Question

a 23000 kg railroad freight car collides with a stationary caboose car. They couple together, and 18 percent of the initial kinetic energy is lost. What is the mass of the caboose

Answer 1

5048.78kg

Step-by-step explanation:

Given
`m_1=2.3*10^4kg` and
`E_l=0.18K`, From the law of conservation of momentum we have:

`m_1v_1=(m_1+m_2)v`

Hence,
`v=(m_1v_2)/(m_1+m_2)`

Since 18% of initial
`KE` is lost:-

`K_f=(0.82)/(2)m_1v_1^2=0.5(m_1+m_2)v^2`

Therefore, by substituting with
`v`:

`K_f=(0.82)/(2)m_1v_1^2=0.5(m_1^2v_1^2)/(m_1+m_2)\\\\0.82=(m_1)/(m_1+m_2)`

`m_2+23000=23000/0.82\\m_2=5048.78kg`

The mass of the caboose is 5048.78kg