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’.

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’.