Balance

Balance without friction

If several forces work on the given body, it can happen that their work compensate in a way not to make any influence on the motion. In that case we can say that the body is in balance. The balance of the body, when  under work of outer forces is somewhat broader that 1. Newton law, since the uniform circular motion is included. 

The conditions for the balance

If we want to have balance of the body, it not enough that several forces work on the given body, but it is also necessary to that those forces work in the same direction. Observe now three forces which work in the same plane and which are unparallel: F1, F2, F3. Point of application of the force that works on the rigid body can be moved freely on the line on which the force is working. In that way points of application of the forces F1 and F2 can always be brought into the same point (as two straight lines always cross) and the forces F1 and F2 can be exchanged for their resultant R (picture - page 115). Now we have the action of only two forces R and F3. The balance will be obtained if forces R and F3 are equal and act in the same direction.

The first condition of the balance is: (sigma)Fx=0.

The second condition of the balance is: Mz=0 (the sum of the moment of the force must be equal to 0).

The kinds of balance

When the body that is in the state of balance is slightly moved from the balance position, the size and direction of the forces that act can be changed. If the work of the forces in the changed position is so that the body is moved into the initial position, we can say that the balance is stable. If, in opposite, forces work so that the position makes the body more out of balance that we can say that balance is labile. If the body in other case, being moved, keeps in balance then we can say that the balance is indifferent.

The example of the all those kinds of balance is shown on the picture. Cone put on it's base is in the stable balance (a). The cone put on it's peak is in labile balance (b). The cone put on it's side is in the indifferent balance (c).

The balance in the presence of friction

Whenever it happens that the surface of one body is gliding over the other body, each of those bodies act to the other one with the friction force, which act in the direction parallel to the touch of the surfaces and opposite to the direction of the body movement. We can observe the forces which act on the cube laid on the horizontal surface. (picture - page 121.). The weight of the cube G and work of the surface P on the cube are annulled and the cube is in balance. We can now tie the cube with the thin thread and pull the thread slightly, in a manner not to move the cube. As the body is still in balance, three forces P, G and T (the tension of the thread) must annul, in other words, P must have the horizontal component equal and of the opposite direction to the tension T. So the force is in this case leaned left and not vertical like in the preceding case. The component of the force P parallel to the surface  will be called the force of the static friction fs. The vertical component of the force P, marked as N is  the normal component of the force acting on the cube itself. We can so see that the surface acts on the cube by the force n (equal to the weight of the body) and force fs, which acts parallel to the surface in the direction opposite to the tension of the thread. The resultant force P is leaned oppositely to the direction of the acting of the thread tension.

If we enlarge the tension of the thread, in other words if we pull stronger, we will reach a critical point Tk, at which the cube will be moved. In other words, the static friction fs can reach a critical value above which it can not raise any more, so the acting of the thread tension will be stronger.