Solutions to Hwk set 3

1. Many solutions. The most quantitative is perhaps coefficient of restitution (.5 to .8) and elongational measurements with known weights.

2a. Courtesy of Bian
2b. Courtesy of Steve (and Mathematica) If the strain rate tensor is not large, neither will the stress (tensor components). Then the equations decouple and the shear stress becomes a simple inhomogeneous 1st order ODE with the result

           t = h_o(1-e^-t/l)

The normal force like that below  is given by the p+ t₂₂ -p_atm . But a comparison on the lateral interface shows p - p_atm = -t₁₁             

3. Courtesy of Chris (an Maple) Area is shrinking with time, while the length grows exponentially.