Question

An empty 20,000 kg coal wagon is moving on a level track at 5 m/s. Suddenly 5000 kg of coal is dumped into it from directly above. The coal initially has zero horizontal velocity. The final speed of the wagon is:
(A) 3 m/s
(B) 2 m/s
(C) 8 m/s
(D) 4 m/s

Answer 1

Hint:To solve this problem we can see that only mass increases but no external force acts on the system. Since, there is no external force acting, the total momentum of the system must be conserved, that is total momentum before dumping must be equal to the total momentum after dumping.

Complete step by step answer:
The initial mass of the system, \[{{m}_{1}}=\]20000 kg
The final mass of the system, \[{{m}_{2}}=\]20000+5000= 25000kg
Initial velocity, u=5 m/s
Final velocity, v=?
Using the law of conservation of the momentum, we get \[{{m}_{1}}u={{m}_{2}}v\]
\[\begin{align}
  & 20000\times 5=25000\times v \\
 & v=4 \\
\end{align}\]
Thus, the value of the final velocity of the system is 4 m/s
Hence, the correct option is (D).

Additional Information: When no external force acts on the system, Momentum is said to be conserved over time; that is, momentum is neither created nor destroyed. Momentum depends upon the variables mass and velocity of the body involved.

Note:This is the easiest way to solve this problem. Momentum conservation is a universal law which holds until there are no external force acts on the system. Also, there is no loss of energy taking place in the system. All the units must be in standard SI convention.