A copper cube measures 6.40cm on each side. The bottom face is held in place by

Question

A copper cube measures 6.40cm on each side. The bottom face is held in place by very strong glue to a flat horizontal surface, while a horizontal force F is applied to the upper face parallel to one of the edges.

Show that the glue exerts a force F on the bottom face that is equal but opposite to the force on the top face.

How large must F be to cause the cube to deform by 0.210mm ?

If the same experiment were performed on a lead cube of the same size as the copper one, by what distance would it deform for the same force as in part B?

Explanation / Answer

shear modulus of copper = 44 GPa
shear modulus of lead = 13.1 Gpa

G = FL / A?x

For copper, 44* 10^9 = F* 0.064 / (0.064)^2*(0.00021)

So, F = 591360 N = 5.91360*10^5 N

For lead:

?x = FL/AG

   = 591360* 0.064 / [ (0.064)^2*13.1* 10^9 ]

     = 7.053 *10^-4 m = 0.7053 mm

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