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Assignment No. 1
RESULTANT OF COPLANAR FORCES
(I) Problems on Law of Parallelogram of Forces:
1. Two forces of magnitude 10 N and 8 N are acting at a point. If the angle between the two
forces is 600
, determine the magnitude of resultant force. (R = 15.62 N)
2. Two forces are acting at point ‘O’ as shown in Figure 1 below. Determine the resultant in
magnitude and direction. (R = 145.46 N, α = 200 + 150 + 35.100)
Figure 1
(II) Problems on component law of Forces:
3. Find the resultant, its magnitude and direction for following force system as shown in Figure 2.
(R= 48.92 N, θ = 54.150)
Figure 2 Figure 3
4. Find the resultant in magnitude and direction for the following system of forces shown in
Figure 3 above. (R= 161.48 N, θ = 18.810)
2
Problems on to find angle:
5. Determine the angle α if the resultant of three forces is acting along x-axis as shown in
Figure 4 below. (Jan. 2004) (11 marks). α = 6.320
Figure 4
6. Determine the angle ‘α’ if the resultant of following three forces is acting on vertical axis
as shown in Figure 5 below.
Figure 5
7. Determine the angle α if the resultant of following three forces is on vertical as shown in
Figure 6 below. α = 21.730
Figure 6
3
(III) Problems on Varignon’s theorem:
8. Find the resultant, its magnitude, direction and position from point O of a force system as
shown in Figure 7 below. (R = 18.028 kN, ∑M @ O = 90 kNm, d = 4.992 m)
Figure 7
9. Find the resultant, its magnitude, direction and position from point D of a force system as shown
in Figure 8 below. All sides of a square are 20 cm. (R = 18.028 kN, θ = 75.310)
Figure 8
4
10. Four parallel forces of magnitude 100 N, 150 N, 25 N and 200 N are acting as shown in
Figure 9 below. Determine the magnitude of the resultant and also the distance of
resultant from point A. (R = 125 N, x = 3.06 m)
Figure 9
11. Three like forces of magnitude 100 N, 200 N and 300N are acting at points A, B and C
respectively as shown in Figure 10 below. The resultant of all these forces R is acting at a
point D which is at a distance of 45 cm from point A along the line AC. Find out the
magnitude of the resultant R and prove the Varignon’s theorem. (R = 600N, ∑M @ A =
2700 Ncm)
Figure 10
12. The three like forces of magnitude 50N, F and 100 N are as acting at point A, B & D resp. as
shown in Figure 11 below. If the resultant R=250N and is acting at a distance 4 m from A,
then find out
a. Magnitude of force F.
b. Distance of F from A. (F = 100 N, x = 3 m from point A)
Figure 11
5
13. A rectangular plate is subjected to the forces as shown in Figure 12 below.
Determine:
i) An equivalent force-couple system at B.
ii) A resultant with its inclination and intercept on edge BD. (R = 3.121 kN, d = 3.544 m)
Figure 12
14. An equilateral triangular plate of sides 200 mm is acted upon by four forces as shown in
Figure 13 and Figure 14 below. Determine the magnitude, direction and position of the
resultant of this system of forces from point A.
Figure 13 Figure 14 (May 06 11 Mks)
15. Non concurrent forces are acting on a wheel as shown in Figure 15. Find the resultant
force. Also locate its position along X-axis from centre. Radius of wheel = 20 cm. (12)
May 2002. (R = 95.867 N, d = 11.374 cm)
6
Figure 15
16. Three forces of 2P, 3P and 4P act along the three sides of an equilateral triangle of side
100 mm taken in order. Find the magnitude and position of resultant force as shown in
Figure 16. (10)
Figure 16
17. The end B of a weightless bar AB is made to act upon by forces as shown in Figure 17
below. Determine the resultant of forces. Also determine the moment of resultant around
the point A.
Figure 17
18. A bracket is subjected to three forces and a couple as shown in Figure 18 below.
Determine the magnitude direction and the line of action of the resultant.
