An
object of mass 1 kg travelling in a straight line with a velocity of
10 m s ^{ −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 object.

Mass
of the object, *m*_{1}
= 1 kg

Velocity
of the object before collision, *v*_{1}
= 10 m/s

Mass
of the stationary wooden block, *m*_{2}
= 5 kg

Velocity
of the wooden block before collision, *v*_{2}
= 0 m/s

∴ Total
momentum before collision = *m*_{1}
*v*_{1}
+ *m*_{2}
*v*_{2}

= 1 (10) + 5 (0) = 10 kg m s^{−1}

It is given that after collision, the object and the wooden block stick together.

Total
mass of the combined system = *m*_{1}
+ *m*_{2}

Velocity
of the combined object = *v*

According to the law of conservation of momentum:

Total momentum before collision = Total momentum after collision

*m*_{1
}*v*_{1}
+ *m*_{2}
*v*_{2}
= (*m*_{1}
+ *m*_{2})
*v*

1
(10) + 5 (0) = (1 + 5) *v*

The total momentum after collision is also 10 kg m/s.

Total
momentum just before the impact = 10 kg m s^{−1}

Total
momentum just after the impact = (*m*_{1}
+ *m*_{2})
*v *=

Hence, velocity of the combined object after collision =

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