resultant

Examples of resultant in the following topics:

• Superposition of Fields

  • The resultant of multiple electric fields acting on the same point is the sum of the strength of each field's applied force at that point.
  • For example, if forces A and B are constant and simultaneously act upon an object, illustrated as O in , the resultant force will be the sum of forces A and B.
  • Vector addition is commutative, so whether adding A to B or B to A makes no difference on the resultant vector; this is also the case for subtraction of vectors.
  • An overall resultant vector can be found by using the Pythagorean theorem to find the resultant (the hypotenuse of the triangle created with applied forces as legs) and the angle with respect to a given axis by equating the inverse tangent of the angle to the ratio of the forces of the adjacent and opposite legs.
  • Their sum is commutative, and results in a resultant vector c.

• Forces in Two Dimensions

  • For example, when determining what happens when two forces act on the same object, it is necessary to know both the magnitude and the direction of both forces to calculate the result.
  • In this simple one-dimensional example, without knowing the direction of the forces it is impossible to decide whether the net force is the result of adding the two force magnitudes or subtracting one from the other.
  • When two forces act on a point particle, the resulting force or the resultant (also called the net force) can be determined by following the parallelogram rule of vector addition: the addition of two vectors represented by sides of a parallelogram gives an equivalent resultant vector which is equal in magnitude and direction to the transversal of the parallelogram.
  • The magnitude of the resultant varies from the difference of the magnitudes of the two forces to their sum, depending on the angle between their lines of action.

• Diffusion

  • A distinguishing feature of diffusion is that it results in mixing or mass transport without requiring bulk motion.
  • The result of diffusion is a gradual mixing of material.
  • In a phase with uniform temperature, absent external net forces acting on the particles, the diffusion process will eventually result in complete mixing.
  • Discuss the process and results of diffusion, identifying factors that affect its rate

• Superposition and Interference

  • A wave may have a complicated shape that can result from superposition and interference of several waves.
  • Most waves appear complex because they result from several simple waves adding together.
  • If the disturbances are along the same line, then the resulting wave is a simple addition of the disturbances of the individual waves—that is, their amplitudes add.
  • As a result of superposition of waves, interference can be observed.
  • These waves result from the superposition of several waves from different sources, producing a complex pattern.

• Surface Tension

  • The tendency of the surface of a liquid to resist a force and behave like a membrane and is a result of cohesion between liquid molecules.
  • This effect is a result of cohesion of the molecules of the liquid causing the surface of the liquid to contract to the smallest area possible.
  • This results in a contact angle at the interface.
  • If the cohesive forces are greater than the adhesive forces, the resulting contact angles will be large and will form a more circular drop .
  • The contact angle is the angle, measured in the fluid, that results when a liquid-gas interface, meets a solid surface.

• Order to Disorder

  • The result is water at an intermediate temperature of 30.0º C.
  • Three outcomes have resulted:
  • Let us think about each of the results.
  • These three results—entropy, unavailability of energy, and disorder—are not only related but are in fact essentially equivalent.

• Interference

  • In physics, interference is a phenomenon in which two waves (passing through the same point) superimpose to form a resultant wave of greater or lower amplitude.
  • In constructive interference, the two amplitudes of the waves add together and result in a higher displacement than would have been the case if there were only one wave.
  • Destructive interference is when two waves add together and the result is a smaller displacement than would have been the case.
  • When the waves have opposite amplitudes at the point they meet they can destructively interfere, resulting in no amplitude at that point.

• Pressure in the Body

  • Blood can be regarded as a viscous liquid contained within the circulatory system that travels throughout this closed system as a result of pressure and pressure differences within the circulatory system.
  • Pressure differences between the lungs and the atmosphere create a potential for air to enter the lungs, resulting in inhalation.
  • The mechanism resulting in inhalation is due to lowering of the diaphragm, which increases the volume of the thoracic cavity surrounding the lungs, thus lowering its pressure as determined by the ideal gas law.
  • As the diaphragm restores and moves upwards, pressure within the thoracic cavity increases, resulting in exhalation.
  • The cycle repeats itself, resulting in the respiration which as discussed is mechanically due to pressure changes.

• Enhancement of Microscopy

  • The resultant, magnified image is then seen by the eye.
  • Dispersion staining: This results in a colored image of a colorless object; it does not actually require that the object be stained.
  • Since electron beams have a much smaller wavelength than traditional light, the resolution of the resulting image is much higher.

• Adding and Subtracting Vectors Using Components

  • To find the resultant vector, simply place the tail of the vertical component at the head (arrow side) of the horizontal component and then draw a line from the origin to the head of the vertical component.
  • This new line is the resultant vector.
  • Then draw the resultant vector as you did in the previous part.