A 70 lb bag of rice is being pulled by a person by applying a force F at an angl

Question

A 70 lb bag of rice is being pulled by a person by applying a force F at an angle as shown. The force required to drag the bag is given by: 6. F()-n0+cos@ where = 0.35 is the friction coefficient. (a) Determine F() for = 5°, 10°, 15°, 20°, 25°, 30°, 35°. (b) Determine the angle where F is minimum. Do it by creating a vector with elements ranging fro 5° to 35° and spacing of 0.01. Calculate F for each value of and then find the maximum F and associated with MATLAB's built-in function max. 10. The angle between two vectors ul=x,i+y,jtzk and u. =x,i+y2jtzjk can be determined by cos =_ri+nnun, where lu,l=(F+r+ . Given the vectors ul-3.21-68j + 9k and u2 =-4i + 2j + 7k , determine the angle between them (in degrees) by writing one MATLAB command that uses element-by-element multiplication and the MATLAB built-in functions acosd, sum and sqrt.

Explanation / Answer

Answer For 6.(a)

u=0.35;% assign friction coefficient
theta=5:5:35; % theta values range from 5 to 35 with step size of 5 and covers [5 10 15 20 25 30 35]
F= (70*u)./(u*sind(theta)+cosd(theta));% To determine F(theta) for theta =5 10 15 20 25 30 35
theta=theta';
F=F';
a=table(theta,F);%displaying theta and F(theta) in table form

Answer For 6.(b)

u=0.35;% assign friction coefficient
theta=5:0.01:35;% theta values range from 5 to 35 with step size of 0.01
F= (70*u)./(u*sind(theta)+cosd(theta));% To determine F(theta) for theta =5 10 15 20 25 30 35
maxF=max(F)% maximum value of F
thetamax=theta(find(F==maxF))%find theta at whichi F is maximum

Answer for 10

% assign vector values of u1 and u2
x1=3.2;
x2=-4;
y1=-6.8;  
y2=2;
z1=9;
z2=7;
u1=[x1 y1 z1];% arranging elements of vector u1 in a row
u2=[x2 y2 z2];% arranging elements of vector u2 in a row
theta=acosd(sum(u1.*u2)./(sqrt(sum(u1.*u1))*sqrt(sum(u2.*u2))));% u1.*u1 performs element by element multiplication of vector u1
%sum(u2.*u2) performs sum of all the elements in the vector u2.*u2
%acosd(x) performs inverse cos or cos^(-1) on x
theta_value=sprintf('Angle between u1 and u2 is %f',double(theta))

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