Chapter - 2 Force and Laws of Motion

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Force and Laws of Motion


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 object after collision?


Given: Mass of the first object, m_1 = 1.5 kg

Mass of the second object, m_2 = 1.5 kg

Initial velocity of the first object (before collision), u_1 = 2.5 ms^{-1}

Initial velocity of the second object (before collision), u_2 = -2.5 ms^{-1}

{Negative sign is taken for u_2 because the object is moving in opposite direction}

To find: Velocity of the combined object after the collision, v = ?

According to the question, objects stick together after the collision therefore, the final velocity for both the object is equal to v.

So, v_1 = v_2 = v

According to the law of conservation of momentum,

Total momentum before collision = Total momentum after collision

m_1u_1 +m_2u_2 = m_1v_1 +m_2v_2

1.5 	imes 2.5 + 1.5 	imes 2.5 = 1.5v + 1.5v

1.5 	imes 2.5 + 1.5 	imes (-2.5) = 1.5v + 1.5v

1.5 	imes 2.5 - 1.5 	imes 2.5 = 3v

0 = 3v

v = 0

v = 0, implies that the combined object formed comes into rest after the collision.

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