Question

Consider a 42,000 kg train car travelling at 10 m/s toward another train car. After the two cars collide, theycouple together and move along at 6 m/s. What is the mass of the second train car? (28,000 kg) Please show work

Answer 1

Given data:

* The mass of the first train car is,

$m_1=42000\text{ kg}$

* The initial velocity of the first train car is,

$u_1_{}=10\text{ m/s}$

* The velocity of the couple train car is,

$v=6\text{ m/s}$

Solution:

By the law of conservation of momentum,

$p_i=p_f$

where p_i is the initial momentum of net system, and p_f is the final momentum of the net system,

$m_1u_1+m_2u_2=(m_1+m_2)v$

where m_2 is the mass of the second train car, and u_2 is the initial velocity of the second train car,

$\begin{gathered} 42000\times10+0=(42000+m_2)\times6 \\ 420000=252000+m_2\times6 \\ 6m_2=168000 \\ m_2=\frac{168000}{6} \\ m_2=28000\text{ kg} \end{gathered}$

Thus, the mass of the second train car is 28000 kg.