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 (0.30m/s)i, and the second having a mass of 2×10 5 kg and a velocity of (−0.12kg) i ^ . What is the energy lost in this inelastic collision?

Answer 1

7560 Joules

Step-by-step explanation:

`m_1` = Mass of first car =
`1.5* 10^5\ kg`

`m_2` = Mass of second car =
`2* 10^5\ kg`

`u_1` = Initial Velocity of first car = 0.3 m/s

`u_2` = Initial Velocity of second car = -0.12 m/s

v = Velocity of combined mass

As linear momentum of the system is conserved

`m_1u_1 + m_2u_2 =(m_1 + m_2)v\\\Rightarrow v=(m_1u_1 + m_2u_2)/(m_1 + m_2)\\\Rightarrow v=(1.5* 10^5* 0.3 + 2* 10^5* -0.12)/(1.5* 10^5 + 2* 10^5)\\\Rightarrow v=0.06\ m/s`

Energy lost is

`\Delta E=\Delta E_i-\Delta E_f\\\Rightarrow \Delta=(1)/(2)(m_1u_1^2 + m_2u_2^2-(m_1+m_2)v^2)\\\Rightarrow \Delta=(1)/(2)(1.5* 10^5* 0.3^2 + 2* 10^5* (-0.12)^2-(1.5* 10^5 + 2* 10^5)* 0.06^2)\\\Rightarrow \Delta=7560\ J`

The Energy lost in the collision is 7560 Joules