General chemistry problem about asbestos.?
Asbestos is a fibrous silicate mineral with remarkably high tensile strength. But it is no longer used
because airborne asbestos particles can cause lung cancer. Grunerite, a type of asbestos, has a tensile
strength of3.5><10^2 kg/mm^2 (thus, a strand of grunerite with a 1-mm^2 cross-sectional area can hold up to
3.5*10^2 k g). The tensile strengths of aluminum and Steel No . 5137 are 2.5*10^4 lb/in^2 and 5 .0*10^4 lb/in^2, respectively. Calculate the cross-sectional area (in mm^2 ) of wires of aluminum and of Steel No.
5137 that have the same tensile strength as a fiber of grunerite with a cross-sectional area of 1.0 µm^2.
Comments
so.. this is basically just a conversion problem.. And conversions are best done by what technique? that's right "factor label method".. aka.. "Dmensional analsis"
and we apply DA like this
(1).. sort through the problem and identify the "FROM" quantity, the "TO" quantity and all the unit factors
(2).. start with the "from" on the left and convert to the right by multiplying by the appropriate unit factors
(3).. make sure your unit factors have at least as many sig figs as the "from".
(4).. double check to make sure the units cancel properly and are correct before doing all the calcs.
here we go
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and let's use these abbreviations
grun = grunerite
Al = aluminum
st = steel 5137
from:... .1.0μm² grun
to:... ... ..um² Al and μm² st
unit factors given in the problem statement:..
(3.5x10² kg grun /mm² grun)
(2.5x10^4 lb Al / in² Al)
(5.0x10^4 lb st / in² st)
and here's the conversions:
to Al.....
1.0 μm² grun x (1mm / 1000μm)² x (3.5x10² kg grun / mm² grun) x (1 lb / 0.45359 kg) x (1lb Al / 1lb grun) x (1in² Al / 2.5x10^4lb Al) x (25.4mm / 1in)² = 2.0x10^-5 mm²
to st....
1.0 μm² grun x (1mm / 1000μm)² x (3.5x10² kg grun / mm² grun) x (1 lb / 0.45359 kg) x (1lb Al / 1lb grun) x (1in² Al / 5.0x10^4lb Al) x (25.4mm / 1in)² = 1.0x10^-5 mm²
enter...
1 / 1000² x 3.5e2 / 0.45359 / 2.5e4 x 25.4² =
and
1 / 1000² x 3.5e2 / 0.45359 / 5e4 x 25.4² =
*****
make sense or no? the key is to set the strength of al and st to strength of grunerite. that's the 1lb al / 1lb grun) unit factor.
Grunerite