A bullet of mass m and speed v passes completely through a pendulum bob of mass M as shown in the figure below. The bullet emerges with a speed of v/2. The pendulum bob is suspended by a stiff rod of length L and negligible mass. What is the minimum value of v such that the bob will barely swing through a complete vertical circle? (Use any variable or symbol stated above along with the following as necessary: g.) v =

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Helmholtz Free Energy

The Helmholtz free energy is a thermodynamic potential used to calculate the measure of useful work from a closed system. This system is kept at constant temperature and volume. German physicist Hermann Helmholtz introduced this concept in 1882.