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Tutorial -1: Force Vectors 1. Determine the magnitude of the resultant force and its direction, measured counterclockwise from the positive x axis. (Ans: FR = 546 N, θ = 253 ° )

2. Determine magnitude of the resultant force and its direction, measured counterclockwise from the positive x axis. (Ans: FR = 217 N, θ = 87 °)

3. If θ = 60° and F= 20 kN, determine the magnitude of the resultant force and its direction measured clockwise from the positive x axis. (FR = 60.3 kN, θ = 15 °)

4. Determine the magnitude and orientation, measured counterclockwise from the positive y axis, of the resultant force acting on the bracket , if FB = 600 N and θ = 20 ° (Ans: 839 N, 14.8°)

5. If F2 = 150 kN and θ = 55°, determine the magnitude and orientation, measured clockwise from the positive x axis, of the resultant force of the three forces acting on the bracket. ( Ans: 161 kN , 38.3 °)

6. The boat is to be pulled onto the shore using two ropes. If the resultant force is to be 400N, directed along the keel aa as shown, determine the magnitude of forces T and P acting in each rope and the angles θ of P so that the magnitude of P is a minimum. T acts at 30° from the keel as shown. ( Ans: θ= 60° , P= 200 N, T = 346 N)

7. Determine the magnitude and directional sense of moments of the force at A about point O and P. ( Ans: Mo = 2.88 kNm (CCW) , Mp = 3.15 kNm(CCW)

8. Determine the magnitude and directional sense of the resultant moment of the forces about point O. {Ans: Mo = 2.42kNm (CW)}

9. Determine the moment about point A of each of the three forces acting on the beam.

{Ans: 600 Nm (CW), 1120 (CW), 518.53 (CW)}

10. The pole is subjected to the force F which has components F x = 1.5 kN and Fz = 1.25 kN If β = 75° , determine the magnitude of F and Fy. ( Ans: 2.02 kN , 0.523 kN)

11. Determine the magnitude of the moments of the force F about x, y and z axes. Solve the problem using Cartesian vector approach (Ans: Mx = 15 kNm, My = 4 kNm and Mz = 36 kNm)

12. Determine the moment of the force at A about the point O. Express the result as a Cartesian vector. Also determine the moment of force at A about point P and express the result as a Cartesian vector. (Ans: MO = {260 i + 180 j + 510 k} Nm M P = {440 i + 220 j + 990 k } Nm)...