Question

A freight car with a mass of 10 metric tons is rolling at 108 km/h along a level track when it collides with another freight car, which is initially at rest. If the speed of the cars after they couple together is 36 km/h, what is the mass of the second car?1) 40 metric tons2) 20 metric tons3) 10 metric tons4) 5 metric tons

Answer 1

Given data:

* The mass of the first car is 10 metric tons.

* The initial speed of the first car is 108 km/h

* The speed of couple of both the cars after the collision is 36 km/h.

* The initial speed of the second car is zero. ial

Solution:

By the law of conservation of momentum,

$mu_1+Mu_2=mv_1_{}_{}+Mv_2$

where m is the mass of first car, M is the mass of second car, u_1 is the initial velocity of first car, u_2 is the initial velocity of second car, v_1 is the final velocity of first car, and v_2 is the final velocity of second car,

Substituting the known values,

$\begin{gathered} 10\times108+0=(m+M)\times36 \\ 1080=(10+M)\times36 \\ 10+M=30 \\ M=20\text{ metric tons} \end{gathered}$

Thus, the mass of the second car is 20 metric tons.

Hence, option 2 is the correct answer.