first | unit 1 resolution and composition of forces 19

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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:
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:
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°,
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↓
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:
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)
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:
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
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:
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’.

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:
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:
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°,
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↓
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:
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)
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:
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
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:
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’.

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