For a certain type of steel, stress is always proportional to strain with Young’s modulus as shown in Table 12.1. The steel has the density listed for iron in Table 14.1. It will fail by bending permanently if subjected to compressive stress greater than its yield strength σy = 400 MPa. A rod 80.0 cm long, made of this steel, is fired at 12.0 m/s straight at a very hard wall, or at another identical rod moving in the opposite direction.
(a) The speed of a one-dimensional compressional wave moving along the rod is given by √Y/P where p is the density and Y is Young’s modulus for the rod. Calculate this speed.
(b) After the front end of the rod hits the wall and stops, the back end of the rod keeps moving, as described by Newton’s first law, until it is stopped by excess pressure in a sound wave moving back through the rod. How much time elapses before the back end of the rod receives the message that it should stop?
(c) How far has the back end of the rod moved in this time? Find
(d) The strain in the rod and
(e) The stress.
(f) If it is not to fail, show that the maximum impact speed a rod can have is given by the expression σ √pY.