por He translational balance It is a state that an object as a whole is in when all the forces acting on it balance out, resulting in a zero net force. Mathematically it is equivalent to saying that F1+ F2 + F3 +…. = 0, where F1, F2, F3… are 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 movement of any object is a composition of translations and rotations. The translations can be as shown in figure 2: linear or curvilinear.
But if one of the points of the object is fixed, then the only possibility for it 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 by limiting the movements that the object is capable of making.
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Determination of translational balance
For a particle in equilibrium it is valid to ensure that:
RF = 0
Or in summation notation:
It is clear that for a body to be in translational equilibrium, the forces that act 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 usually will. That is why most of the movements consist of combinations of translation and rotation.
Rotation of an object
When rotational balance is important, you may need to ensure that the object does not rotate. Then it is necessary to study if there are torques or moments acting on it.
Torque is the vector magnitude on which 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 by pushing the object at point P with the force F, it is possible to make it rotate around point O, with counterclockwise rotation. But the direction in which the force is applied is also important. For example, the force applied in the middle figure will not be able to make the object rotate, although it certainly can move it.
Applying the force directly at point O will not serve to rotate the object either. Then it is clear that to achieve a rotation 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.
torque definition
The torque or moment of a force, denoted as τ, the vector magnitude responsible for putting all these facts together, is defined as:
τ=r xF
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 = rFsin what
The most effective torque occurs when r and F they are perpendicular.
Now, if it is desired that there are no rotations or that they occur with constant angular acceleration, it is necessary that the sum of the torques acting on the object be null, in a similar way to what was considered for the forces:
equilibrium conditions
Equilibrium 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+ F2 + F3 +…. = 0
2) τ1+ τ2 + τ3 +…. = 0
The first condition guarantees translational equilibrium and the second the rotational one. Both must be true if the object is to remain in static balance (absence of movement of any kind).
Applications
Equilibrium conditions are applicable to numerous structures, since when buildings or various 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 fall apart.
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 the uniform rectilinear movement is an extreme simplification of the movement, which rarely occurs in nature, it must be remembered that the speed of light in a vacuum is constant, and that of sound in air too, if we The medium is considered homogeneous.
In many man-made moving structures it is important that a constant speed be maintained: for example, on escalators and assembly lines.
Translational Equilibrium Examples
This is the classic exercise of the tensions that hold the lamp in balance. It is known that the lamp weighs 15 kg. Find the magnitudes of the stresses required to hold it in this position.
Solution
To solve it, we focus on the knot where the three strings meet. The respective free body diagrams for the knot and for the lamp are shown in the figure above.
The weight of the lamp is W = 5kg. 9.8 m/s2 = 49N. For the lamp to be in equilibrium, it is enough that the first equilibrium condition is fulfilled:
T3–W=0
T3 = W = 49 N.
tensions T1 and T2 should break down:
T1y + T2y – T3 = 0 (Summation of forces along the y-axis)
–T1x +T2x = 0 (Summation of forces along the x-axis)
Applying trigonometry:
T1.cos 60º +T2 .cos 30º = 49
– T1.sin60º +T2.sin30º = 0
It is a system of two equations with two unknowns, whose answer is: T1 = 24.5N and T2 =42.4N.
References
Rex, A. 2011. Fundamentals of Physics. pearson. 76-90. Serway, R., Jewett, J. (2008). Physics for Science and Engineering. Volume 1. 7th. Ed. Cengage Learning. 120 – 124. Serway, R., Vulle, C. 2011. Fundamentals of Physics. 9th Ed. Cengage Learning. 99-112. Tippens, P. 2011. Physics: Concepts and Applications. 7th Edition. MacGraw Hill. 71 – 87. Walker, J. 2010. Physics. Addison Wesley. 332 -346.