- #1

lichenguy

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## Homework Statement

A block of mass ##m = 1.00 kg## is being dragged through some viscous fluid by

an external force ##F = 10.0 N##. The resistive force can be written as ##R = -bv##,

where ##v## is the speed and ##b = 4.00 kg/s## is a phenomenological constant. You

may ignore gravity (we imagine that the block is floating inside the fluid). The

following integrals may come in handy:

$$\int \frac 1 { z } dz = ln(z), \int e^{-at} dt = \frac 1 a e^{-at}$$

a) Using the three physical quantities provided, use dimensional analysis to

find the terminal velocity of the motion ##v_T## and the characteristic time ##τ## .

b) Assuming that the block starts from rest, find ##v(t)##.

c) Find the distance traveled as a function of time ##x(t)##.

Some of the work done by the force F on the system becomes internal energy,

some becomes kinetic energy.

d) How much internal energy has been generated by the time the

block reaches half the terminal velocity, ##v(t) = v_T/2##? How big a fraction of

the total work is that?

## The Attempt at a Solution

##m=M##

##F=\frac {ML} {T^2}##

##R=-\frac {LM} {T^2}##

##v_T = \frac L T = m^aF^bR^c##

##M=0=a+b+c##

##L=1=b+c##

##T=-1=-2b-2c##

This doesn't work. So I'm kinda stuck.

I also don't know what is meant by "characteristic time".

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