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:
[tex]E_i =K= \frac{1}{2}m_b v^2 [/tex]
where [tex]m_b = 0.075 kg[/tex] 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:
[tex]E_f = U = (m_b+m_p)gh[/tex]
where [tex]m_p = 0.350 kg[/tex] is the mass of the pendulum.
For the law of conservation of energy, [tex]E_i=E_f[/tex] , so we can find the initial speed v of the ball:
[tex] \frac{1}{2}m_bv^2 = (m_b+m_p)gh[/tex]
[tex]v= \sqrt{ 2 \frac{m_b+m_p}{m_b}gh } =4.0 m/s[/tex]
2) The kinetic energy lost in the collision is the initial kinetic energy of the ball:
[tex]K= \frac{1}{2}m_bv^2= \frac{1}{2}(0.075 kg)(4.0 m/s)^2=0.6 J [/tex]
