FM Tute Quest week 7 2019 3D vectors 3D forces PDF

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The School of Computing, Engineering and Maths 300463 Fundamentals of Mechanics 2019 Tutorial Questions (Dr Jonathan Vincent) Week 7 – Due date: at your tute class on 9 to 13 September 1. Read the following sections from the text book.  Article 7 in Appendix C  Article 2/7 (article 7 in chapter 2) 2. Work though the following sample problems in the text book, using the solutions given to guide you.  Sample problem 2/10 3. Answer the following problems, and hand them in at your tute class. 4. Use the cover sheet at the end of this document. 5. Your tutorial set will be returned during tutorial classes. However, if you are absent, they will not be brought back a second time. 6. If you have trouble with the questions, ask during your tutorial class, or work through a similar worked example from the text book.

The following question will be answered in the lecture-tute Question 1 Z

v=2m

z=56.648

 y=60

Y

x=48

X

A displacement vector v of magnitude 2m is shown in the figure. a) Express vector v in terms of the unit vectors i, j and k. Find an expression for a unit vector in the direction of v.

The following question will be answered in the lecture-tute Question 2 A second vector g is known to be magnitude 12m, and have direction cosines of: l = 0.5,

m = - 0.4,

n = 0.768

Add vectors v and g and find the angles that their sum makes with the positive x, y and z axes. Question 3 Calculate the dot product v.g . Question 4 Calculate the angle between v and g.

Question 5 Evaluate the cross product v  g. Express your answer as a vector, and find its magnitude.

Question 6 A third vector is given by p = 7i + 4j + 6k. Determine the projection of p onto g, both as a vector and as a scalar.

Question 9 The rigid pole and cross-arm assembly is supported by the three cables shown. A turnbuckle at D is tightened until it induces a tension T in CD of 1.2 kN. Express T as a vector. Does it make any difference in the result which coordinate system is used?

The following question will be answered in the lecture-tute Question 7 Express F as a vector in terms of the unit vectors i, j, and k. Determine the projection, both as a scalar and as a vector, of F onto line OA which lies in the XY plane.

The following question will be answered in the lecture-tute Question 8 A force F has a magnitude of 900 N and acts along the diagonal of a rectangular prism as shown. Express F in terms of its magnitude times the appropriate unit vector and determine its X, Y, and Z components.

Question 10 Use the results for question 9 to determine the magnitude of the projection of T onto line GF. Question 11 Determine the angle  between the 200 N force and line OC.

The following question will be answered in the lecture-tute Question 12 The rectangular plate is supported by hinges along its side BC and by the cable AE. If the cable tension is 300 N, determine the projection onto line BC of the force exerted on the plate by the cable. Note that E is the mid point of the horizontal upper edge of the structural support.

Assignment Cover Sheet 300463 Fundamentals of Mechanics School of Computing, Engineering and Maths

STUDENT NAME: STUDENT NUMBER: TUTOR’S NAME: TUTORIAL SET NUMBER(S): QUESTIONS COMPLETED:

DUE DATE: DATE SUBMITTED: CAMPUS OF ENROLMENT:

DECLARATION:   

I have completed all of the questions that I have listed above. I have kept a photocopy of my solution. I hereby certify that no part of this assignment or product has been copied from any other student’s work or from any other source except where due acknowledgement is made in the assignment. No part of this assignment/product has been written/produced for me by any other person except where such collaboration has been authorised by the subject lecturer/tutor concerned. Signature:

Note:

...........................................................................................

Marks may be deducted for an incomplete or inaccurate cover sheet. An examiner or lecturer/tutor has the right not to mark this assignment if the above declaration has not been signed....