00:10 Good day everyone. My name is Mr. Bakare. I'm your physics teacher today and today's topic

00:21 we'll be talking about equilibrium of forces. Now before we move on, let's look at the objectives

00:29 of the topic. At the end of this lesson, students should be able to define static and dynamic

00:38 equilibrium, distinguish between resultant and equilibrium forces, define moment of force,

00:46 state conditions equilibrium of equilibrium under the action of co-planar forces,

00:55 state the principles of moment and of course be able to solve some simple problems

01:03 under this topic. Now what is equilibrium of forces? When forces act on a body,

01:12 it may change the position of rest of the body or cause the body to rotate about its fixed

01:21 axis. A body is set to be in equilibrium when it is at rest or in a state of uniform motion.

01:32 When the body is at rest, it experiences what we call static equilibrium, that is the body is

01:41 not moving. And when it undergoes uniform motion, it experiences dynamic equilibrium. That's

01:51 a body that moves with time. A body is set to be in equilibrium when all the forces

01:58 acting on the body cancel out, that is, the resultant of all the forces acting on the body is zero.

02:08 What is resultant and equilibrium forces? For a body to be in equilibrium,

02:18 the sum of forces in one direction must be equal to the sum of forces in the opposite direction.

02:25 For instance, if we have like a tug of war, a rope is being set in between two students

02:37 that are facing each other and they are pulling the rope. If none of them is falling, that means

02:47 the rope is in equilibrium. But if one is falling and the other is not falling, that means there's no

02:55 equilibrium. Now from the first board experiments, the resultant R of two forces A and B, as shown

03:09 in that diagram, acting at point O is found using parallelogram method. And it is found to be

03:18 equal in magnitude by opposite in direction to the third force.

03:23 This third force, which is equal in magnitude by opposing direction of resultant force,

03:33 is called equilibrium force. Therefore, resultant force is that single force that act alone

03:43 and has the same effect in magnitude and direction as two or more forces acting together. Now what

03:50 they mean by that, if you have three forces A, B and C. Now A is an equilibrium of forces B and C,

04:03 that is, if A has the same effect as B and C, the same thing with B is an equilibrium of C and A.

04:17 If B has the same magnitude with C and A, an equilibrium force is a single force,

04:28 which we balance all other forces taking together. Let's look at example now. We have three forces

04:40 that act in at the point, force 1, force 2 and force 3. If F1, F2, F3 are in equilibrium,

04:50 then F1 is the equilibrium of F2 and F3. F3 is the equilibrium of F1 and F2. And of course F2

05:05 is the equilibrium of F1 and F3. Now what is moment of a force? For instance,

05:18 almost every day we observe this moment of a force. There is no way you can wake up in the morning

05:30 and not open a door. There is no way you can wake in the morning and not turn on the tap

05:37 and so on and so forth. So when taps are turned, the toning effect of the force experiences,

05:45 the same thing when doors are opened, the toning effect applied brings about what we call the moment

05:54 of a force. So the toning effect experienced in each case is known as moment of a force.

06:02 Moment of a force about the point mathematically can be defined as the product of the force

06:11 and the perpendicular distance from the line of action to the pivot of the point.

06:19 Now mathematically, moment equal to force times perpendicular distance, F represents the force

06:33 and D represents distance. Now we can see there. So the unit of a moment is

06:45 newton meter because the unit of force is newton. Newton times the unit of distance is

06:54 meter. So we can say it is newton meter and this unit is a vector quantity. Of course,

07:06 we talked about vector quantity in the previous class that is a quantity that has both magnitude

07:13 and direction. Let's look at another way of defining our moment of a force.

07:25 If the force is inclined at an angle theta, like we can see on the board, then the moment

07:33 will be F times D sine theta. That is F D sine theta. So this is our force and this is our

07:50 distance, force times distance. The magnitude of moments depends on the force applied.

08:03 The force applied and the perpendicular distance from the pivot to the line of action of the force.

