Thursday, July 8, 2010

The density of ball bearings and oil?

Can someone calculate these densities because I always seem to get a wrong answer.



1) A ball bearing of radius 12.68mm and a mass of 66g

2) A ball bearing of radius 9.95mm and a mass of 27.97g

3) Oil of 200ml and a mass of 264g
density is just mass/volume



1) the volume of a sphere is 4/3 * Pi* r^3... convert 12.68mm to m: 0.01268m. 66g = 0.066kg

V = 4/3 * Pi* 0.01268^3

=8.535 * 10^-6 m^3



density = 0.066/8.535 * 10^-6

=7732.461 kg/m^3



2) same deal. remember to convert masses and volumes

V = 4.124 *10^-6



density = 0.02797/4.124 *10^-6

=6781.954 kg/m^3



3)here, the volume is in mL

200mL = 0.2L



otherwise everything is the same



density = 0.264/0.2

=1.32 kg/L



there are also 1000L per m^3

so it could also be 1320 kg/m^3
For sphere

Volume=4/3(p*r^3)

density=mass/volume



And ml is a unit of liquid.
A sphere has a volume of (4/3) (r^3)



You wish to have volumes in units of cm^3



1) v=(4/3)(3.1415)(1.268^3)



=8.54 cm^3



density = m/v = 66/8.54 = 7.73 g/(cm^3)



2) v=(4/3)(3.1415)(0.995^3)



=4.13 cm^3



density = m/v = 27.97/4.13 = 6.77 (g/cm^3)



3) 1 ml = 1 cm^3



density = m/v = 264/200 = 1.32 g/(cm^3)

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