Q11 of 31 Page 128

Two objects, each of mass 1.5 kg, are moving in the same straight line but in opposite directions. The velocity of each object is 2.5 ms-1 before the collision during which they stick together. What will be the velocity of the combined objects after collision?

Given,

Mass of first object, m1 = 1.5 kg


Velocity of first object, v1 = 2.5 m/s


Momentum of first object = m1 × v1


= 1.5 × 2.5


= 3.75 kg m/s


Mass of second object, m2 = 1.5 kg


Velocity of first object, v2 = - 2.5 m/s


So, Momentum of second object, m2 × v2


= 1.5 × (-2.5)


= - 3.75 kg m/s


So, Total momentum = 3.75 + (-3.75)


= 0 kg m/s (i)


Combined mass = m1 + m2


= 1.5 + 1.5


= 3.0 kg


Let, the velocity of the combined objects after collision will be v m/s.


Total momentum = (m1 + m2) × v


= 3.0 × v (ii)


We know that,


According to the principle of conservation of momentum:


Total momentum before collision = Total momentum after collision


0 = 3.0 × v


v =


= 0 m/s


Therefore, the velocity of the combined objects after the collision will be 0 m/s.


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