7
Figure 18
19. A bracket is subjected to four forces as shown in Figure 19 below. Determine the
magnitude direction and the line of action of the resultant.
Figure 19
20. A bracket is subjected to four forces and a couple as shown in Figure 20 below.
Determine the magnitude direction and the line of action of the resultant.
8
Figure 20
21. Non-concurrent co-planar force system is shown is acting on a lamina as shown in Figure
21 below. Determine the magnitude of force ‘P’ such that resultant passes through point
A. Hence find the resultant. (If resultant passes through A i.e. Moment @ A is equal to
zero).
Figure 21 Figure 22
22. Determine the resultant of three forces acting on a dam section as shown in Figure 22 below and
locate its intersection with base AB with respect to point B. (Dec. 2007)
9
Assignment No. 1
General Principles and Theorems
Theory Questions:
1) Define force and body. (Dec. 2004 2 Mks)
2) State and explain the law of transmissibility of forces. (May 2009 4 Mks)
Or
3) What is law of transmissibility of forces? State its limitations. (Dec. 2004 4 Mks)
4) For a co-planar force system explain analytical and graphical conditions of
equilibrium. (Dec 2004 4 Mks) (May 2007 5 Mks)
5) State and explain the triangle law and polygon law to determine the resultant of
concurrent forces. (Dec. 2009 6 Mks).
6) State and explain idealization in mechanics. (Dec. 2010 4 Mks)
7) State the characteristics of couple. (Dec. 2010 3 Mks)
8) Define Force system. Name the different Force systems. (May 2007 5 Mks).
9) State and prove Varignon’s theorem.
10) State how the resultant of three or more co-planar and non concurrent forces is
calculated? (May 2004 2 Mks)
Problems:
1) Find the resultant of the following force system.
2) Find the resultant of the following force system as shown in Figure below and locate it
from point ‘O’.
3) The resultant of three forces is 60 N as shown in Fig. below. Two of the three forces
are 120 N and 65 N. Determine completely the third force. (May 2007 12
Mks).
10
4) Find the angle ‘𝛼’ if the resultant of three forces is acting along x-axis.
5) Find the angle ‘𝛼’ if resultant of three forces is vertical, also find corresponding
magnitude of resultant.
6) A bracket is subjected to three forces and a couple as shown in Fig. below. Determine
magnitude, direction and line of action of resultant. (Dec. 2009 8 Mks).
7) Find the unknown forces P and Q if the resultant of given forces system is zero. (as
shown in Fig. below) (Dec 2004 12 Mks)
11
8) An equilateral triangular plate 200mm is acted upon by four forces as shown in Fig.
below. Determine the magnitude, direction and position of resultant of this force
system. (May 2006 11 Mks).
9) A non-concurrent co-planar force system is acting on a lamina as shown in Fig.
below. Determine magnitude of force P such that the resultant passes through point
A. Hence find the resultant. (Dec. 2005 12 Mks)
10) A regular hexagon with all sides 5 cm carries forces as shown in Fig. below. The
resultant of all forces is 1000 N and goes horizontally towards left. Determine P and
Q to suit the conditions. Accordingly determine location of resultant with respect to
AB.
12
11) Resolve a force of 300 N into two components P and such that P is inclined at an
angle of 300 0n one side of the given force and on the other side of it Q lies Q is two
times P in magnitude. Find the value of P and Q.
12) Find the equilibrant, its magnitude, direction and position from point A of a force
system as shown in Figure below.
13) Three forces 60 N, 80 N and 130 N acts at the vertices of a triangle ABC as shown in
Figure below. AB = BC = CA = 40 cm. Find the resultant of this force system. Locate
the point D on BC where resultant cuts BC. Find the distance of d from C.
