Answer:
D) 50%
Explanation:
According to conservation of momentum:
[tex]m_{1} v_{1i} + m_{2} v_{2i} = m_{1} v_{1f} + m_{2} v_{2f}[/tex]
Assuming that the second taffy started at rest, both pieces have the same mass and that they combined after the collision, their final velocity is:
[tex]m v_{1i} = (m+m) v_{f}\\v_{f} = 0.5 v_{1i}[/tex]
The initial kinetic energy of the system is:
[tex]E_{ki} = \frac{m*v_{1i}^2}{2}[/tex]
Since the second taffy was not moving, it had no kinetic energy at first.
The initial kinetic energy of the system is:
[tex]E_{kf} = \frac{2m*v_{f}^2}{2}\\E_{kf} = \frac{2m*(0.5v_{1i})^2}{2}\\E_{kf} = \frac{0.5m*v_{1i}^2}{2}[/tex]
The percentage of kinetic energy that becomes heat is given by:
[tex]H=1 - \frac{E_{kf}}{E_{ki}}\\H=1 - \frac{\frac{0.5m*v_{1i}^2}{2}}{\frac{m*v_{1i}^2}{2}}\\\\H=1- 0.5 = 0.5[/tex]
THerefore, 50% of the kinetic energy becomes heat
