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Do not change the extension of the file. The file must end in .sagews or nothing will work

See the file in this folder with the assignment instructions for updated homework instructions.

Problems to work on your own:

The following are list of problems for you to work offline. These will not be collected but quiz questions may be based on these questions. If you got lower than 70% on the last exam you will want to work all of these problems in order to do well in this class. Additionally, these are very basic questions that will help you learn how to work the problems. Partial solutions for all of these problems are included in the text on pages 620-669. Problems that start with a P are preliminary problems (fairly basic skills) and problems starting with F are fundamental problems, that are a little more challenging but cover the fundamental skills you need to solve the problems in the chapter.

P4-1, P4-2

F4-1, F4-2, F4-4, F4-6, F4-9, F4-12

The first several cells show how to calculate cross products in SageMath. I've worked through the example problems for you.

### The following is the SageMath computational solution for Example 4.3 on page 130 in your text.
r_A=vector([0,0,12])
r_B=vector([4,12,0])

line_of_action=r_B-r_A   #Vector from point A to point B

F_hat=line_of_action/line_of_action.norm()  #.norm() gives the magnitude of a vector so this is a vector divided by its magnitude
pretty_print("The direction of the force is $\hat{F} = $ ", F_hat)
F=2000*F_hat    #This is the force vector


M=r_A.cross_product(F)   # This is r_A x F
pretty_print(r"The moment of the force (the torque) about point O is $\vec{M}_O = $", n(M,digits=3))

The direction of the force is

\hat{F} =

\displaystyle \left(\frac{1}{19} \, \sqrt{19},\,\frac{3}{19} \, \sqrt{19},\,-\frac{3}{19} \, \sqrt{19}\right)

The moment of the force (the torque) about point O is

\vec{M}_O =

\displaystyle \left(-16500.,\,5510.,\,0.000\right)

### The following is the computational solution for Example 4.4 on page 131 in the Hibbeler text

r_A=vector([0,5,0])
r_B=vector([4,5,-2])

F_1=vector([-60,40,20])
F_2=vector([80,40,-30])

### The moment due to force F_1 applied at point r_A about the origin O is:
M_1=r_A.cross_product(F_1)

### The torque due to force F_2 applied at point r_B about the origin O is:
M_2 = r_B.cross_product(F_2)

### The total moment of force about the origin at O is:
M_tot=M_1+M_2

pretty_print(r"The total torque about point O is $\vec{M}_{O} = $", M_tot, "ft lb.")

The total torque about point O is

\vec{M}_{O} =

\displaystyle \left(30,\,-40,\,60\right)

ft lb.

### Example 4.5 on page 133 using vectors rather than principle moments



F_x=5000*cos(45/180*pi)
F_y=-5000*sin(45/180*pi)
F_z=0
F=vector([F_x,F_y,F_z])

r=vector([3*cos(30/180*pi),3*sin(30/180*pi),0])

M=r.cross_product(F)
M
n(M,digits=3)
M_z=n(M[2],digits=3)

pretty_print(r"The moment of force (i.e. the torque) about point O due to force $\vec{F}$ is $M_z = $", M_z, "ft lb $\circlearrowright$")

(0, 0, -3750*sqrt(3)*sqrt(2) - 3750*sqrt(2))
(0.000, 0.000, -14500.)

The moment of force (i.e. the torque) about point O due to force

\vec{F}

M_z =

\displaystyle -14500.

ft lb

\circlearrowright

### Example 4.6 on page 134 in Hibbler - Vector analysis

r=vector([.4,-.2,0])
F=vector([400*sin(30/180*pi), -400*cos(30/180*pi),0])

M_O = r.cross_product(F)
n(M_O,digits=3)

(0.000, 0.000, -98.6)

Problem 1

Solve problem 4-8 on page 138

Problem 2

Solve problem 4-19 on page 140

Problem 3

Solve problem 4-30 on page 141

Problem 4

Solve problem 4-44 on page 143

Problem 5 - Summary of Assignment

Describe what you learned in this homework and what things you already knew from previous classes. List any insights or deeper understanding you gained while completing this assignment.

Things I used that I already knew:

Explain (briefly) what skills you already knew that you used here. e.g. I used sines and cosines which I learned about in a trigonometry course

Things I learned completing this assignment:

What new skills did you learn while completing this assignment? e.g. I learned how to calculate Cartesian components of a vector

Insights and understanding gained:

What insights or understanding did you gain by completing this assigment? e.g. I now have a better understanding of how Cartesian vector notation is related to the scalar vector notation and what those two types of notation mean

Rename this file as Chapter_4_Assignment_TurnIn.sagews