Q1. If the ultimate shear strength of steel is taken to be 2.50 x 10^9 Pa, what force is required to punch through a steel plate 2.20 cm thick? Suppose the superhero's fist has cross-sectional area of 8.00 x 10^1 cm2 and is approximately circular.

Q2. Two heavy pendula of mass m are suspended from strings of length l inside a railroad car of mass M that can roll freely on horizontal tracks (ignore the moment of inertia of the wheels).

a) Write down the Lagrangian for the three degree of freedom in the problem.

b) Use momentum conservation to eliminate one of the degree of freedom and rewrite Lagrangian accordingly.

c) Find out the frequencies of the normal modes.