A bullet of mass m and speed v is fired into a ballistic pen

A bullet of mass m and speed v is fired into a ballistic pendulum of mass M. The bullet remains in the pendulum bob. The pendulum bob is suspended by a massless rod of length L. What is the minimum value of the bullet speed, v, such that the bob will barely swing through a complete vertical circle? A bullet of mass m and speed v is fired into a ballistic pendulum of mass M. The bullet remains in the pendulum bob. The pendulum bob is suspended by a string of length L and a negligible mass. What is the minimum value of the bullet speed, v, such that the bob will barely swing through a complete vertical circle?

Solution

For a power output of 1000 MW with 60 % efficiency we get

Power Input = 1000 / 0.6   = 1666.7 MW

Take calorific Value of coal = 20 MJ/kg

Take calorifc value of CH4   = 55 MJ/kg

mass of CH4 required for power input = 1666.7 / 55 = 30.3 kg/s

mass of Coal required for power input = 1666.7 / 20 = 80.33 kg/s

1 mole of CH4 produces 1 mole of CO2

Therefore mass of CO2 produced = 44 * 30.3 / 16 = 83.325 kg/s

1 mole of C100H100S2 produces 100 mole of CO2

Therefore mass of CO2 produced = 100 * 44 * 83.33 / 1364 = 268.8 kg/s

Ratio   = 83.325 / 268.8 = 0.31