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KE26303 APPLIED MECHANICS

Assignment

1. The magnitude of the force F is 400N. Express F as a vector in terms of unit vector i and j. Identify both the scalar and vector components of F.

2. A cable stretched between the fixed supports A and B is under tension T of 900N. Express the tension as a vector using the unit vectors i and j, first, as a force TA acting on A and second, as a force TB acting on B.

3. The guy cables AB and AC are attached to the top of the transmission tower. The tension in

cable AC is 8kN. Determine the required tension T in cable AB such that the net effect of the two cable tensions is a downward force at point A. Determine the magnitude R of this downward force.

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4. The 180N force is applied at the end of body OAB. If = 50o, determine the equivalent force-couple system at the shaft axis O.

5. Determine and locate the resultant R of the two forces and one couple acting on the I-beam.

6. Determine the horizontal and vertical components of reaction at pin A and the reaction of the rocker B on the beam. (P5-10).

7. The uniform 7m steel shaft has a mass of 200kg and is supported by a ball-and-socket joint at A in the horizontal floor. The ball end B rests against the smooth vertical walls as shown. Compute the forces exerted by the walls and the floor on the ends of the shaft.

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8. Rod AB below is subjected to a 200N force. Determine the reactions at the ball-and-socket joint A and the tensions in the cables BD and BE.

9. The pole is subjected to the two forces as shown. Determine the components of reaction at A assuming it to be a ball-and-socket joint. Also, compute the tension in each of the guy wires, BC and ED. (P5-72).

10. If the roller at B can sustain a maximum load of 3 kN, determine the largest magnitude of each of the three forces that can be supported by the truss.

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11. Determine the reactions at fixed support A and roller E when a force of 1350N is applied at P.

12. Draw the shear and moment diagrams for the following beams. (P7-45) a. b.

c. d.

13. Determine the magnitude and direction of the friction force acting on the 100kg block shown if, first, P=500N and second, P=100N. The coefficient of static friction is 0.2 and the coefficient of kinetic friction is 0.17. The forces are applied with the block initially at rest.

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14. A horizontal force of P=100N is just sufficient to hold the crate from sliding down the plane, and a horizontal force of P=350N is required to just push the crate up the plane. Determine the coefficient of static friction between the plane and the crate, and find the mass of the crate.

15. Using the method of virtual work, determine the required force P to maintain the equilibrium

of the scissors linkage when = 60o. The spring is unstretched when = 30o. Neglect the mass of the links.

16. The scissors linkage is subjected to a force of P = 150N. Determine the angle for

equilibrium. The spring is unstretched at = 0o. Neglect the mass of the links.