A body falling in a relatively dense fluid, oil for example, is acted on by three forces: the weight W due to gravity (acting downwards), a resistence force R and a bouyant force B (both actin upwards). The wieght W of the object of mass m is mg. The bouyant force B is equal to the weight of the fluid displaced by the object. If the mass of the fluid is mf,this force is B=mf*g. For a slowly moving spherical body of radius, r, the resistive force is given by stokes law;R=6*pi*mu*r*v, where v is the velocity of the body and mu is the coefficient of viscosity of the surrounding fluid.
a) what is the differential equation for the velocity that the object has at any given time t
b) if the product 6*pi*mu is equal to 3.2, the mass of the spherical object of radius 0.05 meters is 0.5kg adn the mass of the fluid is 0.1kg, solve the differential equation from part a
c) find teh velocity 5 seconds after the object is dropped with the initial velocity of 0;3 meters per second© BrainMass Inc. brainmass.com October 25, 2018, 1:44 am ad1c9bdddf
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Real Life Applications of Complex or Imaginary Numbers
When solving a quadratic equation using the quadratic formula, it is possible for the b2 - 4ac term inside the square root (the discriminant) to be negative, thus forcing us to take the square root of a negative number. The solutions to the equation will then be complex numbers (i.e., involve the imaginary unit i).
In the real world, where might these so-called imaginary numbers be used?
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