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so i got a block with mass=m traveling on an oiled surface. the block suffers a viscous resistance given:
[tex] F(v)= -cv^{3/2} [/tex]
the initial speed of the block is [tex] v_{o} [/tex] at x=0, i have to show that the block cannot travel farther than [tex] 2mv_{o}^{1/2} /c [/tex]
so far i have;
[tex] ma=-cv^{3/2} [/tex]
[tex] m \frac{dv}{dx} \frac{dx}{dt} = -cv^{3/2} [/tex]
[tex] mvdv=-cv^{3/2} dx [/tex]
[tex] dx= \frac {mvdv}{cv^{3/2}} [/tex]
where should i go from here?
[tex] F(v)= -cv^{3/2} [/tex]
the initial speed of the block is [tex] v_{o} [/tex] at x=0, i have to show that the block cannot travel farther than [tex] 2mv_{o}^{1/2} /c [/tex]
so far i have;
[tex] ma=-cv^{3/2} [/tex]
[tex] m \frac{dv}{dx} \frac{dx}{dt} = -cv^{3/2} [/tex]
[tex] mvdv=-cv^{3/2} dx [/tex]
[tex] dx= \frac {mvdv}{cv^{3/2}} [/tex]
where should i go from here?