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Second Law of Motion

A railway wag...

Question

A railway wagon of mass $2000 k g$ moving with a velocity of $18 k m / h$ collides head-on with stationary wagon of mass $3000 k g$ . If the two wagons move together after collision, calculate (i) their common velocity and (ii) loss of kinetic energy due to collision.

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Solution

$M_{1} = 2000 k g$ $M_{2} = 3000 k g$ and $v_{1} = 18 k m / h = 5 m / s$ and $v_{2} = 0$

Let final common velocity be $v$

Using conservation of momentum-

$(M_{1} + M_{2}) v = M_{1} v_{1} + M_{2} v_{2}$

$⟹ 5000 v = 2000 \times 5$

$⟹ v = 2 m / s$

Initial K.E. $= K_{1} = \frac{1}{2} M_{1} v_{1}^{2} = \frac{1}{2} 2000 \times 5^{2} = 25000 J$

Final K.E. $= K_{2} = \frac{1}{2} (M_{1} + M_{2}) v^{2} = \frac{1}{2} 5000 \times 2^{2} = 10000 J$

Loss in K.E $= Δ K = K_{1} - K_{2} = 15000 = 15 k J$

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