The translational equilibrium It is a state in which an object as a whole is found when all the forces acting on it are compensated, resulting in a zero net force. Mathematically equivalent to saying that F1+ Ftwo + F3 +…. = 0, where F1, Ftwo, F3... the forces involved.
The fact that a body is in translational equilibrium does not mean that it is necessarily at rest. This is a particular case of the definition given above. The object may be in motion, but in the absence of acceleration, this will be a uniform rectilinear motion.
So if the body is at rest, it continues like this. And if it already has movement, it will have constant speed. In general, the motion of any object is a composition of translations and rotations. Translations can be as shown in figure 2: linear or curvilinear.
But if one of the object's points is fixed, then the only chance it has to move is to rotate. An example of this is a CD, whose center is fixed. The CD has the ability to rotate around an axis that passes through that point, but not to translate.
When objects have fixed points or are supported on surfaces, we speak of links. The links interact limiting the movements that the object is capable of making.
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For a particle in equilibrium it is valid to ensure that:
FR = 0
Or in summation notation:
It is clear that for a body to be in translational equilibrium, the forces acting on it must be compensated in some way, so that their resultant is zero..
In this way, the object will not experience acceleration and all its particles are at rest or undergoing rectilinear translations with constant speed..
Now if objects can rotate, they generally will. That is why most of the movements consist of combinations of translation and rotation..
When rotational balance is important, it may be necessary to ensure that the object does not rotate. Then you have to study if there are torques or moments acting on it.
Torque is the vector magnitude on which the rotations depend. It requires a force to be applied, but the point of application of the force is also important. To clarify the idea, consider an extended object on which a force acts F and let's see if it is capable of producing a rotation about some axis O.
It is already intuited that when pushing the object at point P with the force F, it is possible to rotate it around point O, with a counterclockwise rotation. But the direction in which the force is applied is also important. For example, the force applied to the figure in the middle will not make the object rotate, although it can certainly move it..
Applying force directly to point O will not turn the object either. So it is clear that to achieve a rotational effect, the force must be applied at a certain distance from the axis of rotation and its line of action must not pass through said axis..
The torque or moment of a force, denoted as τ, the vector magnitude in charge of putting all these facts together, is defined as:
τ = r x F
The vector r it is directed from the axis of rotation to the point of application of the force and the participation of the angle between r and F is important. Therefore, the magnitude of the torque is expressed as:
τ = r.F.sen what
The most effective torque occurs when r Y F they are perpendicular.
Now, if it is desired that there are no rotations or these take place with constant angular acceleration, it is necessary that the sum of the torques acting on the object is zero, analogously to what was considered for the forces:
Balance means stability, harmony and balance. For the movement of an object to have these characteristics, the conditions described in the previous sections must be applied:
1) F1+ Ftwo + F3 +…. = 0
2) τ1+ τtwo + τ3 +…. = 0
The first condition guarantees translational equilibrium and the second, rotational equilibrium. Both must be met if the object is to remain in static equilibrium (absence of movement of any kind).
Equilibrium conditions are applicable to many structures, since when buildings or diverse objects are built, it is done with the intention that their parts remain in the same relative positions with each other. In other words, that the object does not disassemble.
This is important for example when building bridges that remain firm underfoot, or when designing habitable structures that do not change position or have a tendency to tip over..
Although it is believed that uniform rectilinear motion is an extreme simplification of motion, which rarely occurs in nature, it must be remembered that the speed of light in vacuum is constant, and that of sound in air, too, if consider the medium homogeneous.
In many man-made mobile structures it is important that a constant speed is maintained: for example, on escalators and assembly lines.
This is the classic exercise of the tensions that hold the lamp in balance. The lamp is known to weigh 15 kg. Find the magnitudes of the stresses necessary to hold it in this position.
To solve it, we focus on the knot where the three strings meet. The respective free-body diagrams for the node and for the lamp are shown in the figure above..
The weight of the lamp is W = 5 Kg. 9.8 m / stwo = 49 N. For the lamp to be in equilibrium, it is sufficient that the first equilibrium condition is fulfilled:
T3 - W = 0
T3 = W = 49 N.
Tensions T1 Y Ttwo must decompose:
T1y + T2 and - T3 = 0 (Sum of forces along the y-axis)
-T1x +T2x = 0 (Sum of forces along the x axis)
Applying trigonometry:
T1.cos 60º + Ttwo .cos 30º = 49
- T1.sen60º + Ttwo.sin30º = 0
It is a system of two equations with two unknowns, whose answer is: T1 = 24.5 N Y Ttwo = 42.4 N.
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