Engineering Mechanics

Problems

1. A boat is moved uniformly along a canal by two horses pulling with forces P = 890 N and Q = 1068 N acting under an angle ∝ = 60°. Determine the magnitude of the resultant pull on the boat and the angles βand γas shown in the figure.

2. Two forces are applied at point B of beam AB. Determine the magnitude

and direction of their resultant using (a) the parallelogram law, (b) the

triangle rule.

3. Determine the x and y components of each of the forces shown.

4. A ball of weight Q = 53.4 N rests in a right-angled trough, as shown in Fig.

Determine the forces exerted on the sides of the trough at D and E if all

surfaces are perfectly smooth.

5. A right circular roller of weight W rests on a smooth horizontal plane and is held in position by an inclined bar AC as shown in Fig. Find the tension S in the bar AC and the vertical reaction Rh at B if there is also a horizontal force P acting at.

6. Two cables are tied together at C and are loaded as shown. Knowing that P = 500 N and α = 60°. Determine the tension (a) in cable AC, (b) in cable BC.

7. Two identical rollers, each of weight Q = 445 N, are supported by an inclined plane and a vertical wall as shown in Fig. Assuming smooth surfaces, find the reactions induced at the points of support A, B and C.

8. A weight Q is suspended from a small ring C, supported by two cords AC and BC (Fig.). The cord AC is fastened at A while the cord BC passes over a frictionless pulley at B and carries the weight P as shown. If P = Q and α= 50°, find the value of the angle β.

9. A load Q is applied to the pulley C, which can roll on the cable ACB. The pulley is held in the position shown by a second cable CAD, which passes over the pulley A and supports a load P. Knowing that P = 750 N, determine (a) the tension in cable ACB, (b) the magnitude of load Q.

10. Three cables are joined at the junction ring C. Determine the tensions in cables AC and BC caused by the weight of the 30-kg cylinder.

Moment of Force

Problems

11. A boat is suspended on two identical davits like ABC which is pivoted at A and supported by a guide at B (Fig). Determine the reactions Ra and Rb

at the points of support A and B if the vertical load transmitted to each davit at C is 4272 N. Friction in the guide at B should be neglected.

12. A 667.5 N man stands on the middle rung of a 222.5 N ladder, as shown in Fig. Assuming a smooth wall at B and a stop at A to prevent slipping. Find the reactions at A and B.

13. A weightless bar AB is supported in a vertical plane by a hinge at A and a tie bar DC, as shown in Fig. Determine the axial force S induced in the tie bar by the action of a vertical load P applied at B.

14. A roller of radius r = 304.8 mm. and weight Q = 2225 N is to be pulled over a curb of height h = 152.4 mm by a horizontal force P applied to the end of a string wound around the circumference of the roller (Fig.). Find the magnitude of P required to start the roller over the curb.

15. A bracket ACB can slide freely on the vertical shaft BC but is held by a small collar attached to the shaft as shown in Fig. Neglecting all friction, find the reactions at B and C for the vertical load shown.