Coin Weight Variation Tolerance Calculation

[donjt81]

Find variation - really need help!

guys i really need your help on this. I don't even know which section to look for here. can some one please get me started for this problem.

Problem: A manufacturer contracts to mint coins for the federal government. how much variation dr in the radius of the coins can be tolerated if the coins are to weigh within 1/50 of their ideal weight? Assume the thickness does not vary.

 

[xman]

I do not know if this is correct, but what I'm thinking is:

1) assume the material is homogeneous and isotropic
2) assume the thickness is constant
3) assume the volume may be written as the product of the area of a circle and its constant height

Then, we can write the mass as the usual density, i.e. $$m=\rho V$$ then the weight is just g times the mass. So, note that
$$dm = \rho dV=\rho (2\pi r dr) t$$
where t is the constant thickness. So, if we compare to its ideal weight, note the constant g drops out, along with a lot of other stuff. So
$$\frac{dm}{m} = \frac{\rho dV}{\rho V}=\frac{2dr}{r}$$
So, plugging in what we know we have
$$\frac{1}{50} =\frac{2dr}{r} \Rightarrow \frac{dr}{r}=\frac{1}{100}$$
So the variation in the radius must be within 1/100. Does this make sense? I think it works.

 

[donjt81]

Thanks xman... yes it looks correct...

can anyone else look at it and confirm it? I want to make sure i do the homework right.