932 
12. The Force Function, G(x) 
Copper spheres have been calibrated at UERL by measuring deformations 
produced by means of known weights dropped from known heights, i-e., measuring 
the energy E required to produce various deformations x. The force function 
is then given by: 
G(x) = a F(z) (I-61) 
It has been found empirically that over the initial region of deformation, 
the function E(x) is parabolic: 
E(x) = =x (I-62) 
G(x) = kx (I-63) 
From a series of calibrations (made Feb. 6, 1946) on spheres to be used 
on Operation Crossroads: 
5 
k = 1.51 x 10° 1b/ft ~64 
5/32 in. / (1-64) 
5 
k = 3.60 x 10° 1b/ft -65 
3/8 ine = 2 / (I ) 
In the case of the 5/32 ine spheres, the force function is linear up to 
deformations of about 0-05 ine or 1600 1b/in.* in a step wavee For the 3/8 in. 
spheres, the force function is linear to deformations of 0-09 ine or 7000 1b/in® 
in a step wavee Since the deviation from linearity is not very great in the 
region just above the values quoted, the systems can probably be considered 
linear, without appreciable error, to pressures of 2000 and 10,000 1b/in2, 
respectively. 
The data of Section 13 of this appendix give: 
wo = Vi/M 
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