Question

Train cars are coupled together by being bumped into one another. Suppose two loaded cars are moving toward one another, the first having a mass of 1.50×10 5 kg and a velocity of 0.30 m/s i, and the second having a mass of 2×10 5 kg and a velocity of −0.12m/s i. What is the energy lost in this inelastic collision?

Answer 1

Answer:7.56 kJ

Step-by-step explanation:

mass of first train
`m_1=1.50* 10^5 kg`

mass of second train
`m_2=2* 10^5 kg`

velocity of first train
`v_1=0.3\hat{i} m/s`

velocity of second train
`v_2=-0.12 \hat{i} m/s`

conserving momentum

`m_1v_1+m_2v_2=(m_1+m_2)v`

`v=(m_1v_1+m_2v_2)/(m_1+m_2)`

`v=(.50* 10^5* 0.3-2* 10^5* 0.12)/((1.5+2)\cdot 10^5)`

`v=0.06 m/s`

Energy Lost in Inelastic collision

`=(m_1v_1^2)/(2)+(m_2v_2^2)/(2)-((m_1+m_2)v^2)/(2)`

`=(1.50* 10^5* 0.3^2)/(2)+(2* 10^5* (-0.12)^2)/(2)-(3.5* 10^5* 0.07^2)/(2)`

`=((0.135+0.0288-0.0126)* 10^5)/(2)`

`=(0.1512* 10^5)/(2)`

`=7.56 kJ`