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ilikephysics2
Group Title
for a spherical object what is its mass in terms of the density of the material, its diameter and any necessary constants?
 2 years ago
 2 years ago
ilikephysics2 Group Title
for a spherical object what is its mass in terms of the density of the material, its diameter and any necessary constants?
 2 years ago
 2 years ago

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lgbasallote Group TitleBest ResponseYou've already chosen the best response.2
well volume of a sphere is \[\frac 43 \pi r^3\]
 2 years ago

lgbasallote Group TitleBest ResponseYou've already chosen the best response.2
and then density = mass/volume
 2 years ago

UnkleRhaukus Group TitleBest ResponseYou've already chosen the best response.2
\[\rho=\frac mV\] \[m=V\rho\]
 2 years ago

lgbasallote Group TitleBest ResponseYou've already chosen the best response.2
so you have \[m = \frac 43\rho \pi r^3\]
 2 years ago

lgbasallote Group TitleBest ResponseYou've already chosen the best response.2
where \(\rho\) = density
 2 years ago

ilikephysics2 Group TitleBest ResponseYou've already chosen the best response.0
what about its diameter
 2 years ago

lgbasallote Group TitleBest ResponseYou've already chosen the best response.2
change r to d/2
 2 years ago

UnkleRhaukus Group TitleBest ResponseYou've already chosen the best response.2
and \(r\) is the radius (half the diameter) \(r=\frac d2\)
 2 years ago

lgbasallote Group TitleBest ResponseYou've already chosen the best response.2
radius = diameter/2 so just change r to d/2
 2 years ago

ilikephysics2 Group TitleBest ResponseYou've already chosen the best response.0
ok so thats the final solution?
 2 years ago

lgbasallote Group TitleBest ResponseYou've already chosen the best response.2
replace r with d/2....
 2 years ago

ilikephysics2 Group TitleBest ResponseYou've already chosen the best response.0
ok cool and can i give you guys both metals or does just one of you get it?
 2 years ago

ilikephysics2 Group TitleBest ResponseYou've already chosen the best response.0
hey so its (4/3)p(pi)(d/2)^3
 2 years ago

ilikephysics2 Group TitleBest ResponseYou've already chosen the best response.0
is that right?
 2 years ago

UnkleRhaukus Group TitleBest ResponseYou've already chosen the best response.2
you can simplify the numbers a bit
 2 years ago

ilikephysics2 Group TitleBest ResponseYou've already chosen the best response.0
unkle...it won't let me give you a metal now
 2 years ago

ilikephysics2 Group TitleBest ResponseYou've already chosen the best response.0
why cant i give it to both of you
 2 years ago

UnkleRhaukus Group TitleBest ResponseYou've already chosen the best response.2
i dont mind about that
 2 years ago

UnkleRhaukus Group TitleBest ResponseYou've already chosen the best response.2
\[m=\frac43\rho\pi\left(\frac d2\right)^3\] use \[\left(\frac{a}{b}\right)^n=\frac {a^n} {b^n}\]
 2 years ago

ilikephysics2 Group TitleBest ResponseYou've already chosen the best response.0
so it simplifies to 4p(pi)(d/2)?
 2 years ago

ilikephysics2 Group TitleBest ResponseYou've already chosen the best response.0
i crossed out the 3's
 2 years ago

lgbasallote Group TitleBest ResponseYou've already chosen the best response.2
what he meant was distribute the exponent
 2 years ago

UnkleRhaukus Group TitleBest ResponseYou've already chosen the best response.2
you can not cancel an index with denominator like that
 2 years ago

ilikephysics2 Group TitleBest ResponseYou've already chosen the best response.0
oh so whats it turn to?
 2 years ago

UnkleRhaukus Group TitleBest ResponseYou've already chosen the best response.2
\[\left(\frac{a}{b}\right)^n=\frac {a^n} {b^n}\] \[\left(\frac{d}{2}\right)^3=\frac {d^3} {2^3}\]
 2 years ago

ilikephysics2 Group TitleBest ResponseYou've already chosen the best response.0
thanks :)
 2 years ago

UnkleRhaukus Group TitleBest ResponseYou've already chosen the best response.2
can you simplify the numbers in the equation now?
 2 years ago

ilikephysics2 Group TitleBest ResponseYou've already chosen the best response.0
yes (4/3)p(pi)(d^3/8) ?
 2 years ago

lgbasallote Group TitleBest ResponseYou've already chosen the best response.2
you can simplify it further
 2 years ago

lgbasallote Group TitleBest ResponseYou've already chosen the best response.2
you can multiply the denominators
 2 years ago

ilikephysics2 Group TitleBest ResponseYou've already chosen the best response.0
so 4p(pi)(d/8) ? ?
 2 years ago

lgbasallote Group TitleBest ResponseYou've already chosen the best response.2
what happened?
 2 years ago

ilikephysics2 Group TitleBest ResponseYou've already chosen the best response.0
can you simplify it?
 2 years ago

lgbasallote Group TitleBest ResponseYou've already chosen the best response.2
you canceled the denominaotr and teh exponent???
 2 years ago

ilikephysics2 Group TitleBest ResponseYou've already chosen the best response.0
it can't be simplified?
 2 years ago

lgbasallote Group TitleBest ResponseYou've already chosen the best response.2
it can...you just simplified it wrong....multiply the denominators
 2 years ago

lgbasallote Group TitleBest ResponseYou've already chosen the best response.2
don't touch anything else
 2 years ago

ilikephysics2 Group TitleBest ResponseYou've already chosen the best response.0
so it (4/24)p(pi)(d^3) ?
 2 years ago

UnkleRhaukus Group TitleBest ResponseYou've already chosen the best response.2
thats better!
 2 years ago

lgbasallote Group TitleBest ResponseYou've already chosen the best response.2
yes. now express 4/24 in lowest terms
 2 years ago

ilikephysics2 Group TitleBest ResponseYou've already chosen the best response.0
ok so 1/6 p(pi)(d^3) ? thats final!!!!
 2 years ago

lgbasallote Group TitleBest ResponseYou've already chosen the best response.2
right!!
 2 years ago

lgbasallote Group TitleBest ResponseYou've already chosen the best response.2
your turn @UnkleRhaukus
 2 years ago

UnkleRhaukus Group TitleBest ResponseYou've already chosen the best response.2
\[\color{red}\checkmark\]
 2 years ago

UnkleRhaukus Group TitleBest ResponseYou've already chosen the best response.2
so the constants necessary to express the volume in terms of diameter are ; the natural number; 6 the density of the material rho; \(\rho\) the geometrical constant pi; \(\pi\) the diameter of the sphere \(d\) and the dimensional constant \(3\)
 2 years ago
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