What is the significance of using a number like 2x10-10 in Intro Physics?

[lab-rat]

I'm not quite sure where to start with this.

Thank you in advance

 

[Hootenanny]

I'm not quite sure where to start with this.

Thank you in advance

You must have some idea as to where to start. We can't help you unless you at least attempt the problem first.

 

[lab-rat]

Well my professor hasn't given any examples yet on this and I can't find any in my textbook either. I was hoping someone could give me pointers on where to start.

 

[lewando]

You can start by looking on the interweb for things like "measuring the diameter of a molecule".

 

[lab-rat]

I haven't done any physics or math in over a year which is probably why I'm having trouble with pretty basic problems.

Here's my attempt:

(a) Area of slick = $\pi$r²
diameter of slick = 2x10¹⁰
volume of slick= area x thickness
volume of oil=volume of slick= 1L = 0.001m³

0.001m³=($\pi$r²
r=1261.57m
d=2523m


(b) $\rho$=M/V
V=$\pi$r³
=$\pi$(1x10^-10)³
V=3.14x10^-30m³
M=850kg/m³ x 3.14x10^-30m³

M=2.67x10^-27kg

does that make sense?

 

[lewando]

(a) Area of slick = $\pi$r²
diameter of slick [you mean thickness of slick] = 2x10¹⁰
volume of slick= area x thickness
volume of oil=volume of slick= 1L = 0.001m³

0.001m³=($\pi$r²
r=1261.57m
d=2523m

Looks okay, too many significant digits though.

(b) $\rho$=M/V
V=$\pi$r³
=$\pi$(1x10^-10)³
V=3.14x10^-30m³
M=850kg/m³ x 3.14x10^-30m³

M=2.67x10^-27kg

does that make sense?

V=$(4/3)\pi$r³

 

[lab-rat]

Thank you!

The diamete/thickness was a typo, I wrote it properly on my sheet :)

As for the significant digits, does 2.5x10³m work?

 

[lewando]

If you are using a number like 2x10^-10, I think one SD would suffice.