Q. 153.9( 129 Votes )

# An object of mass 1 kg travelling in a straight line with a velocity of 10 ms^{-1} collides with, and sticks to, a stationary wooden block of mass 5 kg. Then they both move off together in the same straight line. Calculate the total momentum just before the impact and just after the impact. Also, calculate the velocity of the combined objects.

Answer :

Given,

Mass of object, m_{1} = 1 kg

Velocity of object, v_{1}= 10 m/s

Momentum of object = m_{1} × v_{1}

= 1× 10 kg m/s

= 10 kg m/s (i)

Mass of wooden block, m_{2} = 5 kg

Velocity of wooden block, v_{2} = 0 (As it is stationary)

Momentum of wooden block = m_{2} × v_{2}

= 5 × 0

= 0 kg m/s (ii)

From (i) and (ii), we get:

Total momentum = 10 + 0

Before impact = 10 kg m/s (iii)

Total momentum (after impact) =10 kg m/s[Law of conservation of momentum]

Total mass of object = 1 kg + 5 kg

= 6 kg

Velocity of object and wooden block = *v* m/s

10 = 6 × *v*

v =

v = 1.67 m/s

Therefore, the velocity of the object and wooden block together is 1.67 m/s.

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