Solids Elasticity (Bulk Modulus)

AI Thread Summary
When water freezes, it expands by approximately 9%, leading to a pressure increase in an automobile engine block. The bulk modulus of ice is given as 2.00 x 10^9 N/m^2. Calculating the pressure change forward in time yields ΔP = 0.09B, while calculating it backward results in ΔP = 0.0826B. The discrepancy arises because the two calculations account for different volume changes, demonstrating that they do not yield the same magnitude. Understanding this concept is crucial for accurately applying the bulk modulus in real-world scenarios.
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Homework Statement


When the water freezes it expands by about 9.00%. What pressure increase would occur inside your automobile engine block if the water in it froze?(The bulk modulus of ice is 2.00 x 10^9 N/m^2).

Homework Equations


B=\frac{\Delta P}{\Delta V / V_i}

The Attempt at a Solution


If I solve the problem "forward in time" I get this:
\Delta P=\frac{1.09V_i-Vi}{Vi}B=0.09B

but if solving the problem "backwards in time"

\Delta P = \frac{V_i-1.09V_i}{1.09V_i}B = 0.0826B

Shouldn't both answers have the same magnitude?
 
Last edited:
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No; 90% of 110% of x is not x, for example.
 
Of Course. Thanks
 
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