; b = 5; m 10; % Number of particles n 3: Dimension of vector rand('seed', 1); P = a + (b-a). rand(m,n,1); % Generate inter-particle forces in A F CB A = -1.5; B = 1.5; FEA (B-A). rand(a,m, 1); Inter-particle force matrix for i = 1: F(1, 1) = 0; end % Compute resultant force at particle Pi u_PiPj - zeros(1,3); Unit vector between particle pairs (Pi, Pj) (directed Pi to Pj) F Pi = zeros(m, 3); Force vector at particle Pi for i = 1:m Fix particle Pi for j = 1:m Range through all other particles Pj if( i--)) % Compute unit vector between particle pairs (Pi, Pj) (directed from Pit u PiPj = ADD CODE % Convert unit vector into force vector at particle Pi and sum F_Pili,:) = F_Pii, :) + F(1,3) "u_PiPj; end end end % Calculate moment about a point (origin O =(0,0,0) and point T = (1,2,3)] MO - zeros(m, 3); MT - zeros(m, 3); for 11: M0(1,:) = ADD CODE MT(1,:) ADD CODE end % Calculate external force to equilibrate each particle FE = ADD CODE % Check force equilibrium of the entire system F_resultant = ADD CODE % Check moment equilibrium MO_resultant = ADD CODE MT_resultant = ADD CODE % Create force plot plot 3(P(:,1),P(1,2),P(:,3),'., 'MarkerSize', 29) hold on grid axis equal quiver 3(P(:,1),P(:,2),P(:,3), F_Pi(:,1),F_P1(3,2).F_P:(:,3),-)