Assignment No. 1 RESULTANT OF COPLANAR FORCES

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1 Assignment No. 1 RESULTANT OF COPLANAR FORCES Theory Questions: 1) Define force and body. (Dec Mks) 2) State and explain the law of transmissibility of forces. (May Mks) Or 3) What is law of transmissibility of forces? State its limitations. (Dec Mks) 4) For a co-planar force system explain analytical and graphical conditions of equilibrium. (Dec Mks) (May Mks) 5) State and explain the triangle law and polygon law to determine the resultant of concurrent forces. (Dec Mks). 6) State and explain idealization in mechanics. (Dec Mks) 7) State the characteristics of couple. (Dec Mks) 8) Define Force system. Name the different Force systems. (May 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 Mks) (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 60 0, determine the magnitude of resultant force. (R = N) 2. Two forces are acting at point O as shown in Figure 1 below. Determine the resultant in magnitude and direction. (R = N, α = ) Figure 1 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 = 54.15 0 ) Figure 2 Figure 3 4.

2 (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= N, θ = ) Figure 2 Figure 3 4. Find the resultant in magnitude and direction for the following system of forces shown in Figure 3 above. (R= N, θ = ) 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 = 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 2

3 7. Determine the angle α if the resultant of following three forces is on vertical as shown in Figure 6 below. α = (III) Problems on Varignon s theorem: Figure 6 8. Find the resultant, its magnitude, direction and position from point O of a force system as shown in Figure 7 below. (R = kn, O = 90 knm, d = 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 = kn, θ = ) Figure 8 3

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 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, A = 2700 Ncm) Figure 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 4

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 = kn, d = m) Figure 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 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 (R = N, d = cm) 5

6 Figure 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 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 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. 6

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.

7 Figure 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 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. 7

8 Figure 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. A is equal to zero). Figure 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) Figure 22 8

9 Assignment No. 1 General Principles and Theorems Theory Questions: 11) Define force and body. (Dec Mks) 12) State and explain the law of transmissibility of forces. (May Mks) Or 13) What is law of transmissibility of forces? State its limitations. (Dec Mks) 14) For a co-planar force system explain analytical and graphical conditions of equilibrium. (Dec Mks) (May Mks) 15) State and explain the triangle law and polygon law to determine the resultant of concurrent forces. (Dec Mks). 16) State and explain idealization in mechanics. (Dec Mks) 17) State the characteristics of couple. (Dec Mks) 18) Define Force system. Name the different Force systems. (May Mks). 19) State and prove Varignon s theorem. 20) State how the resultant of three or more co-planar and non concurrent forces is calculated? (May 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. 9

10 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 Mks). 4) Find the angle if the resultant of three forces is acting along x-axis. 5) Find the angle 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 Mks). 7) Find the unknown forces P and Q if the resultant of given forces system is zero. (as shown in Fig. below) (Dec Mks) 10

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 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 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 11

12 Q to suit the conditions. Accordingly determine location of resultant with respect to AB. 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 rad Derived quantities Symbol Unit Velocity V m/s Acceleration a m/s 2 Force F N Work & Energy W J Power P W 12

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