08:11 Resultant moment. Went to or more forces act on the body. The resultant moment on the body

08:24 about any point can be obtained using algebraic moments using the clockwise moments and the

08:33 anticlockwise moments about the same point. If the clockwise moment is taken as positive,

08:40 like we have in a clock. Let's assume this is a clock. Normally, our clock goes like this

08:54 in this direction. But if it goes like this, that is anticlockwise negative. If it goes like this,

09:02 that is clockwise moments. So if the clockwise moment is taken as positive, then the anticlockwise

09:10 moment is taken as negative. Let's look at this a bar with some forces acting downward.

09:25 We have the ACW there represent anticlockwise in this direction and the CW represent clockwise

09:35 in this direction. For instance, if we have something like this and if force is being applied here,

09:49 we expect. Let's assume this is a bar and someone is sitting on this side of the bar. We expect that

10:00 this bar will turn in the clockwise direction because if force is being exerted at the end of the

10:09 bar. So clockwise moments about O must be equal to anticlockwise moments about O for this bar

10:19 to balance horizontally. So for anything to be articulated from all the forces that are acting

10:27 or need must be zero. So it means the most balance for us to have an equilibrium.

10:34 Now let's look at what resultant moment is. When two more than two forces act on the body,

10:42 the resultant moment on the body about any point can be obtained using algebraic moment.

10:51 And using the clockwise moment and anticlockwise moments about the same point.

10:58 If the clockwise moment is taken as positive, then the anticlockwise are negative.

11:04 Like, let's assume this is the clock. This is the movement of the direction of the clock.

11:15 If it is moving in the other direction, that is anticlockwise. In the normal direction,

11:21 we have the clockwise direction. So we tend the normal direction of the clock as clockwise,

11:27 which is positive and the anticlockwise as negative. Then looking at this bar,

11:34 the clockwise moment about O is the midpoint of the bar.

11:51 O is the midpoint of the bar. So from distance here to distance here, we have X1.

12:00 And this is the force F1. Here we have F2 with a distance, this is X2.

12:16 So we are saying that the anticlockwise moment must be equal to the clockwise moment

12:25 for this particular bar to balance horizontally. If they are not equal,

12:30 there is no equilibrium at all. Now, how do we get our moment? We have F1.

12:40 F1, we said, the moment is force times the perpendicular distance. So the force times the distance

12:49 between the force and the fucrum. That is X1. So F1 times X1 must be equal to F2 times X2.

13:02 So those X, they are distances. They are distances covered. So if we have this

13:09 anticlockwise moment, we have F1 times X1 minus F2 times X2 must be equal to 0.

13:26 Let's look at the conditions of equilibrium under the action of Coplana forces.

13:32 Now what are Coplana forces? They are forces that lie in the same plane.

13:39 And parallel forces are forces whose lines of action are parallel to each other.

13:50 The conditions of equilibrium of Coplana parallel forces are, we have forces and moments.

13:58 Now the first one, forces. The algebraic sum of the forces acting on the body in any given

14:07 direction must be zero. In other words, the forces that are acting upward must be equal to the

14:16 forces that are acting downward for that body to be at equilibrium.

14:22 Then for that of moment, the algebraic sum of moments of all the forces about any point

14:32 on the body must be zero. That is, the total clockwise moment about a point must be equal to the

14:41 total anticlockwise moment about the same point. Now let's look at principle of moment.

14:52 The principle of moment states that if a body is in equilibrium, the sum of clockwise moments

15:02 about any point must be equal to the sum of the anticlockwise moment about the same point.

15:12 Examples now. Let's look at this. A 100-metre uniform road,

15:23 100-metre uniform road, as a load of 40 Newton suspended at 20 centimeters from one end.

15:34 If the full crew is at the center of gravity, calculate the force that must be applied at its

15:42 other end to keep it in horizontal equilibrium. Let's look at the diagram. We have

15:53 100-metre uniform road, now from zero to 100-metre. Now the full crew we're told is at the center of gravity.

16:07 The center of gravity here, looking at it, is 50. So if the full crew is here, that means that is 50.

