Examples for Practice [magnitude of resultant]

Examples for Practice

Q.1 

Three coplanar forces act at a point as shown in Fig. 2.10.50. Determine the value of angle 'a' such that the resultant of the three forces will be vertical. Also find the magnitude of resultant. 

[Ans. : R = 80 N, α = 36.87°]

Q.2

Resolve the 100 N force into components acting along the u and v axes and determine the magnitudes of the components. Refer Fig. 2.10.51.

 [Ans. : Fx = 173.2 N, Fy = 100 N]

Q.3

Two wires are attached to a bolt in a foundation as shown in Fig. 2.10.526650 N Determine the pull exerted by the bolt on the foundation.

[Ans. : R 4528.17 N, Q2 = 45.73° ]

Q.4

To move a boat uniformly along the river at a given speed, a resultant force R = 520 N is required. Two men pulling with forces P and Q by means of ropes are represented in Fig. 2.10.53 If (a) θ1 = 30°, and θ2 = 40° find P and Q.(b) θ1 = 30°  find θ2 such that force in rope Q is minimum. Also find this minimum force Q.

[Ans. : a) P = 3555.7 N, Q = 276.7 N_b) θ2 = 60o, Q = 260 N]

Q.5

Resolve the force of 500 kN into its components along the directions OA and OB shown in Fig. 2.10.54. [Ans. : FA = 742.79 N, FB = 326.35 N]

Q.6

The 26 kN force is the resultant of two forces. One of which is as shown in Fig. 2.10.55. Determine the other force. 

[Ans. : F = 18.11 kN, θ = 83.66° ]

Q.7 

Three forces acting on a hook are as shown in Fig. 2.10.56. Determine the direction of the fourth force of magnitude 100 N such that the hook is pulled in X direction only. Determine the resultant force in X direction. 

[ Ans. : R = 286.19 kN, θ = 39.73° ]

Q.8

Determine the force F and its inclination à required, so as to lift a block of weight 500 N as shown in Fig. 2.10.57.

[Ans. : F = 400.6 N, α = 8.614o]

Q.9

Two cables which have known tensions T1 = 2 kN and T2 = 4 kN are attached at the point B of a mast AB. A third cable BC is used as a guy wire and is attached at B. Determine the required tension in cable BC, so that the resultant of the forces exerted trby the three cables will be vertical. Also find the magnitude of the resultant. Refer Fig. 2.10.58. 

[Ans. : TBC = 6.57 kN, R = 7.14 kN ↓]

Q.10

A truck is to be pulled along a straight road as shown in Fig. 2.10.59. i) If the force applied along rope A is 5 kN inclined at 30°, what should be the force in the rope B, which is inclined at 20°, so that vehicle moves along the road?

ii) If force of 4 kN is applied in rope B at what angle rope B should be inclined so that the vehicle is pulled along the road?

[Ans. : FB = 7.31 kN, α = 36.68°]