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In physics and engineering, a free body diagram (FBD; also called a force diagram) [1] is a graphical illustration used to visualize the applied forces, moments, and resulting reactions on a free body in a given condition. It depicts a body or connected bodies with all the applied forces and moments, and reactions, which act on the body(ies).
An object resting on a surface and the corresponding free body diagram showing the forces acting on the object. The normal force N is equal, opposite, and collinear to the gravitational force mg so the net force and moment is zero. Consequently, the object is in a state of static mechanical equilibrium.
In chemistry, the lever rule is a formula used to determine the mole fraction (x i) or the mass fraction (w i) of each phase of a binary equilibrium phase diagram.It can be used to determine the fraction of liquid and solid phases for a given binary composition and temperature that is between the liquidus and solidus line.
Iron-55 (55 Fe) is a radioactive isotope of iron with a nucleus containing 26 protons and 29 neutrons. It decays by electron capture to manganese-55 and this process has a half-life of 2.737 years. The emitted X-rays can be used as an X-ray source for various scientific analysis methods, such as X-ray diffraction .
There is an algorithm to compute the linking number of two curves from a link diagram. Label each crossing as positive or negative, according to the following rule: [1] The total number of positive crossings minus the total number of negative crossings is equal to twice the linking number. That is:
In quantum mechanics, for systems where the total number of particles may not be preserved, the number operator is the observable that counts the number of particles. The following is in bra–ket notation : The number operator acts on Fock space .
The latter tend to be rather more unstable than iron(II) complexes and often dissociate in water. Many Fe–O complexes show intense colors and are used as tests for phenols or enols. For example, in the ferric chloride test, used to determine the presence of phenols, iron(III) chloride reacts with a phenol to form a deep violet complex: [71]
The goal of modal analysis in structural mechanics is to determine the natural mode shapes and frequencies of an object or structure during free vibration.It is common to use the finite element method (FEM) to perform this analysis because, like other calculations using the FEM, the object being analyzed can have arbitrary shape and the results of the calculations are acceptable.