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Let's say an object of mass 1 kg is moving 10 m/s. A second object of mass $m_2$ is at rest. When the two objects collide, they stick together and move 8 m/s. what is $m_2$?

I understand how to solve this problem using the Law of Conservation of Momentum:

$m_1v_1$ = $(m_1 + m_2)v_2$ so 1(10) = (1 + $m_2$)(8)

Therefore, $m_2$ = 0.25 kg


However, I don't understand why I can't use the energy approach to solve this problem.

$KE_1$ = $KE_s$ (KE of first object = KE of two objects after collision)

$(1/2) * 1 * 10^2 = (1/2) * (1 + m_2) * 8^2$

Therefore, $m_2$ = 0.5625 kg, which is incorrect

Why isn't it correct to use the energy approach in this problem?

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If the objects collide non-elastic , a part of the total energy transforms into inner energy (usually deformation energy and thus temperature), which lowers the kinetic energy of the new object.

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