Question

(9%) Problem 4: In this problem you will consider the effect that thermal expansion due to temperature will have on Archimedes' principle. Take the densities of water and copper at O'C to be 1.00 x 10 kg/m and 8.90 x 10 kg/m", respectively. 50% Part(a) Calculate the fraction of a copper block's weight that is supported by the buoyant force at O'C. F/Wc.(0°C) = 0 Grade Summary Deductions 00 Potential 1004 ( 7 8 9 E A 4 5 6 sino cos) tano cotano asino acos) atan acotan sinho cosho tanho cotanho) Degrees Radians Submissions Attempts remaining: ( Operatiempo) detailed view 3 + 0 No около CLIA Submit Hints deaction per hint. Hins remaining Feedback deduction per feedback 50% Part (b) Calculate the fraction of a copper block's weight that is supported by the buoyant force at 95°C. Assume the volume expansion coefficient of copper is Bc - 5.10 x 105 1rc.

Answer 1

So we can write weight of copper block as

$W_C =mg= \sigma Vg$

Here sigma is density of copper and V is volume of copper.

And Buyoncy force due to displaced water on copper block then

$F_C= \rho Vg$

Here rho is density of water and V is volume of copper.

So fraction of buyoncy force to weight we write,

$\frac{F_C}{W_c}=\frac{ \rho}{\sigma }=\frac{1.00\times 10^3} {8.9\times 10^3}= 0.1123$