16:18 Ah, the question says that a load of 40 Newton is suspended at 20 centimeters. So let's

16:27 assume this place is 20 centimeters. There is a load of 40 Newton. So suspended at that,

16:36 the full crew is at the center, calculate the force that must be applied in the other end. So we're

16:44 looking for the force that must be applied in this other end. We're looking for the force that

16:53 must be applied at the other end, I would say end, end, as the end, as the on-dread centimeter point.

17:03 Now based on the knowledge of movement, we say that movement is defined as the product of force

17:13 and the perpendicular distance. And we also say that the total clockwise movement must be equal to

17:20 the total anticlockwise movement. For you to answer this question, you must write that the sum of

17:32 the sum of clockwise must be equal to the sum of anticlockwise. Very important, for you to write that.

17:48 So let's look at it. Now this force times the distance between the force and the full crew.

17:55 We don't know the force, that's what we're looking for. Times, now the distance between the force and

18:01 the full crew is 50 on red minus 50. So the distance is 50, must be equal to the force here, that's 40,

18:15 times the distance between the force and the full crew here, that's 50 minus 20, which is 30.

18:24 So we can easily get our f to be 40 times 30 divided by 50. So f equal to

18:38 24 newton. So that means the force that should be applied at this other end for this particular

18:54 bar to balance, oh, must be 24 newton. Let's look at another one, a light rod,

19:05 a light rod, CD sits on a pivot, AB, a load of 30 newton hands at 4 meter from the pivot support

19:21 at A. Find the value of the reaction forces at A and B as shown. Let's look at the diagram.

19:28 So that's the diagram there. So we are looking for E, okay, the reaction forces at A and B as shown.

19:41 Now we have three forces acting. We have three forces acting on this road CD, force E, force F

19:56 and force 30 newton. Now we said that the conditions for crew planar forces to occur,

20:05 one of these forces. And we said that the total forces that are acting on the body

20:10 upward and downward, most balance up for that road to be in equilibrium. Definitely that means

20:18 our E, our E plus F must be equal to 30 newton. For that road to balance horizontally.

20:36 Good, so from condition of equilibrium of the parallel forces, total upwards force must be

20:42 called the total downward force. So let's say that equation is a equation one. Then using principle

20:50 of movements now, the total clockwise movement, equal the total anticlockwise movement and taking

20:58 movement about A, point A, this point A. Taking movement about point A, we can say that the force

21:11 times the distance between the force and A. The force is 30 times distance between 30 and A.

21:28 Is 6. This time between 30 and A is 6. Most be equal to another force, that's force F.

21:40 Times the distance between F and E or A. Then it's in point. This time between F and A,

21:53 we have 8 m plus 6 m and that's 14 m, force times distance. So we can easily get our F by making

22:07 the subduer formula, which is 30 times 6 divided by 14. So our F equal to 12.9 newton.

22:24 So our force F equal to 12.9 newton. Mind you, we derived an equation based on the law

22:37 that the sum of the forces acting upward must be equal to the sum of forces acting downward,

22:41 that is E plus F equal to 30. Now we have gotten our F. So very easy for us to get E. So therefore,

22:50 E plus F equal to 30. We have E plus 12.9 equal to 30.

23:07 E equal to 30 minus 12.9.

23:15 E equal to 30 minus 12.9.

23:32 That's 1, 7, 1, 17.1 to 17.1 newton. So that's our E. Very easy.

23:52 Now let's look at the evaluation questions. Distinguish number one, distinguish between

24:00 equilibrium and resultant forces. What is dynamic equilibrium?

24:08 State the conditions of equilibrium under the action of coplanar forces.

24:17 There is a calculation here. A metarule is balanced at 45 centimeter mark when the body of mass 50

24:24 gram is suspended at 80 centimeter mark. The balance point is found to be 25 centimeter mark.

24:32 Find the mass of the metarule. In this case, let me just give you an hint. The mass of the metarule

24:40 we are looking for weird because the mass of any body or any objects is at the center of that object

24:48 unlike the example that we did. Thank you for watching. My name is Mr. Bakari. Till next time.