A 0.9 kg block of ice is initially at a temperature of -5°C.

label Physics
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Apr 16th, 2015

This has a vertical component (Fv) of 2050 * Sin(27) 
= 930.68 N 

and a horizontal component (Fh) of 2050 * Cos(27) 
= 1826.56 N 

We have to assume that the lead brick will undergo elastic deformation rather than plastic deformation. 

(a) 
Young's modulus for Lead is 16 GPa (from Wikipedia) 

= Fv * h / (A * dh) (from Wikipedia) 

where h is the height = 0.02 m 
A is the top area = 0.06 * 0.05 = 0.003 m^2 
dh = the change in height 

16 * 10^9 = 930.68 * 0.02 / (0.003 * dh) 

dh = 930.68 * 0.02 / (0.003 * 16 * 10^9) 
= 387.78 * 10^-9 m 
= 3.878 * 10^-7 m 

(b) 
Shear modulus for Lead = 5.6 GPa (from Wikipedia) 

= Fh * h / (A * dx) 

where dx is the amount the top surface will move horizontally because of the defromation (from Wikipedia) 

5.6 * 10^9 = 1826.56 * 0.02 / (0.003 * dx) 

dx = 1826.56 * 0.02 / (0.003 * 5.6 * 10^9) 
= 2174.5 * 10^-9 m 
= 2.175 * 10^-6 m

Apr 16th, 2015

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