14)
Basic quantities Symbol Unit
Length l Meter (m)
Mass m Kg
Time t s or sec
Temperature T K
Electric current I A
Plane angle 𝜃 rad
Derived quantities Symbol Unit
Velocity V m/s
Acceleration a m/s2
Force F N
Work & Energy W J
Power P W

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Assignment no 1

  • 1. 1 Assignment No. 1 RESULTANT OF COPLANAR FORCES (I) Problems on Law of Parallelogram of Forces: 1. Two forces of magnitude 10 N and 8 N are acting at a point. If the angle between the two forces is 600 , determine the magnitude of resultant force. (R = 15.62 N) 2. Two forces are acting at point ‘O’ as shown in Figure 1 below. Determine the resultant in magnitude and direction. (R = 145.46 N, α = 200 + 150 + 35.100) Figure 1 (II) Problems on component law of Forces: 3. Find the resultant, its magnitude and direction for following force system as shown in Figure 2. (R= 48.92 N, θ = 54.150) Figure 2 Figure 3 4. Find the resultant in magnitude and direction for the following system of forces shown in Figure 3 above. (R= 161.48 N, θ = 18.810)
  • 2. 2 Problems on to find angle: 5. Determine the angle α if the resultant of three forces is acting along x-axis as shown in Figure 4 below. (Jan. 2004) (11 marks). α = 6.320 Figure 4 6. Determine the angle ‘α’ if the resultant of following three forces is acting on vertical axis as shown in Figure 5 below. Figure 5 7. Determine the angle α if the resultant of following three forces is on vertical as shown in Figure 6 below. α = 21.730 Figure 6
  • 3. 3 (III) Problems on Varignon’s theorem: 8. Find the resultant, its magnitude, direction and position from point O of a force system as shown in Figure 7 below. (R = 18.028 kN, ∑M @ O = 90 kNm, d = 4.992 m) Figure 7 9. Find the resultant, its magnitude, direction and position from point D of a force system as shown in Figure 8 below. All sides of a square are 20 cm. (R = 18.028 kN, θ = 75.310) Figure 8
  • 4. 4 10. Four parallel forces of magnitude 100 N, 150 N, 25 N and 200 N are acting as shown in Figure 9 below. Determine the magnitude of the resultant and also the distance of resultant from point A. (R = 125 N, x = 3.06 m) Figure 9 11. Three like forces of magnitude 100 N, 200 N and 300N are acting at points A, B and C respectively as shown in Figure 10 below. The resultant of all these forces R is acting at a point D which is at a distance of 45 cm from point A along the line AC. Find out the magnitude of the resultant R and prove the Varignon’s theorem. (R = 600N, ∑M @ A = 2700 Ncm) Figure 10 12. The three like forces of magnitude 50N, F and 100 N are as acting at point A, B & D resp. as shown in Figure 11 below. If the resultant R=250N and is acting at a distance 4 m from A, then find out a. Magnitude of force F. b. Distance of F from A. (F = 100 N, x = 3 m from point A) Figure 11
  • 5. 5 13. A rectangular plate is subjected to the forces as shown in Figure 12 below. Determine: i) An equivalent force-couple system at B. ii) A resultant with its inclination and intercept on edge BD. (R = 3.121 kN, d = 3.544 m) Figure 12 14. An equilateral triangular plate of sides 200 mm is acted upon by four forces as shown in Figure 13 and Figure 14 below. Determine the magnitude, direction and position of the resultant of this system of forces from point A. Figure 13 Figure 14 (May 06 11 Mks) 15. Non concurrent forces are acting on a wheel as shown in Figure 15. Find the resultant force. Also locate its position along X-axis from centre. Radius of wheel = 20 cm. (12) May 2002. (R = 95.867 N, d = 11.374 cm)
  • 6. 6 Figure 15 16. Three forces of 2P, 3P and 4P act along the three sides of an equilateral triangle of side 100 mm taken in order. Find the magnitude and position of resultant force as shown in Figure 16. (10) Figure 16 17. The end B of a weightless bar AB is made to act upon by forces as shown in Figure 17 below. Determine the resultant of forces. Also determine the moment of resultant around the point A. Figure 17 18. A bracket is subjected to three forces and a couple as shown in Figure 18 below. Determine the magnitude direction and the line of action of the resultant.
