Summary Mechanical Engineering Design Question and answers4

2022/05/25 7:26 PM C:\Users\ThinkPad\Desktop\MODELLIN... 1 of 2

%218110626
clc
clear
close all
%Data
F=120;%N
%SOLUTION 1.1
syms x y z P Q R
S=@(x,y,z)sqrt(x^2+y^2+z^2);
Vx=@(x,y,z)x/S(x,y,z);
Vy=@(x,y,z)y/S(x,y,z);
Vz=@(x,y,z)z/S(x,y,z);
eq1=F*Vx(0,-8,-12)+P*Vx(6,8,-12)+Q*Vx(-6,6,-12)==R*Vx(0,0,-1);
eq2=F*Vy(0,-8,-12)+P*Vy(6,8,-12)+Q*Vy(-6,6,-12)==R*Vy(0,0,-1);
eq3=F*Vz(0,-8,-12)+P*Vz(6,8,-12)+Q*Vz(-6,6,-12)==R*Vz(0,0,-1);
[P Q R]=solve([eq1 eq2 eq3],[P Q R]);
P=double(P)
Q=double(Q)
R=double(R)
%1.2)Direct Method
syms x y z P Q R
S=@(x,y,z)sqrt(x^2+y^2+z^2);
V=@(x,y,z)[x/S(x,y,z);y/S(x,y,z);z/S(x,y,z)];
eq=F*V(0,-8,-12)+P*V(6,8,-12)+Q*V(-6,6,-12)==R*V(0,0,-1);
[P Q R]=solve([eq],[P Q R]);
P1=double(P)
Q1=double(Q)
R1=double(R)
%1.3)
%Force Vector
F1=F*Vx(0,6,-6);
F2=F*Vy(-8,8,6);
F3=F*Vz(-12,-12,-12);
%Force array
FV=[F1;F2;F3];
%distance array
D=@(x,y,z)[x;y;z];
%Moment
Ma=cross(D(0,-8,0),FV)

%Question2
%2,1)
%Data
P1=900;%Kpa
P2=500;%Kpa
P3=100;%Kpa
P4=?;%Kpa
v1=0.2;%m^3
v2=0.6;%m^3