Chapter - 2 Force and Laws of Motion

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Q
Force and Laws of Motion

Question:

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 object.

Answer:

Given: Mass of the object, m_1 = 1\ kg

Mass of the block, m_2 = 5\ kg

Initial velocity of the object, u_1 = 10\ ms^{-1}

Initial velocity of the block, u_2 = 0

Mass of the combined object, M = m_1 + m_2 = 1\ kg + 5\ kg = 6\ kg

Velocity of the combined object, v = ?

Total momentum before the collision = m_1u_1 + m_2u_2

Total momentum before the collision = 1 \times 10 + 5 \times 0 = 10\ kgm/s

As per the law of conservation of momentum, the total momentum before the collision is equal

to the total momentum after the collision. Therefore, the total momentum after the collision is

also 10\ kgm/s

Calculating the velocity(v) of the combined object.

Using the law of conservation of momentum.

Total momentum before the collision = Total momentum after the collision

10\ kgm/s = Mv

10\ kgm/s = 6\ kg \times v

v = \frac{10}{6}

v = 1.66\ ms^{-1}

The combined object moves with a velocity of 1.66 m/s.


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