 Now, we have this you know displayed the tutorial problem number 1. So, just you know what we will do we will just keep let us say 10 minutes to solve this problem. And once I start hearing the final answers you can simply give me the final answers. Then we can you know show you the solution or any point you want to discuss please raise your hands ok. Yeah, just go ahead what was the query? Yeah, actually in fact we can do it in a simple way. This problem can be taken the forces at point B, D, C with the force vectors fx, fy, fz at B, D, C. And we can join the point A to B, point A to B, point A to C and find out the position vector with the coordinates using x, y, z. Yeah, I think that is. So, we have joined the points from A to B, A to D and A to C, yes. Yeah, find out the three position vectors. Yes. And then find out the force vectors at B, D, C and add up three that is determinants. Yes, yes that is how it is solved right. So, this way we can do it in a simple way. Yeah, I have explained that the simpler way to solve would be just look at the component wise. So, for example as I said can we get the moment about the z axis which is passing through the A. So, I am interested in finding out the moment about z axis passing through A. The simplest way to solve that if we just look at the action of the different forces, I can clearly see that 125 kilo, the forces that are at B they do not participate. Similarly, force at D that also does not participate. So, the only force that is participating is point C that is acting at the point C right. So, that means that 300 Newton would be only responsible to produce a moment about z axis. Now that z axis is passing through the A right. The simplest way to get that component would be simply 300 multiplied by 30. So, if we apply the right hand thumb rule just look at it 300 multiplied by the perpendicular distance from the z axis right. So, that will be simply 300 multiplied by 30 that will be 9 Newton meter. And you can see exactly using the vector approach also I have a result equals to 9 Newton meter that is the z component of the moment right is that clear. So, there are two ways one is the you know defining the position vector and do the r cross f that is the you know general way of doing it. But if I want to get the sense of all of the moments it will be good to do this component wise clear. So, we are now going to display the solution. So, ultimately we get a moment resultant at point B. So, m B as we can see that is negative 120 Newton centimeter and that is actually should be clockwise here because it got a negative sign here. And the resultant force if we look at it has two components i component is negative and z component is positive. So, that would indicate its direction right. So, direction is now indicated as well. So, we get the x intercept as I said that x intercept can be obtained it should be 10.3 centimeter from the left of B ok. And the y intercept that should be down from B by 4.36 centimeter. So, ultimately the final answer should be represented like this way. I have a single resultant force R that magnitude I have already shown the line of action is given by this whose x intercept is 10.3 centimeter y intercept is 4.36 centimeter ok. So, now we will move to the next problem the problem involves. So, that of a raft which is floating on water let us say and three childrens are standing. So, three childrens the weights are for A, B and C are 85 kg, 60 kg and 90 kg respectively. So, a fourth child of weight 95 kg climbs onto the raft. So, what is being asked determine where that children should stand if the other children remains in the position shown. So, that the line of action of the resultant of the four weights is to pass through the center of the raft. So, ultimately in this problem the unknown is the location of the fourth child on the raft. So, you have to get the coordinate of the fourth child in terms of let us say x d and z d let us say that child is at point d. So, what should be the x d and what should be the z d such that now what is given the line of action of the resultant of the four weights has to pass through the center of the raft. So, the condition is already given that the resultant force must pass through the center of the raft. So, it is a parallel force system example and as you can see that there will be two unknowns. Two unknowns are x d and the z d and there will be two conditions as well I mean the line of action of the resultant force is already given. So, two equations two unknowns and we have to solve for the x d and z d the d is the position of the fourth child. So, again just take 5 to 10 minutes let us say and post your answers as you are done. I am getting some correct answers actually remote center 1005 answer is correct x should be 7.03 x coordinate of the four children should be 7.03 and z coordinate should be 3.55. So, there are correct answers 1, 2, 1, 4 is there any query. Sir one question sir. In system of forces reduction to force and couple in that how to assume the sign convention for the couple sir. Yes. So, sign convention will be as per the right hand thumb rule. So, it is always as per the right hand thumb rule right. Right hand thumb rule. Yes. Yeah when you do see couple in the sense you have r cross f right. See when you are doing r cross f that moment vector should be perpendicular to the plane containing r and f and the direction should be as per the right hand thumb rule. So, you have to go from r towards f then your right hand thumb whichever direction it points that will be the direction of the moment. I will just display the solution. See just to explain the basic idea see we have to clearly draw. So, this is my original force system and here I have the equivalent force system right and what was asked in the question that the resultant force of this 4 child should pass through the center. So, what is already known to me the position of this resultant force this is already given here 7.5 7.5 please excuse me these are all in FPS unit, but does not matter we have simply converted it to we have replaced the foot by meter and pound by kg ok. So, no issue over there as such. So, what we are interested to find out is the position of the 4 child. So, we have taken the position from the origin O 1 is the x d and 1 is the z d ok. So, then we have balanced the moment about x. So, we take the moment of x of this system and moment about x from this system. So, once I equate this 2 I should be able to get the value of z d right. So, that z d will come out which is 3.55. Similarly, if I want to get the value of x d then I should equate the moment from this system about the z axis and from this system about the z axis. So, that is done here. So, moment about z axis is taken and then finally, I have the answer for x d ok. So, x d is 7.03 meter and z d will be 3.55 meter ok. I think of so equivalent system that we have studied. So, we have mostly work on a parallel force system and the coplanar force system and we have worked out the examples of those and also in the lecture problems I have also discussed a 3D system how to get the equivalent system of that. So, we are able to find out the force resultant and the moment resultant. So, now so far we have only looked at the concentrated forces. Now, the next question that comes into play if the forces are distributed. So, if the forces are distributed as it can happen in many situation as you know that if I take a simple beam let us say and let us say in fact the depth of this beam is varying. So, weight itself will be a distributed or you can have different types of load on the beam such as triangular or any other pattern. So, how do I replace those distributed force system to a equivalent force couple system again or rather we are just going to look at replacing the distributed force system by a single equivalent force. So, to do so now we have to also look at the centroids or to find out you know the mass center of certain problem. So, we are mostly going to look at the distributed load and how to replace that by a equivalent force which will be simply the area of the distributed load and this centroid will be the line of action of the equivalent single force. So, next session we are simply going to discuss about the centroids how to calculate centroids.