As shown below, a bullet of mass m and speed v is fired at an initially stationary sphere, The bullet goes through the sphere, and exits with a speed of . The sphere is attached to a rigid pole of length L and negligible mass. What is the minimum value of v such that the sphere will barely swing through a complete vertical circle? (Use the following as necessary: m, L, g, and M for the mass of the sphere.) physPad Operations

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Shock Waves

Shock waves are common in continuum mechanics, and their dominance is attributable to the fact that they are stronger (or even less) compressible. Substantial perturbations propagated as sudden dynamic changes of a compressible medium supersonically. Shock waves are all around us in our daily lives. Lightning, earthquakes, volcanic eruptions, and meteorite impact all produce them in nature. Even the earth, which is protected by its magnetic field, generates a shock wave as in solar wind that travels around 20 Earth radiuses. These shock waves might be either constant, linked to the body, or unsteady, i.e., moving around with time. All of the shocks mentioned above can be damaging, so precautions must be taken to reduce their impact.