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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)

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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

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(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

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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

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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)

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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.

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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.

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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)

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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).

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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)

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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.

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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