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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

UnkleRhaukus
 2 years ago
Best ResponseYou've already chosen the best response.2so 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 \(3\)
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