A block of mass m_1 = 1.30 kg moving at v_1 = 1.20 m/s undergoes a completely in

Question

A block of mass m_1 = 1.30 kg moving at v_1 = 1.20 m/s undergoes a completely inelastic collision with a stationary block of mass m_2 = 0.700 kg. The blocks then move, stuck together, at speed v_2. After a short time, the two-block system collides inelastically with a third block, of mass m_3 = 2.60 kg, which is initially at rest. The three blocks then move, stuck together, with speed v_3. Assume that the blocks slide without friction.


ind rac{v_2}{v_1}, the ratio of the velocity v_2 of the two-block system after the first collision to the velocity v_1 of the block of mass m_1 before the collision.
rac{v_2}{v_1} =


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Part B
Find rac{v_3}{v_1}, the ratio of the velocity v_3 of the three-block system after the second collision to the velocity v_1 of the block of mass m_1 before the collisions.
rac{v_3}{v_1} =


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Explanation / Answer

   m1 = 1.3 kg ; v1 = 1.2 m/s    m2 = 0.7 kg ; u2 = 0    After collision the two are stick together. So they have the same    final velocity = v2, and is given by the formula    v2 = (m1v1 + m2u2) / (m1 + m2)    v2 = 0.78 m/s        The mass of the above two block system, m = m1 + m2 = 2 kg    The initial velocity of two block system, v2 = 0.78 m/s    The mass third block, m3 = 2.6 kg    The initial velocity of third block, u3 = 0    After the collision the two are afix and travells with same velocity = v3    and is given by the formula    v3 = (mv2) / (m + m3) = 0.34 m/s    Part A :       (v2 / v1)   = 0.78 / 1.2 = 0.65    Part B :       (v3 / v1)   = 0.34 / 1.2 = 0.283    v2 = 0.78 m/s        The mass of the above two block system, m = m1 + m2 = 2 kg    The initial velocity of two block system, v2 = 0.78 m/s    The mass third block, m3 = 2.6 kg    The initial velocity of third block, u3 = 0    After the collision the two are afix and travells with same velocity = v3    and is given by the formula    v3 = (mv2) / (m + m3) = 0.34 m/s    Part A :       (v2 / v1)   = 0.78 / 1.2 = 0.65    Part B :       (v3 / v1)   = 0.34 / 1.2 = 0.283

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