Chapter - 2 Force and Laws of Motion

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Q
Force and Laws of Motion

Question:

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?

Answer:

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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