UTAR,UEME1132_201405-STATICS Tutorial 2

1. Determine the magnitude and direction and F1, so that the resultant force is directed vertically upward and has a magnitude of 800 N.

Question 1

2 Express each of the three forces acting on the column in Cartesian vector form and compute the magnitude of the resultant force.

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Question 2

3 Three cables pull on the pipe such that they create a resultant force having a magnitude of 900N. if two of the cables are subjected to known forces as shown in the figure, determine the direction of the third cable so that the magnitude of force F in this cable is a minimum. All forces lie in the x-y plane. What is the magnitude of F? Hint: First find the resultant of the two known forces.

4 Three forces act on the bracket. Determine the magnitude and direction of F1 so that the resultant force is directed along the positive x axis and has a magnitude of 1 kN.

Question 3 Question 4

5 The pole is subjected to the force F which has components Fx = 1.5 kN and Fy = 1.25 kN. If = 75o, determine the magnitude of F and Fy.

Question 5

6 Three forces act on the hook. If the resultant force FR has a magnitude and direction as shown, determine the magnitude and the coordinate direction angles of force F3. Determine also the coordinate direction angles of F1 and FR.

Question 6

7 Determine the angle between the tails of the two vectors.

Question 7

8 Determine the magnitude of the projected component of r1 along r2 and the projection of r2 along r1.

9 Determine the cross product U V of the vectors U = 4i + 6j 10k and V = -8i + 12j + 2k. Prove that the vector U V is perpendicular to U and V.

Question 8

10 The bar AB is 6 m long and is perpendicular to the bars Ac and AD. Use the cross product to determine the coordinates xB, yB, zB of point B.

Question 10

11 Locate the centroid of the shaded area.

12 Determine the location y&&& of the centroid x&&& of the beams cross sectional area. Neglect the size of the corner welds at A and B for the calculation. Determine also the moment of inertia of the beams cross section area about the x&&& axis.

Question 11

Question 12

13 Determine the moment of inertia of the shaded area about the x axis.

[Ans: Ix = (2/15)bh3] Student to verify the correct answer !

Question 13

14 Determine the moment of Inertia Iy of the shaded area about the y axis.

Question 14