In summary, the conversation discusses a problem involving an expression that depends on a variable, while the given answer only provides a concrete number. The question asks why the assumption of constant dr/dt was made, and the answer explains that it is due to the constant volume flow rate. The conversation also mentions rearranging the expression to solve for dr/dt, which leads to the answer for part (b) and helps explain the behavior in part (c). Finally, the conversation suggests calculating dV/dr and using it to inform the answer.
#1
Idan9988
9
0
Homework Statement
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Relevant Equations
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I'm struggling with section a. This is my calculation:
The expression remains depend on the variable t, while in the answer is a concrete number:
[itex]r = r_0 + 0.9t[/itex] is only valid if [itex]dr/dt[/itex] is constant.
Why did you assume that [itex]dr/dt[/itex] was constant? The question only tells you that [itex]dr/dt = 0.900\,\mathrm{cm}/\mathrm{s}[/itex] when [itex]r = 6.50\,\mathrm{cm}[/itex].
#3
harveysnaf
2
2
Agree,
The answer (a) has all the information. Since the volume flow rate is constant, then ##\frac {dV}{dt}## is a constant.
##\frac {dr}{dt}## is variable.
If you rearrange the expression to solve for ##\frac {dr}{dt}## and you get the answer to (b) and the behavior that explains (c).