Find the particle's horizontal position x(t) and velocity v(x) at any point in a fluid whose drag force is expressed as Fdrag - kmv where, k is a constant, m is the mass of the particle and v is its velocity. Consider that the particle is initially traveling with a velocity vo.
Find the particle's horizontal position x(t) and velocity v(x) at any point in a fluid whose drag force is expressed as Fdrag - kmv where, k is a constant, m is the mass of the particle and v is its velocity. Consider that the particle is initially traveling with a velocity vo.
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Transcribed Image Text:Find the particle's horizontal position x(t) and velocity v(x) at any point in a fluid whose drag force is expressed as
Fdrag = kmv
where, k is a constant, m is the mass of the particle and v is its velocity. Consider that the particle is initially traveling with a velocity vo.
Solution:
a) To solve for the position as a function of time x(t), we construct the net force in the x-axis as
E F--F
= ma
Then:
-m 4
V = m a
since:
a =
dv/dt
then
-m
V = m dett
by integrating, we obtain the following expression:
voe
Further, employing the rules of integration results to the following expression for position as a function of time
x= (vo/ o
1
as t+ 00, the position becomes
x = vo/k
b) To solve for the velocity as a function of position v(x), we construct the net force in the x-axis as follows
E F=-F
= m e
Then:
-m R
Transcribed Image Text:since:
a = dv/dt
then
-m k
V = m dertet
We can eliminate time by expressing, the velocity on the left side of the equation as
v = dx/dt
Then, we arrive at the following expression
= -k
By integrating and applying the limits, we arrive at the following
= vo-||
which, sows that velocity decreases in a linear maner.
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