One should begin by drawing a free-body diagram, a sketch showing all the forces acting on the supported object.

In calculations for tension, it is best to treat the supporting object -whether it be a rope, picture hook, horizontal strut or some other item -as though it were weightless. (Another way of saying this is that if the tension on the supporting object is equal to the weight it supports, then the supported object is in equilibrium.) One form of equilibrium calculation involves finding tension, or the force exerted by a supporting object on an object in equilibrium -a force that is always equal to the amount of weight supported. Using vector sums, it is possible to make a number of calculations for objects in equilibrium, but these calculations are somewhat more challenging than those in the car illustration. Calculating Force and Tension in Equilibrium By applying the Pythagorean theorem, which states that the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides, one quickly arrives at a figure of 7.07 m (11.4 km) in a northeasterly direction. Because the car traveled north 5 mi and ultimately moved east by 5 mi, returning to a position of 5 mi north, the segment from the resultant forms the hypotenuse of an equilateral (that is, all sides equal) right triangle. In this particular case, the answer is fairly easy.

Resulting shape is always one more than the number of vectors being added the final side is the resultant. Having drawn all the vectors, the only remaining one is between the point where the car's journey ends and the starting point -that is, the resultant. Each vector should be in the form of an arrow pointing in the appropriate direction. First, one draws the vectors on a piece of graph paper, using a logical system that treats the y axis as the north-south plane, and the x axis as the east-west plane. One must calculate its net displacement -in other words, not the sum of all the miles it has traveled, but the distance and direction between its starting point and its end point. Suppose, for instance, that a car travels north 5 mi (8 km), east 2 mi (3.2 km), north 3 mi (4.8 km), east 3 mi, and finally south 3 mi. This is the sum of the vectors, known as a resultant, which measures the net change. It would then be possible to draw a vector from the tail of the first to the head of the last. One would begin by representing each vector as an arrow on a graph, with the tail of each vector at the head of the previous one. The addition of vectors is more challenging, and usually requires drawing a diagram, for instance, if trying to obtain a vector sum for the velocity of a car that has maintained a uniform speed, but has changed direction several times. VECTOR SUMS.Īdding scalars is simple, since it involves mere arithmetic. Force may be in any direction, but the direction of weight is always downward along a vertical plane. So too is weight, a specific type of force equal to mass multiplied by the acceleration due to gravity (32 ft or / sec 2). By contrast, force, equal to mass multiplied by acceleration, is a vector. This might seem odd at first glance, but -on Earth at least, and outside any special circumstances posed by quantum mechanics -time can only move forward. Not only are mass and speed (as opposed to velocity) considered scalars so too is time. On the other hand, if someone or something experiences a displacement, or change in position, of 1 mi to the northeast, then what was a scalar description has been placed in the language of vectors.

Nor is there a directional component involved in the act of moving the distance of 1 mi (1.6 km), since no statement has been made as to the direction of that mile. If one says that a certain piece of property has an area of one acre, there is no directional component. By contrast, a scalar has only magnitude. HOW IT WORKS Equilibrium and VectorsĮssential to calculations in statics is the use of vectors, or quantities that have both magnitude and direction. Statics is also applied in analysis of stress on materials -from a picture frame to a skyscraper. Among the topics of significance in the realm of statics is center of gravity, which is relatively easy to calculate for simple bodies, but much more of a challenge where aircraft or ships are concerned. Those bodies may be acted upon by a variety of forces, but as long as the lines of force meet at a common point and their vector sum is equal to zero, the body itself is said to be in a state of equilibrium. Statics, as its name suggests, is the study of bodies at rest.

Equilibrium 3d statics