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Metal block sliding horizontally

  • Thread starter majinsock
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  • #1
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Homework Statement


A metal block of mass m slides on a horizontal surface that has been lubricated
with a heavy oil so that the block suffers a viscous resistance that varies as the 3/2
power of the speed: F(v) = -cv3/2

If the initial speed of the block is vo at x = 0, show that the block cannot travel farther than 2mvo1/2/c


Homework Equations


F = ma = m[itex]\frac{dv}{dt}[/itex]



The Attempt at a Solution


So, I took

m[itex]\frac{dv}{dt}[/itex] = -cv3/2
I rearranged it and got

dv/v3/2= [itex]\frac{-c}{m}[/itex]dt

I've tried integrating this and I can't seem to end up with the right answer. I'm totally lost. Anyone have any ideas?

EDIT: No help at all?
 
Last edited:

Answers and Replies

  • #2
UltrafastPED
Science Advisor
Gold Member
1,912
216
You are not integrating wrt the correct variables; you need dx, not dt.

Use the chain rule to write dv/dt = dv/dx dx/dt = dv/dx v.

Then when you rearrange the terms you will be integrating dv/sqrt(v) = -c/m dx
The integrals run (v0, v_final) and (0, d); if we carry the integral to v_final = 0 then the distance covered will be d_final.

When I do this I get 2m/c sqrt(v0) = d_final, which supports the expected conclusion.
 
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