Question

Railway wagon of mass 10,000 KG moving at 6 m/s collides with another wagon travelling in the same direction at 2.5 m/s after collision they moving together with a common velocity of 4.5 m/s calculate the mass of second wagon

Answer 1

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Answer 2

Given,

Mass of a railway wagon $m_1$= 10000 kg,

Velocity of mass m1, $u_1$ = 6 m/s,

The velocity of another wagon with which the first wagon collides, $u_2$ = 2.5 m/s,

The final velocity of both the wagons, $v$ = 4.5 m/s.

To find,

Mass of the second wagon.

Solution,

We can solve this problem simply by following the below process.

It is given in the problem, that both the wagons move with a common velocity which means this is the case of a perfectly inelastic collision.

The common velocity with which both wagons move is 4.5 m/s.

Now, for perfectly inelastic collision, only momentum is conserved while there is a loss in the kinetic energy. So, for this condition, we have,

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

Where, subscripts 1 and 2 are for body 1st and 2nd respectively, and,

$m$ = Mass of respective body,

$u$ = Initial velocity, and,

$v$ = Final velocity with which both the bodies move after the collision.

Now, substituting the given values for, m, u, v for the wagons, in the above equation, we get,

(10000)(6) + $m_2(2.5)$ = (10000 + $m_2$)(4.5)

60000 + $2.5m_2$ = 45000 + $4.5m_2$

Rearranging and simplifying,

$4.5m_2-2.5m_2=15000$

⇒ $2m_2=15000$

⇒ $m_2=7500\hspace{2} kg$.

Therefore, for the given problem, the mass of the second wagon will be 7500 kg.