Que. No | Question Statement | Que. No | Question Statement | |

Law of Parallelogram | ||||

1 | Resultant R = 400 N has two components forces P = 240 N & Q = 200 N as shown. Determine direction of component forces i.e. α and β w.r.t. resultant force. Ans: θ = 49.46° β = 22.33° α = 27.13°
| 2 | The two forces act on a bolt at A. Determine their resultant. Ans:
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3 | Forces Fl and F2 act on the bracket as shown. Determine the resultant R. Ans:
| 4 | Determine the resultant R of the two forces shown by applying the parallelogram rule. Ans:
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5 | To move the boat uniformly along the river at a given Speed a resultant force R = 520 N is required. Two men are pulling with force P and Q by means of ropes do this. The ropes make an angle of 30° and 40° respectively with the sides of the river as shown in Fig (i ) Determine the force P and Q (ii) if θ1 = 30°, find the value of θ2 such that the force in the rope Q is minimum. What is the minimum force Q. Ans: P = 355.7 N, Q = 276.69 N θ2 = 60°, Qmin = 260 N | |||

6 | The sum of two concurrent forces P and Q is 270 N and their resultant is of 180 N. If resultant is perpendicular to P. Find P and Q. | 6 | For two forces P and Q acting at a point, maximum resultant is 2000 N and minimum magnitude of resultant is 800 N. Find values of P and Q. | |

7 | The angle between the two concurrent forces is 90° and their resultant is 2500 N. The resultant makes an angle of 46° with one of the force, determine the magnitude of each force. | 8 | The resultant of two forces is 180 N. It makes an angle of 40° with each force. Find magnitude of two forces. | |

Resolution and composition – Resultant of Concurrent Forces | ||||

1 | The resultant of two forces P and Q is 1200 N vertical. Determine the force Q and the corresponding angle θ for the system of forces as shown in Figure. Ans: θ = 23.79°, Q = 743.59 N | 2 | The resultant of two forces P and Q is 1200 N horizontally leftward. Determine the force Q and the corresponding angle θ for the system of force s as shown in Figure. Ans: Q = 1587.45 N θ = 70.89°,
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3 | The angle between the two concurrent forces is 90° and their resultant is 2500 N. The resultant makes an angle of 46° with one of the force; determine the magnitude of each force. Ans: P = 1737 N Q = 1798 N | 4 | Determine the magnitude of force P so that the resultant of the force system as shown in Fig. is vertical and hence find magnitude of resultant force. Ans: P = -318.2 N = 318.2 N← R = 106.07 N↓
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5 | Combine the two forces 800 N and 600 N, which act on the fixed dam structure at B, into a single equivalent force R if AC = 3 m, BC = 6 m and angle BCD = 60°. Refer given Fig. Ans: α = 40.91° R = 523.94 N
Direction of resultant = 48.58° in 4th Quadrant | 6 | The force system shown in Fig. have a resultant of 200 N along positive Y-axis, determine the magnitude and position θ of force F. Ans: θ = 47.6° R = 433.31 N | |

7 | The resultant of two forces P and Q is 1400 N vertical. Determine the force Q and the corresponding angle θ for the system of forces as shown in Fig.
| 8 | The post is to be pulled out of the ground using two ropes A and B. Rope A is subjected to a force of 600 N and is directed at 60° from the horizontal. If the resultant force acting on the post is 1200 N vertically upward, determine force T in rope B and corresponding angle θ. Ans: θ = 23.79° R = 743.7 N | |

9 | A trolley is acted upon by two forces as shown Fig. If θ = 25° and the resultant R of the two forces is vertical, then determine the magnitude of the force P and resultant R. Ans: | 10 | Determine the resultant R of the two forces shown by summing scalar components. Ans:
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11 | The two structural members, one of which is in tension and the other in compression, exert the indicated forces on joint O. Determine the magnitude of the resultant R of the two forces and the angle which R makes with the positive x-axis. | 12 | Knowing that the tension in rope AC is 365 N, determine the resultant of the three forces exerted at point C of post BC. Ans: | |

13 | The following forces act at a point: i) 20 N inclined at 30° towards North of East ii) 25 N towards North iii)30 N towards North West iv) 35 N inclined at 40° towards South of West. Find the magnitude and direction of the resultant force. | Ans: | ||

14 | A disabled automobile is pulled by means of two ropes as shown. Knowing that the tension in rope AB is 3 kN, determine the tension in rope AC and the value of α so that the resultant force exerted at A is a 4.8 kN force directed along the axis of the automobile. Ans:
| 15 | R = 18 kN is the resultant of four concurrent forces out of which only three are known. Find the fourth force in magnitude and direction. Ans: F = 29.83 kN, θ= 64.04° (4th quadrant)
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16 | Determine the components Fa and Fb of the 4 kN force along the oblique axes a and b. Determine the projections Pa and Pb of F onto the a- and b-axes. Ans: | 17 | Four forces act on bolt A as shown. Determine the resultant of the forces on the bolt. Ans: | |

18 | The t-component of the force F is known to be 75 N. Determine the n -component and the magnitude of force F. Ans:
| 19 | Five concurrent coplanar forces act on a body as shown in Fig. Find forces P and Q such that resultant of the five forces is zero. Ans: P = 81 N Q = 10.64 N | |

Resultant of Non Concurrent Forces, Moment, Varignon’s Theorem | ||||

1 | A force of 800 N acts on a bracket as shown. Determine the moment of the force about B. Ans: | 2 | The lever ABC fixed at A shown in Figure is subjected to a 200 N force at C at θ = 30°. Find the moment of this force about A. Also find the value of θ for which the moment about A is Zero. Ans:
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3 | Find resultant moment of two couples for the loading as shown in Fig. [Ans: Resultant moment = 130 N.m (clockwise)] | 4 | Determine the resultant of four forces tangent to the circle of radius 1.5 m as shown in figure. Also find the location of resultant of w.r.t. ‘O’. Ans: R = 19.88 N, α = 50.35° x = 1.51 m from O. | |

5 | A rigid plate ABCD is subjected to forces as shown in figure. Calculate the Magnitude, Direction and line of action of the resultant force system with ref. to point A. | 6 | If the resultant moment about point A is 4800 Nm clockwise, determine the magnitude of F3 if F1=300 N and F2 = 400 N. Ans: F3 = 1592.7 N
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7 | Find the resultant and its point of application on y-axis for the force system acting on triangular plate as shown in Fig. Ans: R = 20 N ← x = 6 m from B | 8 | Determine the magnitude and direction of resultant with reference to point A for the force system as shown in Fig. if side of equilateral triangle is 1 m. Ans:
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9 | The three forces shown in Fig create a vertical resultant acting through point B. If P = 361 N, compute the values of T and F. Ans: F = -581.716 N T = -929.282 N | 10 | 90 N forces is applied to control the rod AB. Determine the moment of this force about point B.
Ans: MB=173.53 N.m | |

11 | For the given force system, find the resultant in magnitude and direction. Also locate point of application of resultant. Ans: R = 7.35 N, α = 55.64° x = 394.75 mm | 12 | For the given force system, find the resultant in magnitude and direction. Also locate point of application of resultant w.r.t. ‘O’. | |