Aball of mass 0.075 kg is fired horizontally into a ballistic pendulum. the pendulum mass is 0.350 kg. the ball is caught in the pendulum, and the centerof mass of the system rises a vertical distance of 0.145 m in the earth's gravitational field. what was the original speed of the ball? assume g=9.80 m/s^2. how much kinetic energy was lost in the collision?

1) In the initial situation, the total mechanical energy of the system is given only by the kinetic energy of the ball that is moving with speed v:

where is the mass of the ball.

In the final situation, where the system (ball+pendulum) rises a vertical distance of h=0.145 m, the system is stationary (v=0) so the total mechanical energy of the system is the gravitational potential energy:

where is the mass of the pendulum.

For the law of conservation of energy, , so we can find the initial speed v of the ball:



2) The kinetic energy lost in the collision is the initial kinetic energy of the ball:

therefore, the efficiency is: