An object of mass 1 kg travelling in a straight line with a velocity of 10 m/s collides with, and sticks to, a stationary block of mass 5 kg. Then they both move off together in the same straight line.
a) Calculate the total momentum just before the impact and just after the impact.
b) Calculate the velocity of the combined object.

$ \stackrel{5}{\longrightarrow} \quad 5 kg $
[3 Marks]
[NCERT]
[Conservation of Momentum]

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Solution

Solution:
Given:
$m_{1} = 1 k g, m_{2} = 5 k g$
$u_{1} = 10 m / s, u_{2} = 0, v = ?$ [1 Mark]

Total momentum before collision = $m_{1} u_{1} + m_{2} u_{2}$
→ Pinitial = (1 kg) × (10 m/s) + 0
= $10 k g . m . s^{- 1}$ [1 Mark]

$P_{i n i t i a l} = P_{f i n a l}$
Total momentum after collision ( $P_{f i n a l}$ ) = $(m_{1} + m_{2}) * v$
→ 10 = $(m_{1} + m_{2}) * v$
→ 10 = (1+5)*v
→ v = 10/6
= 1.66 m/s [1 Mark]

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