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From my understanding, in an inelastic collision there is no loss of kinetic energy. So if we take the following problem:

A 7700kg car is traveling 18 m/s and strikes a second car. The two stick together and move off with a speed of 5.0 m/s. What is the mass of the second car?

And if we know that KE = 1/2mv^2 , why can we not just say:

1/2 ( 7700)(18^2) = 1/2(7700+x)(5)^2

If x is solved for, we get 92092 kg as the mass of the second car, but this answer is not correct. If there is no loss in kinetic energy, why does setting the previous kinetic energy to the combined kinetic energy not work out?

Thank you and I appreciate all help.

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    $\begingroup$ There is no loss of kinetic energy in a completely elastic collision. $\endgroup$
    – BowlOfRed
    Commented May 2, 2019 at 23:57
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    $\begingroup$ Your understanding is incorrect. There is no loss of kinetic energy in an elastic collision. Momentum however is conserved for both elastic and inelastic collisions. $\endgroup$
    – Bob D
    Commented May 2, 2019 at 23:58

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Momentum is conserved in all collisions, but kinetic energy of the bodies, considered as point masses, is only conserved in elastic ones. In an inelastic collision, some of the kinetic energy of motion is transformed into heat. Try again using momentum conservation

$$m_1v_1 = (m_1+m_2)v_2$$.

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  • $\begingroup$ Thank you! I see now I misunderstood and believed kinetic energy was kept in inelastic collision but I see its the other way around. $\endgroup$
    – Andre Ruegg
    Commented May 3, 2019 at 0:00

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