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

Question

6. 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: 70p sino+cos where 0.35 is the friction coefficient. (a) Determine F18) 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 from 5 to 35 and spacing of 0.01. CalculateF 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 ui=x,i +y,jtzik and u.=x.i+y,jtzk can be determined by cos = U2-2 Given the vectors u 3.2i-6.8+ 9k and u42j+ 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 17. The area of a triangle ABC can be calculated z C(-5,-2,11) by ir,48 ×rk1/2, where rAB and rAC are vec- tors connecting the vertices A and B, and A and C, respectively. Determine the area of the triangle shown in the figure. Use the follow ing steps in a script file to calculate the area. First, define the vectors r Fo and roc from knowing the coordinates of points A, B, and C. Then determine the vectors rB and rAC from ra rOB and roc-Finally, determine the area by using MATLAB's built-in functions cross, sum. and sqrt B (-7,9,6) A (8, 5,4)

Explanation / Answer

th=[5:5:35]     %define theta vector for part a

F=70*0.35./(0.35.*sin(th*pi/180)+cos(th*pi/180))    %calculate F for all values of theta

th=[5:0.01:35]   %define theta vector for part b starting from 5 to 35, increasing by 0.01

F=70*0.35./(0.35.*sin(th*pi/180)+cos(th*pi/180))   %calculate F for all values of theta using the formula given for F

[val idx]=max(F)   %prints max F and index. val holds the max value of F while theta holds the angle which corresponds to max value of F

val   %prints the max value of F

5+idx*0.01 % prints the angle in degree. The angle is 5+idx*0.01

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