  • 7. 7 Figure 18 19. A bracket is subjected to four forces as shown in Figure 19 below. Determine the magnitude direction and the line of action of the resultant. Figure 19 20. A bracket is subjected to four forces and a couple as shown in Figure 20 below. Determine the magnitude direction and the line of action of the resultant.
  • 8. 8 Figure 20 21. Non-concurrent co-planar force system is shown is acting on a lamina as shown in Figure 21 below. Determine the magnitude of force ‘P’ such that resultant passes through point A. Hence find the resultant. (If resultant passes through A i.e. Moment @ A is equal to zero). Figure 21 Figure 22 22. Determine the resultant of three forces acting on a dam section as shown in Figure 22 below and locate its intersection with base AB with respect to point B. (Dec. 2007)
  • 9. 9 Assignment No. 1 General Principles and Theorems Theory Questions: 1) Define force and body. (Dec. 2004 2 Mks) 2) State and explain the law of transmissibility of forces. (May 2009 4 Mks) Or 3) What is law of transmissibility of forces? State its limitations. (Dec. 2004 4 Mks) 4) For a co-planar force system explain analytical and graphical conditions of equilibrium. (Dec 2004 4 Mks) (May 2007 5 Mks) 5) State and explain the triangle law and polygon law to determine the resultant of concurrent forces. (Dec. 2009 6 Mks). 6) State and explain idealization in mechanics. (Dec. 2010 4 Mks) 7) State the characteristics of couple. (Dec. 2010 3 Mks) 8) Define Force system. Name the different Force systems. (May 2007 5 Mks). 9) State and prove Varignon’s theorem. 10) State how the resultant of three or more co-planar and non concurrent forces is calculated? (May 2004 2 Mks) Problems: 1) Find the resultant of the following force system. 2) Find the resultant of the following force system as shown in Figure below and locate it from point ‘O’. 3) The resultant of three forces is 60 N as shown in Fig. below. Two of the three forces are 120 N and 65 N. Determine completely the third force. (May 2007 12 Mks).
  • 10. 10 4) Find the angle ‘𝛼’ if the resultant of three forces is acting along x-axis. 5) Find the angle ‘𝛼’ if resultant of three forces is vertical, also find corresponding magnitude of resultant. 6) A bracket is subjected to three forces and a couple as shown in Fig. below. Determine magnitude, direction and line of action of resultant. (Dec. 2009 8 Mks). 7) Find the unknown forces P and Q if the resultant of given forces system is zero. (as shown in Fig. below) (Dec 2004 12 Mks)
  • 11. 11 8) An equilateral triangular plate 200mm is acted upon by four forces as shown in Fig. below. Determine the magnitude, direction and position of resultant of this force system. (May 2006 11 Mks). 9) A non-concurrent co-planar force system is acting on a lamina as shown in Fig. below. Determine magnitude of force P such that the resultant passes through point A. Hence find the resultant. (Dec. 2005 12 Mks) 10) A regular hexagon with all sides 5 cm carries forces as shown in Fig. below. The resultant of all forces is 1000 N and goes horizontally towards left. Determine P and Q to suit the conditions. Accordingly determine location of resultant with respect to AB.
  • 12. 12 11) Resolve a force of 300 N into two components P and such that P is inclined at an angle of 300 0n one side of the given force and on the other side of it Q lies Q is two times P in magnitude. Find the value of P and Q. 12) Find the equilibrant, its magnitude, direction and position from point A of a force system as shown in Figure below. 13) Three forces 60 N, 80 N and 130 N acts at the vertices of a triangle ABC as shown in Figure below. AB = BC = CA = 40 cm. Find the resultant of this force system. Locate the point D on BC where resultant cuts BC. Find the distance of d from C. 14) Basic quantities Symbol Unit Length l Meter (m) Mass m Kg Time t s or sec Temperature T K Electric current I A Plane angle 𝜃 rad Derived quantities Symbol Unit Velocity V m/s Acceleration a m/s2 Force F N Work & Energy W J Power P W