A 6.2 kg block with a speed of 4.5 m/s collides with a 12.4 kg block that has a

Question

A 6.2 kg block with a speed of 4.5 m/s collides with a 12.4 kg block that has a speed of 3.0 m/s in the same direction. After the collision, the 12.4 kg block is observed to be traveling in the original direction with a speed of 3.8 m/s. (a) What is the velocity of the 6.2 kg block immediately after the collision? (b) By how much does the total kinetic energy of the system of two blocks change because of the collision? (c) Suppose, instead, that the 12.4 kg block ends up with a speed of 6.0 m/s. What then is the change in the total kinetic energy?

Explanation / Answer

(a)Let us consider the mass 1(m1) = 6.2 kg
Initial speed of mass 1 (u1) = 4.5 m/s
Mass 2 (m2) =12.4 kg
Initial speed of mass 2 (u2) = 3 m/s
Initial momentum of the system = m1u1 + m2u2
= (6.2*4.5) + (12.4*3) = 65.1 kg-m/s --------------(1)
Now final momentum of the system after the collision
= m1v1 + m2v2
= 6.2v1 + 12.4*3.8 -----------(2)
where v1 is final speed of m1 after the collision
v2 is speed of m2 after collision = 3.8 m/s
Applying the conservation of momentum
6.2v1 + 12.4*3.8 = 65.1
v1 = 2.9 m/s
(b) Initial kinetic energy of the system
= (1/2)m1u12 + (1/2)m2u22
= [(1/2)*6.2*4.52 ] + [(1/2)*12.4*32]
= 62.775 + 55.8 = 118.575 J
Final kinetic energy of the system
= (1/2)m1v12 + (1/2)m2v22
= [(1/2)*6.2*2.92 ] + [(1/2)*12.4*3.82]
= 26.071 + 89.528 = 115.599 J
Energy change = Initial energy - final energy
=118.575 - 115.599 = 2.976 J
(c) If the final velocity of the m2 is v2 = 6 m/s
Then final momentum of the system
= m1v1 + m2v2
= 6.2v1 + 12.4*6 -----------(2)
Applying conservation of momentum
6.2v1 + 12.4*6 = 65.1
v1 = -1.5 m/s
-ve sign indicate that block 1 move in the opposite direction after the collision
Now the final energy of the system
= (1/2)m1v12 + (1/2)m2v22
= [(1/2)*6.2*(-1.5)2 ] + [(1/2)*12.4*62]
= 6.975 + 223.2 = 230.175 J
Now change in energy of the system
= Initial energy - final energy
= 118.575 - 230.175 = -111.6 J
Which means kinetic energy has increased while collision

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