Question

Two pieces of clay are moving directly toward each other. When they collide, they stick together and move as one piece. One piece having mass 300 g is moving to the right at a speed of 1 m/s. The other piece has mass 600 g and is moving to the left at a speed of 0.75 m/s. What fraction of the total initial kinetic energy is lost during the collision?

Answer 1

The fraction of the total initial kinetic energy is lost during the collision is
`(11)/(17)\ J`

Step-by-step 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

`m_(1)v_(1)+m_(2)v_(2)=(m_(1)+m_(2))v`

Put the value intro the formula

`300*10^(-3)*1+600*10^(-3)*(0.75)=(300*10^(-3)+600*10^(-3))v`

`v=(00*10^(-3)*1+600*10^(-3)*(-0.75))/((300*10^(-3)+600*10^(-3)))`

`v=-0.5\ m/s`

We need to calculate the total initial kinetic energy

Using formula of kinetic energy

`K.E_(i)=(1)/(2)m_(1)v_(1)^2+(1)/(2)m_(2)v_(2)^2`

Put the value into the formula

`K.E_(i)=(1)/(2)*300*10^(-3)*1^2+(1)/(2)*600*10^(-3)*(0.75)^2`

`K.E_(i)=0.31875\ J`

We need to calculate the total final kinetic energy

Using formula of kinetic energy

`K.E_(f)=(1)/(2)(m_(1)+m_(2))v^2`

Put the value into the formula

`K.E_(f)=(1)/(2)*(300*10^(-3)+600*10^(-3))*(-0.5)^2`

`K.E_(f)=0.1125\ J`

We need to calculate the energy lost during the collision

Using formula of energy lost

`energy\ lost=(0.31875-0.1125)/(0.31875)`

`energy\ lost=(11)/(17)\ J`

Hence, The fraction of the total initial kinetic energy is lost during the collision is
`(11)/(17)\ J`