Answer:
The kinetic energy decreased 50 % after the inelastic collision.
Explanation:
Since both ball collide and experiments an inelastic collision, the final velocity of the system is found by means of the Principle of Linear Momentum:
[tex]m_{A}\cdot v_{A} + m_{B}\cdot v_{B} = (m_{A}+m_{B})\cdot v[/tex] (1)
Where:
[tex]m_{A}[/tex], [tex]m_{B}[/tex] - Masses of the balls of clay, measured in kilograms.
[tex]v_{A}[/tex], [tex]v_{B}[/tex] - Speeds of the balls of clay before collision, measured in meters per second.
[tex]v[/tex] - Speed of the system after collision, measured in meters per second.
If we know that [tex]m_{A} = m_{B} = 0.055\,kg[/tex], [tex]v_{A} = 1.5\,\frac{m}{s}[/tex] and [tex]v_{B} = 0\, \frac{m}{s}[/tex], then the speed of the system after collision is:
[tex]v = \frac{m_{A}\cdot v_{A}+m_{B}\cdot v_{B}}{m_{A}+m_{B}}[/tex]
[tex]v = \frac{(0.055\,kg)\cdot \left(1.5\,\frac{m}{s} \right)+(0.055\,kg)\cdot \left(0\,\frac{m}{s} \right)}{0.110\,kg}[/tex]
[tex]v = 0.75\,\frac{m}{s}[/tex]
The initial ([tex]E_{o}[/tex]) and final kinetic energies of the system ([tex]E_{f}[/tex]), measured in joules, are now described by the following equations:
[tex]E_{o} = \frac{1}{2}\cdot (m_{A}\cdot v_{A}^{2}+m_{B}\cdot v_{B}^{2})[/tex] (2)
[tex]E_{f} = \frac{1}{2}\cdot (m_{A}+m_{B})\cdot v^{2}[/tex] (3)
And the percentage of lost energy due to inelastic collision is:
[tex]\%e = \left(1-\frac{E_{f}}{E_{o}} \right)\times 100\,\%[/tex] (4)
If we know that [tex]m_{A} = m_{B} = 0.055\,kg[/tex], [tex]v_{A} = 1.5\,\frac{m}{s}[/tex], [tex]v_{B} = 0\, \frac{m}{s}[/tex] and [tex]v = 0.75\,\frac{m}{s}[/tex], then the percentage of lost energy due to inelastic collision is:
[tex]E_{o} = \frac{1}{2}\cdot \left[(0.055\,kg)\cdot \left(1.5\,\frac{m}{s} \right)^{2}+(0.055\,kg)\cdot \left(0\,\frac{m}{s} \right)^{2}\right][/tex]
[tex]E_{o} = 0.062\,J[/tex]
[tex]E_{f} = \frac{1}{2}\cdot (0.110\,kg)\cdot \left(0.75\,\frac{m}{s} \right)^{2}[/tex]
[tex]E_{f} = 0.031\,J[/tex]
[tex]\%e = \left(1-\frac{0.031\,J}{0.062\,J} \right)\times 100\,\%[/tex]
[tex]\%e = 50\,\%[/tex]
The kinetic energy decreased 50 % after the inelastic collision.
