Chapter 3 : Moments and Their Applications 33
- A beam AB 5 m long is supported at its ends A and B. Two point loads W 1 and W 2 are
placed at C and D, 1 m and 3 m respectively from the end A. If the reaction at A is twice
the reaction at B, find the ratio of the loads W 1 and W 2 .[Ans. W 1 : W 2 = 2 : 1] - A beam AB of length 5 m supported at A and B carries two point loads W 1 and W 2 of 3 kN
and 5 kN which are 1 m apart. If the reaction at B is 2 kN more than that at A, find the
distance between the support A and the load 3 kN. [Ans. 2.5 m] - A tricycle weighing 200 N has a small wheel symmetrically placed 500 mm in front
of two large wheels which are placed 400 mm apart. If centre of gravity of the
cycle be at a horizontal distance of 150 mm from the rear wheels and that of the rider,
whose weight is 150 N, be 100 mm from the rear wheels, find the thrust on the ground
under the different wheels.
[Ans. 90 N ; 130 N ; 130 N] - Two identical prismatic bars PQ and RS each weighing 75 N are welded together to form
a Tee and are suspended in a vertical plane as shown in Fig. 3.10.
Fig. 3.10.
Calculate the value of θ, that the bar PQ will make with vertical when a load of 100 N is
applied at S. [Ans. 13.25°]
3.9. APPLICATIONS OF MOMENTS
Though the moments have a number of applications, in the field of Engineering science, yet
the following are important from the subject point of view :
- Position of the resultant force 2. Levers.
3.10. POSITION OF THE RESULTANT FORCE BY MOMENTS
It is also known as analytical method for the resultant force. The position of a resultant force
may be found out by moments as discussed below :
- First of all, find out the magnitude and direction of the resultant force by the method of
resolution as discussed earlier in chapter ‘Composition and Resolution of Forces’. - Now equate the moment of the resultant force with the algebraic sum of moments of the
given system of forces about any point. This may also be found out by equating the sum
of clockwise moments and that of the anticlockwise moments about the point, through
which the resultant force will pass.