Block 1, of mass m1 = 2.50 kg , moves along a frictionless air track with speed v1 = 27.0 m/s. It collides with block 2, of mass m2 = 33.0 kg , which was initially at rest. The blocks stick together after the collision. A. Find the magnitude pi of the total initial momentum of the two-block system. Express your answer numerically. B. Find vf, the magnitude of the final velocity of the two-block system. Express your answer numerically. C. what is the change deltaK= Kfinal- K initial in the two block systems kinetic energy due to the collision ? Express your answer numerically in joules.

a

The total initial momentum of the two-block system is  

b

The magnitude of the final velocity of the two-block system

c

 the change ΔK=Kfinal−Kinitial in the two-block system's kinetic energy due to the collision is  

Explanation:

From the question we are told that

    The mass of first  block  is

      The initial velocity of first   block is

          The mass of second block is  

          initial velocity of second block is  

The magnitude of the of the total initial momentum of the two-block system is mathematically repented as

substituting values

According to the law of linear momentum conservation

Where   is the total final momentum of the system which is mathematically represented as

Where is the final velocity of the system

substituting values

The change in kinetic energy is mathematically represented as

Where is the final kinetic energy of the two-body system  which is mathematically represented as

substituting values

While is the initial kinetic energy of the two-body system

substituting values

So

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