Answer :
Answer:
The fraction of the total initial kinetic energy is lost during the collision is [tex]\dfrac{11}{17}\ J[/tex]
Explanation:
Given that,
Mass of one piece = 300 g
Speed of one piece = 1 m/s
Mass of other piece = 600 g
Speed of other piece = 0.75 m/s
We need to calculate the final velocity
Using conservation of energy
[tex]m_{1}v_{1}+m_{2}v_{2}=(m_{1}+m_{2})v[/tex]
Put the value intro the formula
[tex]300\times10^{-3}\times1+600\times10^{-3}\times(0.75)=(300\times10^{-3}+600\times10^{-3})v[/tex]
[tex]v=\dfrac{00\times10^{-3}\times1+600\times10^{-3}\times(-0.75)}{(300\times10^{-3}+600\times10^{-3})}[/tex]
[tex]v=-0.5\ m/s[/tex]
We need to calculate the total initial kinetic energy
Using formula of kinetic energy
[tex]K.E_{i}=\dfrac{1}{2}m_{1}v_{1}^2+\dfrac{1}{2}m_{2}v_{2}^2[/tex]
Put the value into the formula
[tex]K.E_{i}=\dfrac{1}{2}\times300\times10^{-3}\times1^2+\dfrac{1}{2}\times600\times10^{-3}\times(0.75)^2[/tex]
[tex]K.E_{i}=0.31875\ J[/tex]
We need to calculate the total final kinetic energy
Using formula of kinetic energy
[tex]K.E_{f}=\dfrac{1}{2}(m_{1}+m_{2})v^2[/tex]
Put the value into the formula
[tex]K.E_{f}=\dfrac{1}{2}\times(300\times10^{-3}+600\times10^{-3})\times(-0.5)^2[/tex]
[tex]K.E_{f}=0.1125\ J[/tex]
We need to calculate the energy lost during the collision
Using formula of energy lost
[tex]energy\ lost=\dfrac{0.31875-0.1125}{0.31875}[/tex]
[tex]energy\ lost=\dfrac{11}{17}\ J[/tex]
Hence, The fraction of the total initial kinetic energy is lost during the collision is [tex]\dfrac{11}{17}\ J[/tex]